Revision ecc02a93ab91dcf160aeb7d64a1954671e83ddde authored by Mark Clements on 01 November 2018, 21:30:03 UTC, committed by cran-robot on 01 November 2018, 21:30:03 UTC
1 parent 4f6cced
pm2-3.R
## Utilities
## copied from stats:::format.perc
format.perc <-
function (probs, digits)
paste(format(100 * probs, trim = TRUE, scientific = FALSE, digits = digits),
"%")

## extension of ns() to include different boundary derivatives,
## centering and cure
nsx <-
function (x, df = NULL, knots = NULL, intercept = FALSE,
Boundary.knots = range(x),
derivs = if (cure) c(2,1) else c(2,2),
log=FALSE, # deprecated: only used in rstpm2:::stpm2Old
centre = FALSE, cure = FALSE, stata.stpm2.compatible=FALSE)
{
nx <- names(x)
x <- as.vector(x)
nax <- is.na(x)
if (nas <- any(nax))
x <- x[!nax]
if (!missing(Boundary.knots)) {
Boundary.knots <- sort(Boundary.knots)
outside <- (ol <- x < Boundary.knots[1L]) | (or <- x >
Boundary.knots[2L])
}
else outside <- FALSE
if (!missing(df) && missing(knots)) {
nIknots <- df - 1 - intercept + 4 - sum(derivs)
if (nIknots < 0) {
nIknots <- 0
warning("'df' was too small; have used ", 1 + intercept)
}
knots <- if (nIknots > 0) {
knots <- if (!cure)
seq.int(0, 1, length.out = nIknots + 2L)[-c(1L,
nIknots + 2L)]
else c(seq.int(0, 1, length.out = nIknots + 1L)[-c(1L,
nIknots + 1L)], 0.95)
if (!stata.stpm2.compatible)
stats::quantile(x[!outside], knots)
else stats::quantile(x[!outside], round(knots,2), type=2)
}
}
else nIknots <- length(knots)
Aknots <- sort(c(rep(Boundary.knots, 4L), knots))
if (any(outside)) {
basis <- array(0, c(length(x), nIknots + 4L))
if (any(ol)) {
k.pivot <- Boundary.knots[1L]
xl <- cbind(1, x[ol] - k.pivot)
tt <- spline.des(Aknots, rep(k.pivot, 2L), 4, c(0,
1))$design basis[ol, ] <- xl %*% tt } if (any(or)) { k.pivot <- Boundary.knots[2L] xr <- cbind(1, x[or] - k.pivot) tt <- spline.des(Aknots, rep(k.pivot, 2L), 4, c(0, 1))$design
basis[or, ] <- xr %*% tt
}
if (any(inside <- !outside))
basis[inside, ] <- spline.des(Aknots, x[inside],
4)$design } else basis <- spline.des(Aknots, x, 4)$design
const <- splineDesign(Aknots, rep(Boundary.knots, 3-derivs), 4, c(derivs[1]:2, derivs[2]:2))
if (!intercept) {
const <- const[, -1, drop = FALSE]
basis <- basis[, -1, drop = FALSE]
}
qr.const <- qr(t(const))
q.const <- qr.Q(qr.const, complete=TRUE)[, -(1L:2L), drop = FALSE] # NEW
basis <- as.matrix((t(qr.qty(qr.const, t(basis))))[, -(1L:nrow(const)), drop = FALSE])
n.col <- ncol(basis)
if (nas) {
nmat <- matrix(NA, length(nax), n.col)
nmat[!nax, ] <- basis
basis <- nmat
}
dimnames(basis) <- list(nx, 1L:n.col)
if (centre) {
centreBasis <- nsx(centre,
knots=if (is.null(knots)) numeric(0) else knots,
Boundary.knots=Boundary.knots,
intercept=intercept, derivs=derivs, centre=FALSE, log=log)
oldAttributes <- attributes(basis)
basis <- t(apply(basis,1,function(x) x-centreBasis))
attributes(basis) <- oldAttributes
}
a <- list(degree = 3, knots = if (is.null(knots)) numeric(0) else knots,
Boundary.knots = Boundary.knots, intercept = intercept, derivs=derivs,
centre=centre, log=log, q.const=q.const)
attributes(basis) <- c(attributes(basis), a)
class(basis) <- c("nsx", "basis", "matrix")
basis
}
makepredictcall.nsx <-
function (var, call)
{
if (as.character(call)[1L] != "nsx")
return(call)
at <- attributes(var)[c("knots", "Boundary.knots", "intercept",
"derivs", "centre", "log")]
xxx <- call[1L:2]
xxx[names(at)] <- at
xxx
}
predict.nsx <-
function (object, newx, ...)
{
if (missing(newx))
return(object)
a <- c(list(x = newx), attributes(object)[c("knots", "Boundary.knots",
"intercept", "derivs", "centre", "log")])
do.call("nsx", a)
}
Shat <- function(obj)
{
## predicted survival for individuals (adjusted for covariates)
newobj = survfit(obj,se.fit=FALSE)
surv = newobj$surv rr = try(predict(obj,type="risk"),silent=TRUE) if (inherits(rr,"try-error")) rr <- 1 surv2 = surv[match(obj$y[,ncol(obj$y)-1],newobj$time)]
return(surv2^rr)
}
replaceCall=function(obj,old,new) {
if (is.atomic(obj) && length(obj)>1)
return(as.call(c(quote(c),lapply(as.list(obj),replaceCall,old,new))))
if (is.name(obj) || is.symbol(obj) || (is.atomic(obj) && length(obj)==1)) {
if (obj==old) return(new)
else return(obj)
}
##   if (length(obj)==1 && length(obj[[1]])==1) {
##     if (obj==old) return(new)
##     else return(obj)
##   }
as.call(lapply(obj,replaceCall,old,new))
}
replaceFormula=function(...) as.formula(replaceCall(...))
## replaceFormula(~f(a+b),quote(f),quote(g))
allCall=function(obj) {
if (is.atomic(obj) && length(obj)==1) return(obj)
if (is.atomic(obj) && length(obj)>1) return(as.call(c(quote(c),as.list(obj))))
if (is.name(obj) || is.symbol(obj)) return(obj)
as.call(lapply(obj,allCall))
}
## allCall(as.call(c(quote(ns),list(df=3,knots=c(1,2)))))[[2]]
vector2call=function(obj) {
if (is.atomic(obj) && length(obj)==1) return(obj)
if (is.atomic(obj) && length(obj)>1) return(as.call(c(quote(c),as.list(obj))))
if (is.name(obj) || is.symbol(obj)) return(obj)
lapply(obj,allCall) # is this correct?
}
## vector2call(list(df=3,knots=c(1,2)))
findSymbol <- function(obj,symbol) {
if (is.symbol(obj) && obj==symbol) TRUE else
if (is.symbol(obj)) FALSE else
if (is.atomic(obj)) FALSE else
Reduce(|,lapply(obj,findSymbol,symbol),FALSE)
}
rhs=function(formula)
if (length(formula)==3) formula[[3]] else formula[[2]]
lhs <- function(formula)
if (length(formula)==3) formula[[2]] else NULL
"rhs<-" = function(formula,value) {
newformula <- formula
newformula[[length(formula)]] <- value
newformula
}
"lhs<-" <- function(formula,value) {
if (length(formula)==2)
as.formula(as.call(c(formula[[1]],value,formula[[2]])))
else {
newformula <- formula
newformula[[2]] <- value
newformula
}
}

## numerically calculate the partial gradient \partial func_j \over \partial x_i
## (dim(grad(func,x)) == c(length(x),length(func(x)))
{
h <- .Machine$double.eps^(1/3)*ifelse(abs(x)>1,abs(x),1) temp <- x+h h.hi <- temp-x temp <- x-h h.lo <- x-temp twoeps <- h.hi+h.lo nx <- length(x) ny <- length(func(x,...)) if (ny==0L) stop("Length of function equals 0") df <- if(ny==1L) rep(NA, nx) else matrix(NA, nrow=nx,ncol=ny) for (i in 1L:nx) { hi <- lo <- x hi[i] <- x[i] + h.hi[i] lo[i] <- x[i] - h.lo[i] if (ny==1L) df[i] <- (func(hi, ...) - func(lo, ...))/twoeps[i] else df[i,] <- (func(hi, ...) - func(lo, ...))/twoeps[i] } return(df) } ## numerically calculate the gradient \partial func_i \over \partial x_i ## length(grad(func,x)) == length(func(x)) == length(x) grad1 <- function(func,x,...,log.transform=FALSE) { ny <- length(func(x,...)) if (ny==0L) stop("Length of function equals 0") if (log.transform) { h <- .Machine$double.eps^(1/3)
value <- (func(x*exp(h), ...) - func(x*exp(-h), ...))/2/h/x
} else {
h <- .Machine$double.eps^(1/3)*ifelse(abs(x)>1,abs(x),1) value <- (func(x+h, ...) - func(x-h, ...))/2/h } return(value) } ## predict lpmatrix for an lm object lpmatrix.lm <- function (object, newdata, na.action = na.pass) { tt <- terms(object) if (!inherits(object, "lm")) warning("calling predict.lm(<fake-lm-object>) ...") if (missing(newdata) || is.null(newdata)) { X <- model.matrix(object) } else { Terms <- delete.response(tt) m <- model.frame(Terms, newdata, na.action = na.action, xlev = object$xlevels)
if (!is.null(cl <- attr(Terms, "dataClasses")))
.checkMFClasses(cl, m)
X <- model.matrix(Terms, m, contrasts.arg = object$contrasts) } X } ## fun: takes coef as its first argument ## requires: coef() and vcov() on the object numDeltaMethod <- function(object, fun, gd=NULL, ...) { coef <- coef(object) Sigma <- vcov(object) fit <- fun(coef,...) if (is.null(gd)) gd <- grad(fun,coef,...) se.fit <- as.vector(sqrt(colSums(gd* (Sigma %*% gd)))) if (!is.null(names(fit))) names(se.fit) <- names(fit) if(all(se.fit==0)) warning("Zero variance estimated. Do you need to pass a newdata argument to fun()?") structure(data.frame(fit = fit, se.fit = se.fit, Estimate = fit, SE = se.fit), # vcov=Sigma, class=c("predictnl","data.frame")) } "coef<-" <- function (x, value) UseMethod("coef<-") predictnl <- function (object, ...) UseMethod("predictnl") setGeneric("predictnl") "coef<-.default" <- function(x,value) { x$coefficients <- value
x
}
predictnl.default <- function(object,fun,newdata=NULL,gd=NULL,...)
{
if (!is.null(newdata) || "newdata" %in% names(formals(fun))) {
local1 <- function(coef,newdata,...)
{
coef(object) <- coef
fun(object,newdata=newdata,...)
}
numDeltaMethod(object, local1, newdata=newdata, gd=gd, ...)
}
else {
local2 <- function(coef,...)
{
coef(object) <- coef
fun(object,...)
}
numDeltaMethod(object, local2, gd=gd, ...)
}
}
setMethod("predictnl", "mle2", function(object,fun,newdata=NULL,gd=NULL,...)
{
if (is.null(newdata) && !is.null(object@data))
newdata <- object@data
localf <- function(coef,...)
{
object@fullcoef <- coef # changed from predictnl.default()
fun(object,...)
}
numDeltaMethod(object,localf,newdata=newdata,gd=gd,...)
})
print.predictnl <- function(x, ...)
print(data.frame(fit=x$fit, se.fit=x$se.fit), ...)
confint.predictnl <- function(object,parm,level=0.95,...) {
cf <- object$fit pnames <- names(cf) if (is.null(pnames)) pnames <- 1:length(cf) if (missing(parm)) parm <- pnames else if (is.numeric(parm)) parm <- pnames[parm] a <- (1 - level)/2 a <- c(a, 1 - a) pct <- format.perc(a, 3) fac <- qnorm(a) ci <- array(NA, dim = c(length(parm), 2L), dimnames = list(parm, pct)) ses <- object$se.fit[parm]
ci[] <- as.vector(cf[parm]) + ses %o% fac
ci
}
predictnl.lm <-
function (object, fun, newdata = NULL, ...)
{
if (is.null(newdata) && "newdata" %in% names(formals(fun))) {
stopifnot(!is.null(object$data)) newdata <- object$data
}
predictnl.default(object, fun, newdata, ...)
}
## setMethod("predictnl", "mle", function(object,fun,gd=NULL,...)
##   {
##     localf <- function(coef,...)
##       {
##         object@fullcoef = coef # changed from predictnl.default()
##         fun(object,...)
##       }
##     numDeltaMethod(object,localf,gd=gd,...)
##   })
predict.formula <- function(object,data,newdata,na.action,type="model.matrix",
...)
{
mf <- match.call(expand.dots = FALSE)
type <- match.arg(type)
m <- match(c("formula", "data", "na.action"), names(mf), 0L)
mf <- mf[c(1L, m)]
mf$drop.unused.levels <- TRUE mf[[1L]] <- as.name("model.frame") mf <- eval(mf, parent.frame()) mt <- attr(mf, "terms") xlevels <-.getXlevels(mt, mf) mfnew <- model.frame(mt, newdata, na.action=na.action, xlev=xlevels) if (!is.null(cl <- attr(mt, "dataClasses"))) .checkMFClasses(cl, mfnew) model.matrix(mt, mfnew, contrasts=contrasts) } %call+% <- function(left,right) call("+",left,right) ## bread.stpm2 <- function (x, ...) { rval <- vcov(x) * nrow(x@y) dimnames(rval) <- list(names(coef(x)), names(coef(x))) return(rval) } estfun.stpm2 <- function(obj, weighted=FALSE, ...) { rr <- t(grad(obj@logli,coef(obj))) colnames(rr) <- names(coef(obj)) if (weighted) rr <- rr * obj@weights rr } applyTapplySum <- function(X,index) apply(X, 2, function(col) tapply(col, index, sum)) meat.stpm2 <- function (x, adjust = FALSE, cluster=NULL, ...) { psi <- estfun.stpm2(x, ...) k <- NCOL(psi) n <- NROW(psi) if (!is.null(cluster)) psi <- applyTapplySum(as.matrix(psi),cluster) rval <- crossprod(as.matrix(psi))/n if (adjust) rval <- n/(n - k) * rval rownames(rval) <- colnames(rval) <- colnames(psi) return(rval) } sandwich.stpm2 <- function (x, bread. = bread.stpm2, meat. = meat.stpm2, ...) { if (is.function(bread.)) bread. <- bread.(x) if (is.function(meat.)) meat. <- meat.(x, ...) n <- NROW(estfun.stpm2(x)) return(1/n * (bread. %*% meat. %*% bread.)) } incrVar <- function(var,increment=1) { ##var <- deparse(substitute(var)) ##function(data) "$<-"(data,var,"$"(data,var)+increment) # FAILS n <- length(var) if (n>1 && length(increment)==1) increment <- rep(increment,n) function(data) { for (i in 1:n) { data[[var[i]]] <- data[[var[i]]] + increment[i] } data } } cloglog <- function(x) log(-log(x)) cexpexp <- function(x) exp(-exp(x)) setOldClass("terms") setClassUnion("listOrNULL",c("list","NULL")) setClassUnion("nameOrcall",c("name","call")) setClassUnion("nameOrcallOrNULL",c("name","call","NULL")) ##setClassUnion("numericOrNULL",c("numeric","NULL")) setOldClass("Surv") setOldClass("lm") expit <- function(x) { ifelse(x==-Inf, 0, ifelse(x==Inf, 1, 1/(1+exp(-x)))) } logit <- function(p) { ifelse(p==0, -Inf, ifelse(p==1, Inf, log(p/(1-p)))) } # numerical safety for large values? ## check: weights ## ## adapted from ordinal::drop.coef which.dim <- function (X, silent = TRUE) { stopifnot(is.matrix(X)) silent <- as.logical(silent)[1] qr.X <- qr(X, tol = 1e-07, LAPACK = FALSE) if (qr.X$rank == ncol(X))
return(TRUE)
if (!silent)
message(gettextf("design is column rank deficient so dropping %d coef",
ncol(X) - qr.X$rank)) return(qr.X$pivot[1:qr.X$rank]) } ## link families link.PH <- list(link=function(S) log(-log(as.vector(S))), ilink=function(eta) exp(-exp(as.vector(eta))), gradS=function(eta,X) -exp(as.vector(eta))*exp(-exp(as.vector(eta)))*X, h=function(eta,etaD) as.vector(etaD)*exp(as.vector(eta)), H=function(eta) exp(as.vector(eta)), gradh=function(eta,etaD,obj) obj$XD*exp(as.vector(eta))+obj$X*as.vector(etaD)*exp(as.vector(eta)), gradH=function(eta,obj) obj$X*exp(as.vector(eta)))
H=function(eta) log(1+exp(as.vector(eta))),
as.vector(etaD)*exp(as.vector(eta))*obj$X*expit(-as.vector(eta)) - exp(2*as.vector(eta))*obj$X*as.vector(etaD)*expit(-as.vector(eta))^2 +
exp(as.vector(eta))*obj$XD*expit(-as.vector(eta)) }, gradH=function(eta,obj) obj$X*exp(as.vector(eta))*expit(-as.vector(eta)))
H=function(eta) -log(pnorm(-as.vector(eta))),
-as.vector(eta)*obj$X*dnorm(as.vector(eta))*as.vector(etaD)/pnorm(-as.vector(eta)) + obj$X*dnorm(as.vector(eta))^2/pnorm(-as.vector(eta))^2*as.vector(etaD) +
dnorm(as.vector(eta))/pnorm(-as.vector(eta))*obj$XD }, gradH=function(eta,obj) obj$X*dnorm(as.vector(eta))/pnorm(-as.vector(eta)))
H=function(eta) as.vector(eta),
gradh=function(eta,etaD,obj) obj$XD, gradH=function(eta,obj) obj$X)
link.AO <- function(theta) { # Aranda-Ordaz
if (theta==0) {
} else {
list(link = function(S) log((S^(-theta)-1)/theta),
ilink = function(eta) exp(-log(theta*exp(as.vector(eta))+1)/theta),
gradS = function(eta,X) -as.vector(exp(as.vector(eta))*exp(-log(theta*exp(as.vector(eta))+1)/theta)/(1+theta*exp(as.vector(eta))))*X,
H = function(eta) log(theta*exp(as.vector(eta))+1)/theta,
gradH = function(eta,obj) exp(as.vector(eta))*obj$X/(1+theta*exp(as.vector(eta))), gradh = function(eta,etaD,obj) { eta <- as.vector(eta) etaD <- as.vector(etaD) ((theta*exp(2*eta)+exp(eta))*obj$XD+exp(eta)*etaD*obj$X) / (theta*exp(eta)+1)^2 }) } } ## fd <- function(f,x,eps=1e-5) (f(x+eps)-f(x-eps))/2/eps fd <- function(f,x,eps=1e-5) t(sapply(1:length(x), function(i) { upper <- lower <- x upper[i]=x[i]+eps lower[i]=x[i]-eps (f(upper)-f(lower))/2/eps })) ## test code for the link functions if (FALSE) { Xstar <- cbind(1,1:3) # beta[1] + beta[2]*t betastar <- c(-4,0.5) XDstar <- cbind(0,Xstar[,2]) etastar <- as.vector(Xstar %*% betastar) etaDstar <- as.vector(XDstar %*% betastar) obj <- list(X=Xstar,XD=XDstar) for(link in list(rstpm2:::link.PH,rstpm2:::link.PO,rstpm2:::link.probit,rstpm2:::link.AH,rstpm2:::link.AO(.3))) { print(rstpm2:::fd(function(beta) link$ilink(Xstar%*%beta), betastar)-t(link$gradS(etastar,Xstar))) print(rstpm2:::fd(function(beta) link$h(Xstar%*%beta, XDstar%*%beta), betastar)-t(link$gradh(etastar,etaDstar,obj))) print(rstpm2:::fd(function(beta) link$H(Xstar%*%beta), betastar)-t(link$gradH(etastar,obj))) } } ## general link functions setClass("stpm2", representation(xlevels="list", contrasts="listOrNULL", terms="terms", logli="function", ## weights="numericOrNULL", lm="lm", timeVar="character", time0Var="character", timeExpr="nameOrcall", time0Expr="nameOrcallOrNULL", delayed="logical", interval="logical", frailty="logical", model.frame="list", call.formula="formula", x="matrix", xd="matrix", termsd="terms", Call="call", y="Surv", link="list", args="list" ), contains="mle2") stpm2 <- function(formula, data, smooth.formula = NULL, smooth.args = NULL, df = 3, cure = FALSE, logH.args = NULL, logH.formula = NULL, tvc = NULL, tvc.formula = NULL, control = list(parscale = 1, maxit = 300), init = NULL, coxph.strata = NULL, coxph.formula = NULL, weights = NULL, robust = FALSE, baseoff = FALSE, bhazard = NULL, bhazinit=0.1, timeVar = "", time0Var = "", use.gr = TRUE, optimiser=c("BFGS","NelderMead"), log.time.transform=TRUE, reltol=1.0e-8, trace = 0, link.type=c("PH","PO","probit","AH","AO"), theta.AO=0, frailty = !is.null(cluster) & !robust, cluster = NULL, logtheta=NULL, nodes=9, RandDist=c("Gamma","LogN"), recurrent = FALSE, adaptive = TRUE, maxkappa = 1e3, Z = ~1, contrasts = NULL, subset = NULL, robust_initial=FALSE, ...) { link.type <- match.arg(link.type) link <- switch(link.type,PH=link.PH,PO=link.PO,probit=link.probit,AH=link.AH,AO=link.AO(theta.AO)) RandDist <- match.arg(RandDist) optimiser <- match.arg(optimiser) ## use.gr <- TRUE # old code ## logH.formula and logH.args are deprecated if (!is.null(smooth.formula) && is.null(logH.formula)) logH.formula <- smooth.formula if (!is.null(smooth.args) && is.null(logH.args)) logH.args <- smooth.args ## parse the event expression eventInstance <- eval(lhs(formula),envir=data) stopifnot(length(lhs(formula))>=2) delayed <- length(lhs(formula))>=4 # indicator for multiple times (cf. strictly delayed) surv.type <- attr(eventInstance,"type") if (surv.type %in% c("interval2","left","mstate")) stop("stpm2 not implemented for Surv type ",surv.type,".") counting <- attr(eventInstance,"type") == "counting" interval <- attr(eventInstance,"type") == "interval" timeExpr <- lhs(formula)[[if (delayed && !interval) 3 else 2]] # expression eventExpr <- if (interval) lhs(formula)[[4]] else lhs(formula)[[length(lhs(formula))]] if (interval) time2Expr <- lhs(formula)[[3]] if (timeVar == "") timeVar <- all.vars(timeExpr) ## set up the formulae if (is.null(logH.formula) && is.null(logH.args)) { logH.args$df <- df
if (cure) logH.args$cure <- cure } if (is.null(logH.formula)) { logH.formula <- as.formula(call("~",as.call(c(quote(nsx),call("log",timeExpr), vector2call(logH.args))))) if (link.type=="AH") logH.formula <- as.formula(call("~",as.call(c(quote(nsx),timeExpr, vector2call(logH.args))) %call+% as.call(c(as.name(":"),rhs(formula),timeExpr)))) } if (is.null(tvc.formula) && !is.null(tvc)) { tvc.formulas <- lapply(names(tvc), function(name) call(":", as.name(name), as.call(c(quote(nsx), call("log",timeExpr), vector2call(if (cure) list(cure=cure,df=tvc[[name]]) else list(df=tvc[[name]]) ))))) if (length(tvc.formulas)>1) tvc.formulas <- list(Reduce(%call+%, tvc.formulas)) tvc.formula <- as.formula(call("~",tvc.formulas[[1]])) } if (!is.null(tvc.formula)) { rhs(logH.formula) <- rhs(logH.formula) %call+% rhs(tvc.formula) } if (baseoff) rhs(logH.formula) <- rhs(tvc.formula) full.formula <- formula rhs(full.formula) <- rhs(formula) %call+% rhs(logH.formula) Z.formula <- Z ## ## set up the data ## ensure that data is a data frame ## data <- get_all_vars(full.formula, data) # but this loses the other design information ## restrict to non-missing data (assumes na.action=na.omit) na.action.old <- options()[["na.action"]] options(na.action = "na.pass") on.exit(options(na.action = na.action.old)) subset.expr <- substitute(subset) if(class(subset.expr)=="NULL") subset.expr <- TRUE .include <- complete.cases(model.matrix(formula, data)) & !is.na(eval(eventExpr,data,parent.frame())) & eval(subset.expr,data,parent.frame()) options(na.action = na.action.old) if (!interval) .include <- .include & !is.na(eval(timeExpr,data,parent.frame())) time0Expr <- NULL # initialise if (delayed) { time0Expr <- lhs(formula)[[2]] .include <- .include & !is.na(eval(time0Expr,data,parent.frame())) } if (!is.null(substitute(weights))) .include <- .include & !is.na(eval(substitute(weights),data,parent.frame())) data <- data[.include, , drop=FALSE] ## ## parse the function call Call <- match.call() mf <- match.call(expand.dots = FALSE) m <- match(c("formula", "data", "subset", "contrasts", "weights"), names(mf), 0L) mf <- mf[c(1L, m)] ## ## get variables if (delayed) { if (time0Var == "") time0Var <- all.vars(time0Expr) time0 <- eval(time0Expr, data, parent.frame()) if (any(time0>0 & time0<1e-6)) warning("Some entry times < 1e-6: consider transforming time to avoid problems with finite differences") } time <- eval(timeExpr, data, parent.frame()) if (any(time>0 & time<1e-6)) warning("Some event times < 1e-6: consider transforming time to avoid problems with finite differences") event <- eval(eventExpr,data) ## if all the events are the same, we assume that they are all events, else events are those greater than min(event) if (!interval) event <- if (length(unique(event))==1) rep(TRUE, length(event)) else event <- event > min(event) ## setup for initial values if (!interval) { ## Cox regression coxph.call <- mf coxph.call[[1L]] <- as.name("coxph") coxph.call$subset <- .include
coxph.strata <- substitute(coxph.strata)
coxph.call$data <- quote(coxph.data) coxph.data <- data if (!is.null(coxph.formula)) { coxph.formula2 <- coxph.call$formula
rhs(coxph.formula2) <- rhs(formula) %call+% rhs(coxph.formula)
coxph.call$formula <- coxph.formula2 } if (!is.null(coxph.strata)) { coxph.formula2 <- coxph.call$formula
rhs(coxph.formula2) <- rhs(formula) %call+% call("strata",coxph.strata)
coxph.call$formula <- coxph.formula2 } coxph.call$model <- TRUE
coxph.obj <- eval(coxph.call, coxph.data)
y <- model.extract(model.frame(coxph.obj),"response")
data$logHhat <- if (is.null(bhazard)) { pmax(-18,link$link(Shat(coxph.obj)))
} else  pmax(-18,link$link(Shat(coxph.obj)/exp(-bhazinit*bhazard*time))) if (frailty && is.null(logtheta)) { coxph.data$.cluster <- as.vector(unclass(factor(cluster)))[.include]
coxph.formula <- coxph.call$formula rhs(coxph.formula) <- rhs(coxph.formula) %call+% call("frailty",as.name(".cluster"), distribution=switch(RandDist,LogN="gaussian",Gamma="gamma")) coxph.call$formula <- coxph.formula
coxph.obj <- eval(coxph.call, envir=parent.frame())
logtheta <- log(coxph.obj$history[[1]]$theta)
}
}
if (interval) {
## survref regression
survreg.call <- mf
survreg.call[[1L]] <- as.name("survreg")
survreg.obj <- eval(survreg.call, envir=parent.frame())
weibullShape <- 1/survreg.obj$scale weibullScale <- predict(survreg.obj) y <- model.extract(model.frame(survreg.obj),"response") data$logHhat <- pmax(-18,link$link(pweibull(time,weibullShape,weibullScale,lower.tail=FALSE))) ## if (frailty && is.null(logtheta)) { logtheta <- -1 } } ## ## initial values and object for lpmatrix predictions lm.call <- mf lm.call[[1L]] <- as.name("lm") lm.formula <- full.formula lhs(lm.formula) <- quote(logHhat) # new response lm.call$formula <- lm.formula
dataEvents <- data[event,]
if (interval) {
dataEvents <- data[event>0, , drop=FALSE]
}
lm.call$data <- quote(dataEvents) # events only lm.obj <- eval(lm.call) if (is.null(init)) { init <- coef(lm.obj) } ## ## set up mf and wt mt <- terms(lm.obj) mf <- model.frame(lm.obj) ## wt <- model.weights(lm.obj$model)
wt <- if (is.null(substitute(weights))) rep(1,nrow(data)) else eval(substitute(weights),data,parent.frame())
##
## XD matrix
## lpfunc <- function(delta,fit,dataset,var) {
##   dataset[[var]] <- dataset[[var]]+delta
##   lpmatrix.lm(fit,dataset)
## }
lpfunc <- function(x,fit,data,var) {
data[[var]] <- x
lpmatrix.lm(fit,data)
}
##
bhazard <- substitute(bhazard)
bhazard <- if (is.null(bhazard)) rep(0,nrow(data)) else eval(bhazard,data,parent.frame())
excess <- !all(bhazard==0)
## initialise values specific to either delayed entry or interval-censored
ind0 <- FALSE
map0 <- 0L
which0 <- 0
wt0 <- 0
ttype <- 0
transX <- function(X, data) X
transXD <- function(XD) XD
if (!interval) { # surv.type %in% c("right","counting")
X <- lpmatrix.lm(lm.obj,data)
datat0 <- data
datat0[[timeVar]] <- 0
index0 <- which.dim(X - lpmatrix.lm(lm.obj,datat0))
transX <- function(X, data) {
datat0 <- data
datat0[[timeVar]] <- 0
Xt0 <- lpmatrix.lm(lm.obj,datat0)
(X - Xt0)[, index0, drop=FALSE]
}
transXD <- function(XD) XD[, index0, drop=FALSE]
init <- init[index0]
}
X <- transX(X,data)
## XD <- grad(lpfunc,0,lm.obj,data,timeVar)
## XD <- transXD(matrix(XD,nrow=nrow(X)))
X1 <- matrix(0,nrow(X),ncol(X))
X0 <- matrix(0,1,ncol(X))
if (delayed && all(time0==0)) delayed <- FALSE # CAREFUL HERE: delayed redefined
if (delayed) {
ind0 <- time0>0
map0 <- vector("integer",nrow(X))
map0[ind0] <- as.integer(1:sum(ind0))
map0[!ind0] <- NaN
##which0 <- which(ind0)
which0 <- 1:nrow(X)
which0[!ind0] <- NaN
data0 <- data[ind0,,drop=FALSE] # data for delayed entry times
data0[[timeVar]] <- data0[[time0Var]]
X0 <- transX(lpmatrix.lm(lm.obj, data0), data0)
wt0 <- wt[ind0]
rm(data0)
}
} else { ## interval-censored
## ttime <- eventInstance[,1]
## ttime2 <- eventInstance[,2]
ttype <- eventInstance[,3]
X <- transX(lpmatrix.lm(lm.obj,data),data)
data0 <- data
data0[[timeVar]] <- data0[[as.character(time2Expr)]]
data0[[timeVar]] <- ifelse(data0[[timeVar]]<=0,NA,data0[[timeVar]])
X1 <- transX(lpmatrix.lm(lm.obj, data0), data0)
## XD <- grad(lpfunc,0,lm.obj,data0,timeVar)
## XD <- transXD(matrix(XD,nrow=nrow(X)))
X0 <- matrix(0,nrow(X),ncol(X))
rm(data0)
}
if (frailty) {
Z <- model.matrix(Z, data)
if (ncol(Z)>2) stop("Current implementation only allows for one or two random effects")
if (ncol(Z)==2) {
init <- c(init,logtheta1=logtheta,corrtrans=0,logtheta2=logtheta)
} else init <- c(init, logtheta=logtheta)
}
if (!is.null(control) && "parscale" %in% names(control)) {
if (length(control$parscale)==1) control$parscale <- rep(control$parscale,length(init)) if (is.null(names(control$parscale)))
names(control$parscale) <- names(init) } parscale <- rep(if (is.null(control$parscale)) 1 else control$parscale,length=length(init)) names(parscale) <- names(init) args <- list(init=init,X=X,XD=XD,bhazard=bhazard,wt=wt,event=ifelse(event,1,0),time=time, delayed=delayed, interval=interval, X0=X0, wt0=wt0, X1=X1, parscale=parscale, reltol=reltol, kappa=1, trace = trace, oldcluster=cluster, frailty=frailty, cluster=if(!is.null(cluster)) as.vector(unclass(factor(cluster)))[.include] else NULL, map0 = map0 - 1L, ind0 = ind0, which0 = which0 - 1L, link=link.type, ttype=ttype, RandDist=RandDist, optimiser=optimiser, log.time.transform=log.time.transform, type=if (frailty && RandDist=="Gamma") "stpm2_gamma_frailty" else if (frailty && RandDist=="LogN") "stpm2_normal_frailty" else "stpm2", recurrent = recurrent, return_type="optim", transX=transX, transXD=transXD, maxkappa=maxkappa, Z=Z, Z.formula = Z.formula, thetaAO = theta.AO, excess=excess, data=data, robust_initial = robust_initial, .include=.include) if (frailty) { rule <- fastGHQuad::gaussHermiteData(nodes) args$gauss_x <- rule$x args$gauss_w <- rule$w args$adaptive <- adaptive
if (ncol(args$Z)>1) { use.gr <- FALSE args$type <- "stpm2_normal_frailty_2d"
args$Z <- as.matrix(args$Z)
## args$adaptive <- FALSE # adaptive not defined ## args$optimiser <- "NelderMead" # gradients not defined
} else args$Z <- as.vector(args$Z)
}
negll <- function(beta) {
localargs <- args
localargs$return_type <- "objective" localargs$init <- beta
return(.Call("model_output", localargs, PACKAGE="rstpm2"))
}
gradnegll <- function(beta) {
localargs <- args
localargs$init <- beta localargs$return_type <- "gradient"
return(.Call("model_output", localargs, PACKAGE="rstpm2"))
}
fdgradnegll <- function(beta, eps=1e-6) {
sapply(1:length(beta), function(i) {
betau <- betal <- beta
betau[i] <- beta[i]+eps
betal[i] <- beta[i]-eps
(negll(betau)-negll(betal))/2/eps
})
}
logli <- function(beta) {
localargs <- args
localargs$init <- beta localargs$return_type <- "li"
return(.Call("model_output", localargs, PACKAGE="rstpm2"))
}
parnames(negll) <- parnames(gradnegll) <- names(init)
## MLE
if (frailty) { # first fit without the frailty
args2 <- args
args2$frailty <- FALSE args2$cluster <- NULL
args2$type <- "stpm2" localIndex <- 1:(length(args2$init)-1)
args2$init <- args2$init[localIndex]
args2$parscale <- args2$parscale[localIndex]
fit <- .Call("model_output", args2, PACKAGE="rstpm2")
rm(args2)
args$init <- c(fit$coef,logtheta)
}
fit <- .Call("model_output", args, PACKAGE="rstpm2")
args$init <- coef <- as.vector(fit$coef)
args$kappa.final <- fit$kappa
hessian <- fit$hessian names(coef) <- rownames(hessian) <- colnames(hessian) <- names(init) mle2 <- if (use.gr) mle2(negll, coef, vecpar=TRUE, control=control, gr=gradnegll, ..., eval.only=TRUE) else mle2(negll, coef, vecpar=TRUE, control=control, ..., eval.only=TRUE) mle2@details$convergence <- fit$fail # fit$itrmcd
if (inherits(vcov <- try(solve(hessian)), "try-error")) {
warning("Non-invertible Hessian")
mle2@vcov <- matrix(NA,length(coef), length(coef))
}
warning("Non-invertible Hessian - refitting with Nelder-Mead")
args$optimiser <- "NelderMead" fit <- .Call("model_output", args, PACKAGE="rstpm2") args$init <- coef <- as.vector(fit$coef) args$kappa.final <- fit$kappa hessian <- fit$hessian
names(coef) <- rownames(hessian) <- colnames(hessian) <- names(init)
mle2 <- mle2(negll, coef, vecpar=TRUE, control=control, ..., eval.only=TRUE)
mle2@vcov <- if (!inherits(vcov <- try(solve(hessian)), "try-error")) vcov else matrix(NA,length(coef), length(coef))
mle2@details$convergence <- fit$fail # fit$itrmcd if (inherits(vcov <- try(solve(hessian)), "try-error")) warning("Non-invertible Hessian - refitting failed") } } else { mle2@vcov <- vcov } out <- new("stpm2", call = mle2@call, call.orig = mle2@call, coef = mle2@coef, fullcoef = mle2@fullcoef, vcov = mle2@vcov, min = mle2@min, details = mle2@details, minuslogl = mle2@minuslogl, method = mle2@method, data = data, formula = mle2@formula, optimizer = "optim", xlevels = .getXlevels(mt, mf), ##contrasts = attr(X, "contrasts"), contrasts = contrasts, logli = logli, ##weights = weights, Call = Call, terms = mt, model.frame = mf, lm = lm.obj, timeVar = timeVar, time0Var = time0Var, timeExpr = timeExpr, time0Expr = time0Expr, delayed = delayed, interval = interval, frailty = frailty, call.formula = formula, x = X, xd = XD, termsd = mt, # wrong! y = y, link=link, args=args) if (robust && !frailty) # kludge out@vcov <- sandwich.stpm2(out, cluster=cluster) return(out) } setMethod("show", "stpm2", function(object) { object@call.orig <- object@Call show(as(object,"mle2")) }) setClass("summary.stpm2", representation(frailty="logical",theta="list",wald="matrix",args="list"), contains="summary.mle2") corrtrans <- function(x) (1-exp(-x)) / (1+exp(-x)) setMethod("summary", "stpm2", function(object) { newobj <- as(summary(as(object,"mle2")),"summary.stpm2") newobj@args <- object@args newobj@frailty <- object@frailty newobj@call <- object@Call if (object@frailty && !is.matrix(object@args$Z)) {
coef <- coef(newobj)
theta <- exp(coef[nrow(coef),1])
se.logtheta <- coef[nrow(coef),2]
se.theta <- theta*se.logtheta
test.statistic <- (1/se.logtheta)^2
p.value <- pchisq(test.statistic,df=1,lower.tail=FALSE)/2
newobj@theta <- list(theta=theta, se.theta=se.theta, p.value=p.value)
} else if (object@frailty && is.matrix(object@args$Z) && ncol(object@args$Z)==2) {
## browser()
coef <- coef(object)
index <- (length(coef)-2):length(coef)
coef <- coef[index]
vcov <- vcov(object)[index,index]
rho <- corrtrans(g12 <- coef[2])
theta <- c(theta1=exp(coef[1]),corr=rho,theta2=exp(coef[3]))
se.theta <- c(theta[1]*sqrt(vcov[1,1]),
2*exp(-g12)/(1+exp(-g12))^2*sqrt(vcov[2,2]),
theta[3]*sqrt(vcov[3,3]))
se.logtheta <- c(theta1=sqrt(vcov[1,1]),
corr=sqrt(vcov[2,2])/coef[2],
theta2=sqrt(vcov[3,3]))
test.statistic <- (1/se.logtheta)^2
p.value <- pchisq(test.statistic,df=1,lower.tail=FALSE)/2
newobj@theta <- list(theta=theta, se.theta=se.theta, p.value=p.value)
} else newobj@theta <- list()
newobj@wald <- matrix(NA,1,1) # needed by summary.pstpm2
newobj })
setMethod("show", "summary.stpm2",
function(object) {
show(as(object,"summary.mle2"))
if (object@frailty) {
if (is.matrix(object@args$Z)) { cat("Random effects model: corr=(1-exp(-corrtrans))/(1+exp(-corrtrans))") cat(sprintf("\ntheta1=%g\tse=%g\tp=%g\n", object@theta$theta[1],object@theta$se.theta[1],object@theta$p.value[1]))
cat(sprintf("\ncorr=%g\tse=%g\tp=%g\n",
object@theta$theta[2],object@theta$se.theta[2],object@theta$p.value[2])) cat(sprintf("\ntheta2=%g\tse=%g\tp=%g\n", object@theta$theta[3],object@theta$se.theta[3],object@theta$p.value[3]))
} else {
cat(sprintf("\ntheta=%g\tse=%g\tp=%g\n",
object@theta$theta,object@theta$se.theta,object@theta$p.value)) } } }) setMethod("predictnl", "stpm2", function(object,fun,newdata=NULL,link=c("I","log","cloglog","logit"), gd=NULL, ...) { link <- match.arg(link) ## invlinkf <- switch(link,I=I,log=exp,cloglog=cexpexp,logit=expit) linkf <- eval(parse(text=link)) if (is.null(newdata) && !is.null(object@data)) newdata <- object@data localf <- function(coef,...) { object@fullcoef = coef linkf(fun(object,...)) } dm <- numDeltaMethod(object,localf,newdata=newdata,gd=gd,...) ## ci <- confint(dm, level = level) ## out <- invlinkf(data.frame(Estimate=dm$fit,
##                            lower=ci[,1],
##                            upper=ci[,2]))
## ## cloglog switches the bounds
##   out <- data.frame(Estimate=out$Estimate,lower=out$upper,upper=out$lower) ## return(out) return(dm) }) ## setMethod("predictnl", "aft", function(object,fun,newdata=NULL,link=c("I","log","cloglog","logit"), gd=NULL, ...) { link <- match.arg(link) linkf <- eval(parse(text=link)) if (is.null(newdata) && !is.null(object@args$data))
newdata <- object@args$data localf <- function(coef,...) { object@args$init <- object@fullcoef <- coef
}
numDeltaMethod(object,localf,newdata=newdata,gd=gd,...)
})

residuals.stpm2.base <- function(object, type=c("li","gradli")) {
type <- match.arg(type)
args <- object@args
if (type=="li") {
localargs <- args
localargs$return_type <- "li" out <- as.vector(.Call("model_output", localargs, PACKAGE="rstpm2")) names(out) <- rownames(args$X)
}
localargs <- args
localargs$return_type <- "gradli" out <- .Call("model_output", localargs, PACKAGE="rstpm2") dimnames(out) <- dimnames(args$X)
}
return(out)
}
setMethod("residuals", "stpm2",
residuals.stpm2.base(object=object, type=match.arg(type)))

predict.stpm2.base <-
function(object, newdata=NULL,
grid=FALSE, seqLength=300,
type.relsurv=c("excess","total","other"), ratetable = survival::survexp.us,
rmap, scale=365.24,
se.fit=FALSE, link=NULL, exposed=NULL, var=NULL, keep.attributes=FALSE,
use.gr=TRUE, level=0.95, n.gauss.quad=100, full=FALSE, ...)
{
type <- match.arg(type)
type.relsurv <- match.arg(type.relsurv)
args <- object@args
if (type %in% c("fail","margfail")) {
out <- 1-predict.stpm2.base(object, newdata=newdata,
type=switch(type, fail="surv", margfail="margsurv"),
grid=grid, seqLength=seqLength, type.relsurv=type.relsurv,
ratetable=ratetable, rmap=rmap, scale=scale,
var=var, keep.attributes=keep.attributes,
full=full, ...)
if (se.fit) {temp <- out$lower; out$lower <- out$upper; out$upper <- temp}
return(out)
}
if(args$excess){ link <- switch(type, surv = "log", cumhaz = "I", hazard = "I", hr = "I", sdiff = "I", hdiff = "I", loghazard = "I", link = "I", odds = "log", or = "log", margsurv = "log", marghaz = "I", marghr = "I", meansurv = "I", meanhr = "I", meanhaz = "I", af = "I", fail = "cloglog", uncured = "log", rmst = "I", probcure = "cloglog") } else { link <- switch(type, surv = "cloglog", cumhaz = "log", hazard = "log", hr = "log", sdiff = "I", hdiff = "I", loghazard = "I", link = "I", odds = "log", or = "log", margsurv = "cloglog", marghaz = "log", marghr = "log", meansurv = "I", meanhr="log", meanhaz = "I", af = "I", fail = "cloglog", uncured = "cloglog", rmst = "I", probcure = "cloglog") } } invlinkf <- switch(link,I=I,log=exp,cloglog=cexpexp,logit=expit) linkf <- eval(parse(text=link)) if (type %in% c("uncured","probcure") && is.null(exposed)) exposed <- function(data) data[[object@timeVar]] <- max(args$time[args$event]) if (is.null(exposed) && is.null(var) & type %in% c("hr","sdiff","hdiff","meansurvdiff","meanhr","or","marghr","af","uncured","probcure")) stop('Either exposed or var required for type in ("hr","sdiff","hdiff","meansurvdiff","meanhr","or","marghr","af","uncured","probcure")') if (type %in% c('margsurv','marghaz','marghr','margfail','meanmargsurv') && !object@args$frailty)
stop("Marginal prediction only for frailty models")
## exposed is a function that takes newdata and returns the revised newdata
## var is a string for a variable that defines a unit change in exposure
if (is.null(newdata) && type %in% c("hr","sdiff","hdiff","meansurvdiff","meanhr","or","marghr","uncured"))
stop("Prediction using type in ('hr','sdiff','hdiff','meansurvdiff','meanhr','or','marghr','uncured','probcure') requires newdata to be specified.")
calcX <- !is.null(newdata)
time <- NULL
if (is.null(newdata)) {
##mm <- X <- model.matrix(object) # fails (missing timevar)
X <- object@x
XD <- object@xd
##y <- model.response(object@model.frame)
y <- object@y
time <- as.vector(y[,ncol(y)-1])
newdata <- as.data.frame(object@data)
}
newdata2 <- NULL
lpfunc <- function(newdata)
if (inherits(object,"pstpm2"))
function(x,...) {
newdata2 <- newdata
newdata2[[object@timeVar]] <- x
predict(object@gam,newdata2,type="lpmatrix")
} else
function(x,...) {
newdata2 <- newdata
newdata2[[object@timeVar]] <- x
lpmatrix.lm(object@lm,newdata2)
}
##     function(delta,fit,data,var) {
##     data[[var]] <- data[[var]]+delta
##     lpmatrix.lm(fit,data)
## }
## resp <- attr(Terms, "variables")[attr(Terms, "response")]
## similarly for the derivatives
if (grid) {
Y <- object@y
event <- Y[,ncol(Y)]==1 | object@args$interval time <- object@data[[object@timeVar]] eventTimes <- time[event] tt <- seq(min(eventTimes),max(eventTimes),length=seqLength)[-1] data.x <- data.frame(tt) names(data.x) <- object@timeVar newdata[[object@timeVar]] <- NULL newdata <- merge(newdata,data.x) calcX <- TRUE } if (type=="rmst") { if (nrow(newdata)>1) stop("rmst currently only for single value") stopifnot(object@timeVar %in% names(newdata)) quad <- gauss.quad(n.gauss.quad) a <- 0 b <- newdata[[object@timeVar]] time <- (b-a)/2*quad$nodes + (a+b)/2
weights <- quad$weights*(b-a)/2 newdata <- newdata[rep(1,length(time)),] newdata[[object@timeVar]] <- time calcX <- TRUE } if (args$excess) {
## rmap <- substitute(rmap)
if(type.relsurv != "excess"){
Sstar <- do.call(survexp, list(substitute(I(timeVar*scale)~1,list(timeVar=as.name(object@timeVar))),
ratetable=ratetable,
scale=scale,
rmap=substitute(rmap),
cohort=FALSE,
data=newdata))
Hstar <- -log(Sstar)
if (!is.null(newdata2))
Sstar2 <- do.call(survexp, list(substitute(I(timeVar*scale)~1,list(timeVar=as.name(object@timeVar))),
ratetable=ratetable,
scale=scale,
rmap=rmap,
cohort=FALSE,
data=newdata2))
Hstar <- -log(Sstar)
}
}
if (calcX)  {
if (inherits(object, "stpm2")) {
X <- object@args$transX(lpmatrix.lm(object@lm, newdata), newdata) XD <- grad1(lpfunc(newdata),newdata[[object@timeVar]], log.transform=object@args$log.time.transform)
XD <- object@args$transXD(XD) } if (inherits(object, "pstpm2")) { X <- object@args$transX(predict(object@gam, newdata, type="lpmatrix"), newdata)
XD <- object@args$transXD(grad1(lpfunc(newdata),newdata[[object@timeVar]], log.transform=object@args$log.time.transform))
}
## X <- args$transX(lpmatrix.lm(object@lm, newdata), newdata) ## XD <- grad(lpfunc,0,object@lm,newdata,object@timeVar) ## XD <- args$transXD(matrix(XD,nrow=nrow(X)))
}
## if (type %in% c("hazard","hr","sdiff","hdiff","loghazard","or","marghaz","marghr","fail","margsurv","meanmargsurv","uncured")) {
if (is.null(time)) {
## how to elegantly extract the time variable?
## timeExpr <-
##   lhs(object@call.formula)[[length(lhs(object@call.formula))-1]]
time <- eval(object@timeExpr,newdata,parent.frame())
##
}
## if (object@delayed && !object@interval) {
##   newdata0 <- newdata
##   newdata0[[object@timeVar]] <- newdata[[object@time0Var]]
##   X0 <- lpmatrix.lm(object@lm, newdata0)
##   ## XD0 <- grad(lpfunc,0,object@lm,newdata,object@timeVar)
##   ## XD0 <- matrix(XD0,nrow=nrow(X0))
## }
if (type %in% c("hr","sdiff","hdiff","meansurvdiff","meanhr","or","marghr","af","uncured","probcure")) {
newdata2 <- exposed(newdata)
if (inherits(object, "stpm2")) {
X2 <- object@args$transX(lpmatrix.lm(object@lm, newdata2), newdata2) XD2 <- grad1(lpfunc(newdata2),newdata2[[object@timeVar]], log.transform=object@args$log.time.transform)
XD2 <- object@args$transXD(XD2) } if (inherits(object, "pstpm2")) { X2 <- object@args$transX(predict(object@gam, newdata2, type="lpmatrix"), newdata2)
XD2 <- object@args$transXD(grad1(lpfunc(newdata2),newdata2[[object@timeVar]], log.transform=object@args$log.time.transform))
}
## X2 <- args$transX(lpmatrix.lm(object@lm, newdata2), newdata2) ## XD2 <- grad(lpfunc,0,object@lm,newdata2,object@timeVar) ## XD2 <- args$transXD(matrix(XD2,nrow=nrow(X)))
}
colMeans <- function(x) colSums(x)/apply(x,2,length)
if (object@frailty && type %in% c("af","meansurvdiff") && args$RandDist=="Gamma" && !object@args$interval && !object@args$delayed) { times <- newdata[[object@timeVar]] utimes <- sort(unique(times)) n <- nrow(X)/length(utimes) n.cluster <- length(unique(args$cluster))
beta <- coef(object)
npar <- length(beta)
logtheta <- beta[npar]
theta <- exp(beta[npar])
beta <- beta[-npar]
Hessian <- solve(vcov(object))
eta <- as.vector(X %*% beta)
eta2 <- as.vector(X2 %*% beta)
S <- newlink$ilink(eta) S2 <- newlink$ilink(eta2)
H <- -log(S)
H2 <- -log(S2)
marg <- function(logtheta,H) (1+exp(logtheta)*H)^(-1/exp(logtheta))
margS <- marg(logtheta,H)
margS2 <- marg(logtheta,H2)
dmarg.dlogtheta <- function(logtheta,H) {
theta <- exp(logtheta)
marg(logtheta,H)*(exp(-logtheta)*log(1+theta*H)-H/(1+theta*H))
}
## dmarg.dbeta <- function(logtheta,H,gradH) {
##     theta <- exp(logtheta)
## }
## link <- link.PH; eps <- 1e-5; dmarg.dlogtheta(3,.2); (marg(3+eps,.2)-marg(3-eps,.2))/2/eps
## eps <- 1e-5; dmarg.dlogtheta(3,.2); (marg(3+eps,.2)-marg(3-eps,.2))/2/eps
##
meanS <- tapply(margS,times,mean)
meanS2 <- tapply(margS2,times,mean)
fit <- switch(type,af=1-(1-meanS2)/(1-meanS),meansurvdiff=meanS-meanS2)
se.fit <- vector("numeric",length(utimes))
for (i in 1:length(utimes)) {
index <- which(times==utimes[i])
newobj <- object
newobj@args$X <- X[index,,drop=FALSE] newobj@args$XD <- XD[index,,drop=FALSE]
res <- cbind(margS[index]-mean(margS[index]),margS2[index]-mean(margS2[index]))
res <- apply(res,2,function(col) tapply(col,args$cluster,sum)) res <- cbind(res, gradli) meat <- stats::var(res, na.rm=TRUE) colnames(meat) <- rownames(meat) <- c("S","S0", names(beta),"logtheta") S.hessian <- cbind(-diag(2)*n/n.cluster, rbind(colSums(margS[index]*(-newlink$gradH(eta[index],list(X=X[index,,drop=FALSE]))/(1+theta*H[index])))/n.cluster,
colSums(margS2[index]*(-newlink$gradH(eta2[index],list(X=X2[index,,drop=FALSE]))/(1+theta*H2[index])))/n.cluster), c(sum(dmarg.dlogtheta(logtheta,H[index]))/n.cluster, sum(dmarg.dlogtheta(logtheta,H2[index]))/n.cluster)) par.hessian <- cbind(matrix(0, nrow = npar, ncol = 2), -Hessian / n.cluster) bread <- rbind(S.hessian, par.hessian) ibread <- solve(bread) sandwich <- (ibread %*% meat %*% t(ibread) / n.cluster)[1:2, 1:2] gradient <- switch(type, af=as.matrix(c( - (1 - meanS2[i]) / (1 - meanS[i]) ^ 2, 1 / (1 - meanS[i])), nrow = 2, ncol = 1), meansurvdiff=matrix(c(1,-1),nrow=2)) AF.var <- t(gradient) %*% sandwich %*% gradient ## S.var <- sandwich[1, 1] ## S0.var <- sandwich[2, 2] se.fit[i] <- sqrt(AF.var) } pred <- data.frame(Estimate=fit, lower=fit-1.96*se.fit, upper=fit+1.96*se.fit) if (keep.attributes) attr(pred,"newdata") <- newdata return(pred) } if (object@frailty && type %in% c("meanmargsurv") && args$RandDist=="Gamma" && !object@args$interval && !object@args$delayed) {
## browser()
times <- newdata[[object@timeVar]]
utimes <- sort(unique(times))
n <- nrow(X)/length(utimes)
n.cluster <- length(unique(args$cluster)) newlink <- object@link beta <- coef(object) npar <- length(beta) logtheta <- beta[npar] theta <- exp(beta[npar]) beta <- beta[-npar] Hessian <- solve(vcov(object)) eta <- as.vector(X %*% beta) S <- newlink$ilink(eta)
H <- -log(S)
marg <- function(logtheta,H) (1+exp(logtheta)*H)^(-1/exp(logtheta))
margS <- marg(logtheta,H)
dmarg.dlogtheta <- function(logtheta,H) {
theta <- exp(logtheta)
marg(logtheta,H)*(exp(-logtheta)*log(1+theta*H)-H/(1+theta*H))
}
## eps <- 1e-5; dmarg.dlogtheta(3,.2); (marg(3+eps,.2)-marg(3-eps,.2))/2/eps
##
meanS <- tapply(margS,times,mean)
fit <- meanS
se.fit <- vector("numeric",length(utimes))
for (i in 1:length(utimes)) {
## browser()
index <- which(times==utimes[i])
newobj <- object
newobj@args$X <- X[index,,drop=FALSE] newobj@args$XD <- XD[index,,drop=FALSE]
## ## Attempt to use the sandwich estimator for the covariance matrix with the delta method (-> inflated SEs)
## res <- residuals(newobj,type="gradli")
## meat <- stats::var(res, na.rm=TRUE) # crossprod(res)/n.cluster
## colnames(meat) <- rownames(meat) <- c(names(beta),"logtheta")
## bread <- -Hessian / n.cluster
## sandwich <- ibread %*% meat %*% t(ibread) / n.cluster
## g <- c(colSums(margS[index]*(-newlink$gradH(eta[index],list(X=X[index,,drop=FALSE]))/(1+theta*H[index])))/n.cluster, ## sum(dmarg.dlogtheta(logtheta,H[index]))/n.cluster) ## se.fit[i] <- sqrt(sum(matrix(g,nrow=1)%*%(sandwich %*% g))) gradli <- residuals(newobj,type="gradli") res <- tapply(margS[index]-mean(margS[index]),args$cluster,sum)
res <- cbind(res, gradli)
meat <- stats::var(res, na.rm=TRUE)
## meat <- crossprod(res)/n.cluster
colnames(meat) <- rownames(meat) <- c("S", names(beta),"logtheta")
S.hessian <- c(-n/n.cluster,
colSums(margS[index]*(-newlink$gradH(eta[index],list(X=X[index,,drop=FALSE]))/(1+theta*H[index])))/n.cluster, sum(dmarg.dlogtheta(logtheta,H[index]))/n.cluster) par.hessian <- cbind(matrix(0, nrow = npar, ncol = 1), -Hessian / n.cluster) bread <- rbind(S.hessian, par.hessian) ibread <- solve(bread) sandwich <- (ibread %*% meat %*% t(ibread) / n.cluster)[1, 1] se.fit[i] <- sqrt(sandwich) } pred <- data.frame(Estimate=fit, lower=fit-1.96*se.fit, upper=fit+1.96*se.fit) if (keep.attributes) attr(pred,"newdata") <- newdata return(pred) } local <- function (object, newdata=NULL, type="surv", exposed) { beta <- coef(object) tt <- object@terms link <- object@link # cf. link for transformation of the predictions if (object@frailty) { theta <- exp(beta[length(beta)]) beta <- beta[-length(beta)] if (object@args$RandDist=="LogN") {
gauss_x <- object@args$gauss_x gauss_w <- object@args$gauss_w
Z <- model.matrix(args$Z.formula, newdata) if (ncol(Z)>1) stop("Current implementation only allows for a single random effect") Z <- as.vector(Z) } } eta <- as.vector(X %*% beta) etaD <- as.vector(XD %*% beta) S <- link$ilink(eta)
h <- link$h(eta,etaD) if (!object@args$excess && any(ifelse(is.na(h),FALSE,h<0))) warning(sprintf("Predicted hazards less than zero (n=%i).",sum(ifelse(is.na(h),FALSE,h<0))))
H = link$H(eta) Sigma = vcov(object) if (!args$excess) type.relsurv <- "excess" ## ugly hack
return(eta)
}
if (type=="cumhaz") {
## if (object@delayed) {
##     eta0 <- as.vector(X0 %*% beta)
##     etaD0 <- as.vector(XD0 %*% beta)
##     H0 <- link$H(eta0) ## return(H - H0) ## } ## else return(switch(type.relsurv,excess=H,total=H+Hstar,other=Hstar)) } if (type=="density") return (S*h) if (type=="surv") { return(switch(type.relsurv,excess=S,total=S*Sstar,other=Sstar)) } if (type=="fail") { return(switch(type.relsurv, excess=1-S,total=1-S*Sstar, other=1-Sstar)) } if (type=="odds") { # delayed entry? return((1-S)/S) } if (type=="sdiff") return(link$ilink(as.vector(X2 %*% beta)) - S)
if (type=="hazard") {
return(h)
}
if (type=="loghazard") {
return(log(h))
}
if (type=="hdiff") {
eta2 <- as.vector(X2 %*% beta)
etaD2 <- as.vector(XD2 %*% beta)
h2 <- link$h(eta2,etaD2) return(h2 - h) } if (type=="uncured") { S2 <- link$ilink(as.vector(X2 %*% beta))
return((S-S2)/(1-S2))
}
if (type=="probcure") {
S2 <- link$ilink(as.vector(X2 %*% beta)) return(S2/S) } if (type=="hr") { eta2 <- as.vector(X2 %*% beta) etaD2 <- as.vector(XD2 %*% beta) h2 <- link$h(eta2,etaD2)
return(h2/h)
}
if (type=="or") {
S2 <- link$ilink(as.vector(X2 %*% beta)) return((1-S2)/S2/((1-S)/S)) } if (type=="meansurv") { return(tapply(S,newdata[[object@timeVar]],mean)) } if (type=="meanhaz") { return(tapply(S*h,newdata[[object@timeVar]],sum)/tapply(S,newdata[[object@timeVar]],sum)) } if (type=="meanhr") { eta2 <- as.vector(X2 %*% beta) etaD2 <- as.vector(XD2 %*% beta) h2 <- link$h(eta2,etaD2)
S2 <- link$ilink(eta2) return(tapply(S2*h2,newdata[[object@timeVar]],sum)/tapply(S2,newdata[[object@timeVar]],sum) / (tapply(S*h,newdata[[object@timeVar]],sum)/tapply(S,newdata[[object@timeVar]],sum))) } if (type=="meansurvdiff") { eta2 <- as.vector(X2 %*% beta) S2 <- link$ilink(eta2)
return(tapply(S2,newdata[[object@timeVar]],mean) - tapply(S,newdata[[object@timeVar]],mean))
}
if (type=="af") {
eta2 <- as.vector(X2 %*% beta)
S2 <- link$ilink(eta2) meanS <- tapply(S,newdata[[object@timeVar]],mean) meanS2 <- tapply(S2,newdata[[object@timeVar]],mean) if (object@frailty) { if (object@args$RandDist=="Gamma") {
meanS <- tapply((1+theta*(-log(S)))^(-1/theta), newdata[[object@timeVar]], mean)
meanS2 <- tapply((1+theta*(-log(S2)))^(-1/theta), newdata[[object@timeVar]], mean)
} else {
meanS <- tapply(sapply(1:length(gauss_x),
function(i) link$ilink(eta+Z*sqrt(2)*sqrt(theta)*gauss_x[i])) %*% gauss_w / sqrt(pi), newdata[[object@timeVar]], mean) meanS2 <- tapply(sapply(1:length(gauss_x), function(i) link$ilink(eta2+Z*sqrt(2)*sqrt(theta)*gauss_x[i])) %*%
gauss_w / sqrt(pi),
newdata[[object@timeVar]],
mean)
}
}
return((meanS2 - meanS)/(1-meanS))
}
if (type=="meanmargsurv") {
stopifnot(object@frailty && object@args$RandDist %in% c("Gamma","LogN")) if (object@args$RandDist=="Gamma")
return(tapply((1+theta*H)^(-1/theta), newdata[[object@timeVar]], mean))
if (object@args$RandDist=="LogN") { return(tapply(sapply(1:length(gauss_x), function(i) link$ilink(eta+Z*sqrt(2)*sqrt(theta)*gauss_x[i])) %*%
gauss_w / sqrt(pi),
newdata[[object@timeVar]],
mean))
}
}
if (type=="margsurv") {
stopifnot(object@args$frailty && object@args$RandDist %in% c("Gamma","LogN"))
if (object@args$RandDist=="Gamma") return((1+theta*H)^(-1/theta)) if (object@args$RandDist=="LogN") {
return(sapply(1:length(gauss_x),
function(i) link$ilink(eta+Z*sqrt(2)*sqrt(theta)*gauss_x[i])) %*% gauss_w / sqrt(pi)) } } if (type=="marghaz") { stopifnot(object@frailty && object@args$RandDist %in% c("Gamma","LogN"))
if (object@args$RandDist=="Gamma") { ## margsurv <- (1+theta*H)^(-1/theta) ## return(h*margsurv^theta) return(h/(1+H*theta)) } if (object@args$RandDist=="LogN") {
return(sapply(1:length(gauss_x),
function(i) link$h(eta+Z*sqrt(2)*sqrt(theta)*gauss_x[i],etaD)) %*% gauss_w / sqrt(pi)) } } if (type=="marghr") { stopifnot(object@frailty && object@args$RandDist %in% c("Gamma","LogN"))
eta2 <- as.vector(X2 %*% beta)
etaD2 <- as.vector(XD2 %*% beta)
if (object@args$RandDist=="Gamma") { H2 <- link$H(eta2)
h2 <- link$h(eta2,etaD2) margsurv <- (1+theta*H)^(-1/theta) marghaz <- h*margsurv^theta margsurv2 <- (1+theta*H2)^(-1/theta) marghaz2 <- h2*margsurv2^theta } if (object@args$RandDist=="LogN") {
marghaz <- sapply(1:length(gauss_x),
function(i) as.vector(link$h(eta+Z*sqrt(2)*sqrt(theta)*gauss_x[i],etaD))) %*% gauss_w / sqrt(pi) marghaz2 <- sapply(1:length(gauss_x), function(i) as.vector(link$h(eta2+Z*sqrt(2)*sqrt(theta)*gauss_x[i],etaD2))) %*%
gauss_w / sqrt(pi)
}
return(marghaz2/marghaz)
}
if (type=="rmst") {
return(sum(S*weights))
}
}
if (!se.fit) {
out <- local(object,newdata,type=type,exposed=exposed,  ...)
} else {
gd <- NULL
beta <- coef(object)
## calculate gradients for some of the estimators
if (use.gr) {
colMeans <- function(x) apply(x,2,mean)
collapse <- function(gd)
do.call("cbind",tapply(1:nrow(gd), newdata[[object@timeVar]], function(index) colMeans(gd[index, ,drop=FALSE])))
collapse1 <- function(S)
as.vector(tapply(S, newdata[[object@timeVar]], mean))
fd <- function(f,x,eps=1e-5)
t(sapply(1:length(x),
function(i) {
upper <- lower <- x
upper[i]=x[i]+eps
lower[i]=x[i]-eps
(f(upper)-f(lower))/2/eps
}))
if (type=="hazard" && link %in% c("I","log")) {
## Case: frailty model (assumes baseline hazard for frailty=1)
betastar <- if(args$frailty) beta[-length(beta)] else beta gd <- switch(link, I=t(object@link$gradh(X %*% betastar, XD %*% betastar, list(X=X, XD=XD))),
log=t(object@link$gradh(X %*% betastar, XD %*% betastar, list(X=X, XD=XD))/ object@link$h(X %*% betastar, XD %*% betastar)))
}
if (type=="meanhaz" && !object@frailty && link %in% c("I","log")) {
betastar <- if(args$frailty) beta[-length(beta)] else beta h <- as.vector(object@link$h(X %*% betastar, XD %*% betastar))
S <- as.vector(object@link$ilink(X %*% betastar)) gradS <- object@link$gradS(X%*% betastar,X)
gradh <- object@link$gradh(X %*% betastar,XD %*% betastar,list(X=X,XD=XD)) gd <- if(link=="I") collapse(gradh*S + gradS*h) else collapse(gradh*S + h*gradS)/collapse1(h*S)-collapse(gradS)/collapse1(S) } if (type=="meanhr" && !object@frailty && link == "log") { betastar <- if(args$frailty) beta[-length(beta)] else beta
h <- as.vector(object@link$h(X %*% betastar, XD %*% betastar)) S <- as.vector(object@link$ilink(X %*% betastar))
gradS <- object@link$gradS(X%*% betastar,X) gradh <- object@link$gradh(X %*% betastar,XD %*% betastar,list(X=X,XD=XD))
h2 <- as.vector(object@link$h(X2 %*% betastar, XD2 %*% betastar)) S2 <- as.vector(object@link$ilink(X2 %*% betastar))
gradS2 <- object@link$gradS(X2%*% betastar,X2) gradh2 <- object@link$gradh(X2 %*% betastar,XD2 %*% betastar,list(X=X2,XD=XD2))
}
if (type=="meansurv" && !object@frailty && link=="I") {
gd <- collapse(object@link$gradS(X%*% beta,X)) } if (type=="meansurvdiff" && !object@frailty) { gd <- collapse(object@link$gradS(X2%*% beta,X2) - object@link$gradS(X%*% beta,X)) } if (type=="margsurv" && link %in% c("I","cloglog") && args$RandDist=="Gamma") {
theta <- exp(beta[length(beta)])
betastar <- beta[-length(beta)]
eta <- as.vector(X %*% betastar)
H <- as.vector(object@link$H(eta)) gradH <- object@link$gradH(eta,list(X=X))
S0 <- 1+theta*H
margS <- S0^(-1/theta)
## This depends on the transformation link
gd <- t(cbind(-margS * gradH/(1+theta*H),
margS*(1/theta*log(1+theta*H)-H/(1+theta*H))))
(theta*log(S0)*S0^(-theta)-theta^2*H*S0^(-1-theta))/(S0^(-theta)*(-theta*log(S0)))))
}
if (type=="marghaz" && link %in% c("I","log") && args$RandDist=="Gamma") { theta <- exp(beta[length(beta)]) betastar <- beta[-length(beta)] eta <- as.vector(X %*% betastar) etaD <- as.vector(XD %*% betastar) H <- as.vector(object@link$H(eta))
h <- as.vector(object@link$h(eta,etaD)) gradH <- object@link$gradH(eta,list(X=X))
gradh <- object@link$gradh(eta,etaD,list(X=X,XD=XD)) S0 <- 1+theta*H margS <- S0^(-1/theta) ## This depends on the transformation link if (link=="I") gd <- t(cbind((S0*gradh-theta*h*gradH)/(theta^2*H^2+S0), -(theta*H*h/theta^2*H^2+S0))) if (link=="log") gd <- t(cbind((S0*gradh-theta*h*gradH)/(S0*h), -theta*H/S0)) } if (type=="af" && !object@frailty) { meanS <- collapse1(as.vector(object@link$ilink(X%*%beta)))
meanS2 <- collapse1(as.vector(object@link$ilink(X2%*%beta))) gradS <- collapse(object@link$gradS(X%*%beta,X))
gradS2 <- collapse(object@link$gradS(X2%*%beta,X2)) gd <- t((t(gradS2-gradS)*(1-meanS) + (meanS2-meanS)*t(gradS))/(1-meanS)^2) ## check ## fd(function(beta) collapse1(as.vector(object@link$ilink(X %*% beta))), beta) - gradS # ok
## fd(function(beta) collapse1(as.vector(object@link$ilink(X2 %*% beta))), beta) - gradS2 # ok ## fd(function(beta) collapse1(as.vector(object@link$ilink(X2 %*% beta)-object@link$ilink(X %*% beta)))/collapse1(1-as.vector(object@link$ilink(X %*% beta))),beta) - gd # ok
}
}
pred <- predictnl(object,local,link=link,newdata=newdata,type=type,gd=if (use.gr) gd else NULL,
exposed=exposed,...)
ci <- confint.predictnl(pred, level = level)
out <- data.frame(Estimate=pred$fit, lower=ci[,1], upper=ci[,2]) if (link=="cloglog") out <- data.frame(Estimate=out$Estimate,lower=out$upper,upper=out$lower)
}
if (keep.attributes)
attr(out,"newdata") <- newdata
if (full)
out <- if(is.data.frame(out)) cbind(newdata,out) else cbind(newdata, data.frame(Estimate=out))
return(out)
}

setMethod("predict", "stpm2",
function(object,newdata=NULL,
grid=FALSE,seqLength=300,
type.relsurv=c("excess","total","other"), scale=365.24, rmap, ratetable=survival::survexp.us,
type <- match.arg(type)
type.relsurv <- match.arg(type.relsurv)
predict.stpm2.base(object, newdata=newdata, type=type, grid=grid, seqLength=seqLength, se.fit=se.fit,
type.relsurv=type.relsurv, scale=scale, rmap=rmap, ratetable=ratetable, n.gauss.quad=n.gauss.quad, full=full, ...)
})

##%c% <- function(f,g) function(...) g(f(...)) # function composition
plot.meansurv <- function(x, y=NULL, times=NULL, newdata=NULL, type="meansurv", exposed=NULL, var=NULL, add=FALSE, ci=!add, rug=!add, recent=FALSE,
xlab=NULL, ylab=NULL, lty=1, line.col=1, ci.col="grey", seqLength=301, ...) {
## if (is.null(times)) stop("plot.meansurv: times argument should be specified")
if (is.null(newdata)) newdata <- as.data.frame(x@data)
if (is.null(times)) {
Y <- x@y
event <- Y[,ncol(Y)]==1 | x@args$interval time <- x@data[[x@timeVar]] eventTimes <- time[event] times <- seq(min(eventTimes),max(eventTimes),length=seqLength)[-1] ## data.x <- data.frame(X) ## names(data.x) <- object@timeVar ## newdata <- merge(newdata,data.x) } times <- times[times !=0] if (recent) { newdata <- do.call("rbind", lapply(times, function(time) { newd <- newdata newd[[x@timeVar]] <- newdata[[x@timeVar]]*0+time newd })) pred <- predict(x, newdata=newdata, type=type, keep.attributes=TRUE, se.fit=ci, exposed=exposed, var=var) # requires recent version if (type=="meansurv") pred <- if (ci) rbind(c(Estimate=1,lower=1,upper=1),pred) else c(1,pred) } else { pred <- lapply(times, function(time) { newdata[[x@timeVar]] <- newdata[[x@timeVar]]*0+time predict(x, newdata=newdata, type=type, se.fit=ci, grid=FALSE, exposed=exposed, var=var, keep.attributes=TRUE) }) pred <- do.call("rbind", pred) if (type=="meansurv") { pred <- if (ci) rbind(c(Estimate=1,lower=1,upper=1),pred) else c(1,unlist(pred)) times <- c(0,times) } } if (is.null(xlab)) xlab <- deparse(x@timeExpr) if (is.null(ylab)) ylab <- switch(type, meansurv="Mean survival", af="Attributable fraction", meansurvdiff="Difference in mean survival", meanhaz="Mean hazard", meanhr="Mean hazard ratio") if (!add) matplot(times, pred, type="n", xlab=xlab, ylab=ylab, ...) if (ci) { polygon(c(times,rev(times)),c(pred$lower,rev(pred$upper)),col=ci.col,border=ci.col) lines(times,pred$Estimate,col=line.col,lty=lty,...)
} else {
lines(times,pred,col=line.col,lty=lty,...)
}
if (rug) {
Y <- x@y
eventTimes <- Y[Y[,ncol(Y)]==1,ncol(Y)-1]
rug(eventTimes,col=line.col)
}
return(invisible(y))
}

plot.stpm2.base <-
function(x,y,newdata=NULL,type="surv",
xlab=NULL,ylab=NULL,line.col=1,ci.col="grey",lty=par("lty"),log="",
var=NULL,exposed=incrVar(var),times=NULL,
type.relsurv=c("excess","total","other"), ratetable = survival::survexp.us, rmap, scale=365.24, ...) {
if (type %in% c("meansurv","meansurvdiff","af","meanhaz","meanhr")) {
return(plot.meansurv(x,times=times,newdata=newdata,type=type,xlab=xlab,ylab=ylab,line.col=line.col,ci.col=ci.col,
}
if (is.null(newdata)) stop("newdata argument needs to be specified")
y <- predict(x,newdata,type=switch(type,fail="surv",margfail="margsurv",type),var=var,exposed=exposed,
grid=!(x@timeVar %in% names(newdata)), se.fit=ci, keep.attributes=TRUE,
type.relsurv=type.relsurv, ratetable=ratetable, rmap=rmap, scale=scale)
if (type %in% c("fail","margfail")) {
if (ci) {
y$Estimate <- 1-y$Estimate
lower <- y$lower y$lower=1-y$upper y$upper=1-lower
} else y <- structure(1-y,newdata=attr(y,"newdata"))
}
if (is.null(xlab)) xlab <- deparse(x@timeExpr)
if (is.null(ylab))
ylab <- switch(type,hr="Hazard ratio",hazard="Hazard",surv="Survival",density="Density",
sdiff="Survival difference",hdiff="Hazard difference",cumhaz="Cumulative hazard",
meansurvdiff="Difference in mean survival",meanhr="Mean hazard ratio",
odds="Odds",or="Odds ratio",
margsurv="Marginal survival",marghaz="Marginal hazard",marghr="Marginal hazard ratio", haz="Hazard",fail="Failure",
meanhaz="Mean hazard",margfail="Marginal failure",af="Attributable fraction",meanmargsurv="Mean marginal survival",
uncured="Uncured distribution")
xx <- attr(y,"newdata")
xx <- eval(x@timeExpr,xx) # xx[,ncol(xx)]
if (!add) matplot(xx, y, type="n", xlab=xlab, ylab=ylab, log=log, ...)
if (ci) {
polygon(c(xx,rev(xx)), c(y[,2],rev(y[,3])), col=ci.col, border=ci.col)
lines(xx,y[,1],col=line.col,lty=lty,...)
} else lines(xx,y,col=line.col,lty=lty,...)
if (rug) {
Y <- x@y
eventTimes <- Y[Y[,ncol(Y)]==1,ncol(Y)-1]
rug(eventTimes,col=line.col)
}
return(invisible(y))
}
setMethod("plot", signature(x="stpm2", y="missing"),
function(x,y,newdata=NULL,type="surv",
xlab=NULL,ylab=NULL,line.col=1,ci.col="grey",lty=par("lty"),
var=NULL,exposed=incrVar(var),times=NULL,
type.relsurv=c("excess","total","other"), ratetable = survival::survexp.us,
rmap, scale=365.24,...)
plot.stpm2.base(x=x, y=y, newdata=newdata, type=type, xlab=xlab,
ci=ci, rug=rug, var=var, exposed=exposed, times=times,
type.relsurv=type.relsurv, ratetable=ratetable, rmap=rmap, scale=scale,...)
)
lines.stpm2 <-
function(x,newdata=NULL,type="surv",
col=1,ci.col="grey",lty=par("lty"),
ci=FALSE,rug=FALSE,
var=NULL,exposed=incrVar(var),times=NULL,
type.relsurv=c("excess","total","other"), ratetable = survival::survexp.us,
rmap, scale=365.24, ...)
plot.stpm2.base(x=x, newdata=newdata, type=type,
line.col=col, ci.col=ci.col, lty=lty, add=TRUE,
ci=ci, rug=rug, var=var, exposed=exposed, times=times,
type.relsurv=type.relsurv, ratetable=ratetable, rmap=rmap, scale=scale,...)
setMethod("lines", signature(x="stpm2"), lines.stpm2)
eform <- function (object, ...)
UseMethod("eform")
setGeneric("eform")
eform.stpm2 <- function (object, parm, level = 0.95, method = c("Profile"),
name = "exp(beta)")
{
method <- match.arg(method)
if (missing(parm))
parm <- TRUE
estfun <- switch(method, Profile = confint)
val <- exp(cbind(coef = coef(object), estfun(object, level = level)))
colnames(val) <- c(name, colnames(val)[-1])
val[parm, ]
}
setMethod("eform", signature(object="stpm2"), eform.stpm2)

derivativeDesign <-
function (functn, lower = -1, upper = 1, rule = NULL,
...)
{
pred <- if (length(list(...)) && length(formals(functn)) >
1)
function(x) functn(x, ...)
else functn
if (is.null(rule))
data.frame(x = c(0.993128599185095, 0.963971927277914, 0.912234428251326,
0.839116971822219, 0.746331906460151, 0.636053680726515, 0.510867001950827,
0.37370608871542, 0.227785851141646, 0.0765265211334977, -0.0765265211334974,
-0.227785851141645, -0.373706088715418, -0.510867001950827, -0.636053680726516,
-0.746331906460151, -0.839116971822219, -0.912234428251326, -0.963971927277913,
-0.993128599185094),
w = c(0.0176140071391522, 0.040601429800387,
0.0626720483341092, 0.0832767415767053, 0.101930119817241, 0.11819453196152,
0.131688638449176, 0.14209610931838, 0.149172986472603, 0.152753387130726,
0.152753387130726, 0.149172986472603, 0.142096109318381, 0.131688638449175,
0.11819453196152, 0.10193011981724, 0.0832767415767068, 0.0626720483341075,
0.0406014298003876, 0.0176140071391522))
lambda <- (upper - lower)/(2)
mu <- (lower + upper)/(2)
x <- lambda * rule$x + mu w <- rule$w
eps <- .Machine$double.eps^(1/8) X0 <- pred(x) X1 <- (-pred(x+2*eps)+8*pred(x+eps)-8*pred(x-eps)+pred(x-2*eps))/12/eps X2 <- (-pred(x+2*eps)/12+4/3*pred(x+eps)-5/2*pred(x)+4/3*pred(x-eps)-pred(x-2*eps)/12)/eps/eps X3 <- (-pred(x+3*eps)/8+pred(x+2*eps)-13/8*pred(x+eps)+ 13/8*pred(x-eps)-pred(x-2*eps)+pred(x-3*eps)/8)/eps/eps/eps return(list(x=x,w=w,lambda=lambda,X0=X0,X1=X1,X2=X2,X3=X3)) } smootherDesign <- function(gamobj,data,parameters = NULL) { d <- data[1,,drop=FALSE] ## how to get mean prediction values, particularly for factors? makepred <- function(var,inverse) { function(value) { d <- d[rep(1,length(value)),] d[[var]] <- inverse(value) predict(gamobj,newdata=d,type="lpmatrix") } } smoother.names <- sapply(gamobj$smooth, function(obj) obj$term) lapply(1:length(gamobj$smooth), function(i) {
smoother <- gamobj$smooth[[i]] if (is.null(parameters)) { var <- smoother$term
stopifnot(var %in% names(data))
transform <- I
inverse <- I
} else {
j <- match(smoother$term,names(parameters)) stopifnot(!is.na(j)) var <- parameters[[j]]$var
transform <- parameters[[j]]$transform inverse <- parameters[[j]]$inverse
}
pred <- makepred(var,inverse)
derivativeDesign(pred,
lower=transform(min(data[[var]])),
upper=transform(max(data[[var]])))
})
}
## TODO: If we transform a smoother (e.g. log(time)), we can use information on
## (i) the variable name, (ii) the transform and (iii) the inverse transform.

## penalised stpm2
setOldClass("gam")
setClass("pstpm2", representation(xlevels="list",
contrasts="listOrNULL",
terms="terms",
logli="function",
gam="gam",
timeVar="character",
time0Var="character",
timeExpr="nameOrcall",
time0Expr="nameOrcallOrNULL",
like="function",
model.frame="list",
fullformula="formula",
delayed="logical",
frailty="logical",
x="matrix",
xd="matrix",
termsd="terms",
Call="call",
y="Surv",
sp="numeric",
nevent="numeric",
edf="numeric",
edf_var="numeric",
df="numeric",
args="list"),
contains="mle2")
pstpm2 <- function(formula, data, smooth.formula = NULL, smooth.args = NULL,
logH.args = NULL,
tvc = NULL,
control = list(parscale = 1, maxit = 300), init = NULL,
coxph.strata = NULL, coxph.formula = NULL,
weights = NULL, robust = FALSE,
bhazard = NULL, bhazinit=0.1, timeVar = "", time0Var = "",
sp=NULL, use.gr = TRUE,
criterion=c("GCV","BIC"), penalty = c("logH","h"), smoother.parameters = NULL,
alpha=if (is.null(sp)) switch(criterion,GCV=1,BIC=1) else 1, sp.init=1, trace = 0,
log.time.transform=TRUE,
recurrent = FALSE,
frailty=!is.null(cluster) & !robust, cluster = NULL, logtheta=NULL, nodes=9,RandDist=c("Gamma","LogN"),
adaptive=TRUE, maxkappa = 1e3, Z = ~1,
reltol = list(search = 1.0e-10, final = 1.0e-10, outer=1.0e-5),outer_optim=1,
contrasts = NULL, subset = NULL, robust_initial = FALSE, ...) {
RandDist <- match.arg(RandDist)
optimiser <- match.arg(optimiser)
## logH.args is deprecated
if (!is.null(smooth.args) && is.null(logH.args))
logH.args <- smooth.args
## set up the data
## ensure that data is a data frame
temp.formula <- formula
if (!is.null(smooth.formula)) rhs(temp.formula) <-rhs(temp.formula) %call+% rhs(smooth.formula)
raw.data <- data
## data <- get_all_vars(temp.formula, raw.data)
criterion <- match.arg(criterion)
penalty <- match.arg(penalty)
##
## parse the function call
Call <- match.call()
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data", "subset", "contrasts", "weights"),
names(mf), 0L)
mf <- mf[c(1L, m)]
##
## parse the event expression
eventInstance <- eval(lhs(formula),envir=data)
stopifnot(length(lhs(formula))>=2)
delayed <- length(lhs(formula))>=4
surv.type <- attr(eventInstance,"type")
if (surv.type %in% c("interval2","left","mstate"))
stop("stpm2 not implemented for Surv type ",surv.type,".")
interval <- attr(eventInstance,"type") == "interval"
timeExpr <- lhs(formula)[[if (delayed && !interval) 3 else 2]] # expression
eventExpr <- if (interval) lhs(formula)[[4]] else lhs(formula)[[length(lhs(formula))]]
if (interval)
time2Expr <- lhs(formula)[[3]]
if (timeVar == "")
timeVar <- all.vars(timeExpr)
## restrict to non-missing data (assumes na.action=na.omit)
na.action.old <- options()[["na.action"]]
options(na.action = "na.pass")
on.exit(options(na.action = na.action.old))
subset.expr <- substitute(subset)
if(class(subset.expr)=="NULL") subset.expr <- TRUE
.include <- complete.cases(model.matrix(formula, data)) &
!is.na(eval(eventExpr,data,parent.frame())) &
eval(subset.expr,data,parent.frame())
options(na.action = na.action.old)
if (!interval)
.include <- .include & !is.na(eval(timeExpr,data,parent.frame()))
time0Expr <- NULL # initialise
if (delayed) {
time0Expr <- lhs(formula)[[2]]
.include <- .include & !is.na(eval(time0Expr,data,parent.frame()))
}
if (!is.null(substitute(weights)))
.include <- .include & !is.na(eval(substitute(weights),data,parent.frame()))
data <- data[.include, , drop=FALSE]
## we can now evaluate over data
time <- eval(timeExpr, data, parent.frame())
if (delayed) {
if (time0Var == "")
time0Var <- all.vars(time0Expr)
time0 <- eval(time0Expr, data, parent.frame())
}
event <- eval(eventExpr,data,parent.frame())
if (!interval)
event <- if (length(unique(event))==1) rep(TRUE, length(event)) else event <- event > min(event)
nevent <- sum(event)
##
## set up the formulae
if (is.null(smooth.formula) && is.null(logH.args)) {
logH.args$k <- -1 } if (is.null(smooth.formula)) { smooth.formula <- as.formula(call("~",as.call(c(quote(s),call("log",timeExpr), vector2call(logH.args))))) if (link.type=="AH") { interaction <- function(expr) { if (is.name(expr)) call(":",expr,timeExpr) else if(is.name(expr[[1]]) && as.character(expr[[1]])=="+") interaction(expr[[2]]) %call+% interaction(expr[[3]]) else call(":",expr,timeExpr) } ## interaction(rstpm2:::rhs(~a+I(b)+c-1)) # error smooth.formula <- as.formula(call("~", interaction(rhs(formula)) %call+% as.call(c(quote(s),timeExpr, vector2call(logH.args))))) } } if (!is.null(tvc)) { tvc.formulas <- lapply(names(tvc), function(name) call(":", as.name(name), as.call(c(quote(s), call("log",timeExpr), vector2call(list(k=tvc[[name]])))))) if (length(tvc.formulas)>1) tvc.formulas <- list(Reduce(%call+%, tvc.formulas)) tvc.formula <- as.formula(call("~",tvc.formulas[[1]])) rhs(smooth.formula) <- rhs(smooth.formula) %call+% rhs(tvc.formula) } full.formula <- formula if(link.type=="AH"){ rhs(full.formula) <- rhs(smooth.formula) } else{ rhs(full.formula) <- rhs(formula) %call+% rhs(smooth.formula) } ## left <- deparse(substitute(formula)) tf <- terms.formula(smooth.formula, specials = c("s", "te")) terms <- attr(tf, "term.labels") right <- paste0(terms, collapse = "+") fullformula <- as.formula(paste0(left, "+", right), env = parent.frame()) if (!interval) { ## Cox regression coxph.call <- mf coxph.call[[1L]] <- as.name("coxph") coxph.strata <- substitute(coxph.strata) coxph.call$data <- quote(coxph.data)
coxph.data <- data
if (!is.null(coxph.formula)) {
coxph.formula2 <- coxph.call$formula rhs(coxph.formula2) <- rhs(formula) %call+% rhs(coxph.formula) coxph.call$formula <- coxph.formula2
}
if (!is.null(coxph.strata)) {
coxph.formula2 <- coxph.call$formula rhs(coxph.formula2) <- rhs(formula) %call+% call("strata",coxph.strata) coxph.call$formula <- coxph.formula2
}
coxph.call$model <- TRUE coxph.obj <- eval(coxph.call, coxph.data) y <- model.extract(model.frame(coxph.obj),"response") data$logHhat <- if (is.null(bhazard)) {
pmax(-18,link$link(Shat(coxph.obj))) } else pmax(-18,link$link(Shat(coxph.obj)/exp(-bhazinit*bhazard*time)))
if (frailty && is.null(logtheta)) {
coxph.data$.cluster <- as.vector(unclass(factor(cluster)))[.include] coxph.formula <- coxph.call$formula
rhs(coxph.formula) <- rhs(coxph.formula) %call+%
call("frailty",as.name(".cluster"),
distribution=switch(RandDist,LogN="gaussian",Gamma="gamma"))
coxph.call$formula <- coxph.formula coxph.obj <- eval(coxph.call, enclos=parent.frame()) logtheta <- log(coxph.obj$history[[1]]$theta) } } if (interval) { ## survref regression survreg.call <- mf survreg.call[[1L]] <- as.name("survreg") survreg.obj <- eval(survreg.call, envir=parent.frame()) weibullShape <- 1/survreg.obj$scale
weibullScale <- predict(survreg.obj)
y <- model.extract(model.frame(survreg.obj),"response")
data$logHhat <- pmax(-18,link$link(pweibull(time,weibullShape,weibullScale,lower.tail=FALSE)))
##
if (frailty && is.null(logtheta)) {
logtheta <- -1
}
}
##
## initial values and object for lpmatrix predictions
gam.call <- mf
gam.call[[1L]] <- as.name("gam")
gam.formula <- full.formula
lhs(gam.formula) <- quote(logHhat) # new response
gam.call$formula <- gam.formula gam.call$sp <- sp
if (is.null(sp) && !is.null(sp.init) && (length(sp.init)>1 || sp.init!=1))
gam.call$sp <- sp.init dataEvents <- data[event,] if (interval) { dataEvents <- data[event>0, , drop=FALSE] } gam.call$data <- quote(dataEvents) # events only
gam.obj <- eval(gam.call)
## re-run gam if sp.init==1 (default)
if (is.null(sp) && !is.null(sp.init) && length(sp.init)==1 && sp.init==1) {
sp.init <- gam.call$sp <- rep(sp.init,length=length(gam.obj$sp))
gam.obj <- eval(gam.call)
}
##
## set up X, mf and wt
mt <- terms(gam.obj)
mf <- model.frame(gam.obj)
wt <- if (is.null(substitute(weights))) rep(1,nrow(data)) else eval(substitute(weights),data,parent.frame())
lpfunc <- function(x,...) {
newdata <- data
newdata[[timeVar]] <- x
predict(gam.obj,newdata,type="lpmatrix")
}
##
bhazard <- substitute(bhazard)
bhazard <- if (is.null(bhazard)) rep(0,nrow(data)) else eval(bhazard,data,parent.frame())
excess <- !all(bhazard==0)
## initialise values specific to either delayed entry or interval-censored
ind0 <- FALSE
map0 <- 0L
which0 <- 0
wt0 <- 0
ttype <- 0
transX <- function(X, data) X
transXD <- function(XD) XD
## browser()
smooth <- gam.obj$smooth if (!interval) { # surv.type %in% c("right","counting") X <- predict(gam.obj,data,type="lpmatrix") if (link.type=="AH") { datat0 <- data datat0[[timeVar]] <- 0 index0 <- which.dim(X - predict(gam.obj, datat0, type="lpmatrix")) smooth <- lapply(smooth, function(smoothi) { Sindex <- which((1:ncol(X) %in% index0)[smoothi$first.para:smoothi$last.para]) para <- range(which((1:ncol(X) %in% smoothi$first.para:smoothi$last.para)[index0])) smoothi$S[[1]] <- smoothi$S[[1]][Sindex,Sindex] smoothi$first.para <- para[1]
smoothi$last.para <- para[2] smoothi }) transX <- function(X, data) { datat0 <- data datat0[[timeVar]] <- 0 Xt0 <- predict(gam.obj, datat0, type="lpmatrix") (X - Xt0)[, index0, drop=FALSE] } transXD <- function(XD) XD[, index0, drop=FALSE] ## init <- init[index0] } X <- transX(X,data) XD <- grad1(lpfunc,data[[timeVar]], log.transform=log.time.transform) XD <- transXD(XD) X1 <- matrix(0,nrow(X),ncol(X)) X0 <- matrix(0,1,ncol(X)) if (delayed && all(time0==0)) delayed <- FALSE # CAREFUL HERE: delayed redefined if (delayed) { ind0 <- time0>0 map0 <- vector("integer",nrow(X)) map0[ind0] <- as.integer(1:sum(ind0)) map0[!ind0] <- NaN ## which0 <- which(ind0) which0 <- 1:nrow(X) which0[!ind0] <- NaN data0 <- data[ind0,,drop=FALSE] # data for delayed entry times data0[[timeVar]] <- data0[[time0Var]] X0 <- transX(predict(gam.obj,data0,type="lpmatrix"), data0) wt0 <- wt[ind0] rm(data0) } } else { ## interval-censored ## ttime <- eventInstance[,1] ## ttime2 <- eventInstance[,2] ttype <- eventInstance[,3] X <- transX(predict(gam.obj,data,type="lpmatrix"), data) XD <- grad1(lpfunc,data[[timeVar]], log.transform=log.time.transform) XD <- transXD(matrix(XD,nrow=nrow(X))) data0 <- data data0[[timeVar]] <- data0[[as.character(time2Expr)]] data0[[timeVar]] <- ifelse(data0[[timeVar]]<=0,NA,data0[[timeVar]]) ## lpfunc <- function(x,...) { ## newdata <- data0 ## newdata[[timeVar]] <- x ## predict(gam.obj,newdata,type="lpmatrix") ## } X1 <- transX(predict(gam.obj,data0,type="lpmatrix"), data0) X0 <- matrix(0,nrow(X),ncol(X)) rm(data0) } ## initial values if (is.null(init)) { init <- coef(gam.obj) } if (link.type=="AH") { init <- init[index0] } if (frailty) { init <- c(init,logtheta=logtheta) } ## smoothing parameters ## cases: ## (1) sp fixed ## (2) sp.init ## (3) use GAM if (no.sp <- is.null(sp)) { sp <- if(is.null(gam.obj$full.sp)) gam.obj$sp else gam.obj$full.sp
if (!is.null(sp.init)) sp <- sp.init
}
if (!is.null(control) && "parscale" %in% names(control)) {
if (length(control$parscale)==1) control$parscale <- rep(control$parscale,length(init)) if (is.null(names(control$parscale)))
names(control$parscale) <- names(init) } else { if(is.null(control)) control <- list() control$parscale <- rep(1,length(init))
names(control$parscale) <- names(init) } args <- list(init=init,X=X,XD=XD,bhazard=bhazard,wt=wt,event=ifelse(event,1,0),time=time, delayed=delayed, interval=interval, X0=X0, wt0=wt0, X1=X1, parscale=control$parscale,
smooth=if(penalty == "logH") smooth else design,
sp=sp, reltol_search=reltol$search, reltol=reltol$final, reltol_outer=reltol$outer, trace=trace, kappa=1.0,outer_optim=outer_optim, alpha=alpha,criterion=switch(criterion,GCV=1,BIC=2), oldcluster=cluster, cluster=if(!is.null(cluster)) as.vector(unclass(factor(cluster)))[.include] else NULL, frailty=frailty, map0 = map0 - 1L, ind0 = ind0, which0=which0 - 1L, link = link.type, penalty = penalty, ttype=ttype, RandDist=RandDist, optimiser=optimiser, log.time.transform=log.time.transform, type=if (frailty && RandDist=="Gamma") "pstpm2_gamma_frailty" else if (frailty && RandDist=="LogN") "pstpm2_normal_frailty" else "pstpm2", recurrent = recurrent, maxkappa=maxkappa, transX=transX, transXD=transXD, Z.formula = Z, thetaAO = theta.AO, excess=excess, return_type="optim", data=data, robust_initial=robust_initial, .include=.include) if (frailty) { rule <- fastGHQuad::gaussHermiteData(nodes) args$gauss_x <- rule$x args$gauss_w <- rule$w args$adaptive <- adaptive
args$Z <- model.matrix(Z, data) if (ncol(args$Z)>1) stop("Current implementation only allows for a single random effect")
args$Z <- as.vector(args$Z)
}
## penalty function
pfun <- function(beta,sp) {
sum(sapply(1:length(gam.obj$smooth), function(i) { smoother <- gam.obj$smooth[[i]]
betai <- beta[smoother$first.para:smoother$last.para]
sp[i]/2 * betai %*% smoother$S[[1]] %*% betai })) } negllsp <- function(beta,sp) { localargs <- args localargs$sp <- sp
localargs$init <- beta localargs$return_type <- "objective"
negll <- .Call("model_output", localargs, PACKAGE="rstpm2")
localargs$return_type <- "feasible" feasible <- .Call("model_output", localargs, PACKAGE="rstpm2") attr(negll,"feasible") <- feasible return(negll) } negll0sp <- function(beta,sp) { localargs <- args localargs$sp <- sp
localargs$init <- beta localargs$return_type <- "objective0"
negll <- .Call("model_output", localargs, PACKAGE="rstpm2")
localargs$return_type <- "feasible" feasible <- .Call("model_output", localargs, PACKAGE="rstpm2") attr(negll,"feasible") <- feasible return(negll) } ## unused? dpfun <- function(beta,sp) { deriv <- beta*0 for (i in 1:length(gam.obj$smooth))
{
smoother <- gam.obj$smooth[[i]] ind <- smoother$first.para:smoother$last.para deriv[ind] <- sp[i] * smoother$S[[1]] %*% beta[ind]
}
return(deriv)
}
if (penalty == "h") {
## a current limitation is that the hazard penalty needs to extract the variable names from the smoother objects (e.g. log(time) will not work)
stopifnot(sapply(gam.obj$smooth,function(obj) obj$term) %in% names(data) ||
!is.null(smoother.parameters))
## new penalty using the second derivative of the hazard
design <- smootherDesign(gam.obj,data,smoother.parameters)
pfun <- function(beta,sp) {
sum(sapply(1:length(design), function(i) {
obj <- design[[i]]
s0 <- as.vector(obj$X0 %*% beta) s1 <- as.vector(obj$X1 %*% beta)
s2 <- as.vector(obj$X2 %*% beta) s3 <- as.vector(obj$X3 %*% beta)
h2 <- (s3+3*s1*s2+s1^3)*exp(s0)
sp[i]/2*obj$lambda*sum(obj$w*h2^2)
}))
}
dpfun <- function(beta,sp) {
if (frailty) beta <- beta[-length(beta)]
deriv <- beta*0
for (i in 1:length(design)) {
obj <- design[[i]]
s0 <- as.vector(obj$X0 %*% beta) s1 <- as.vector(obj$X1 %*% beta)
s2 <- as.vector(obj$X2 %*% beta) s3 <- as.vector(obj$X3 %*% beta)
h2 <- (s3+3*s1*s2+s1^3)*exp(s0)
dh2sq.dbeta <- 2*h2*(exp(s0)*(obj$X3+3*(obj$X1*s2+obj$X2*s1)+3*s1^2*obj$X1)+h2*obj$X0) deriv <- deriv + sp[i]*obj$lambda*colSums(obj$w*dh2sq.dbeta) } deriv } } gradnegllsp <- function(beta,sp) { localargs <- args localargs$init <- beta
localargs$return_type <- "gradient" .Call("model_output", localargs, PACKAGE="rstpm2") } gradnegll0sp <- function(beta,sp) { localargs <- args localargs$init <- beta
localargs$return_type <- "gradient0" .Call("model_output", localargs, PACKAGE="rstpm2") } logli <- function(beta) { localargs <- args localargs$init <- beta
localargs$return_type <- "li" return(.Call("model_output", localargs, PACKAGE="rstpm2")) } like <- function(beta) { eta <- as.vector(X %*% beta) etaD <- as.vector(XD %*% beta) h <- link$h(eta,etaD) + bhazard
H <- link$H(eta) ll <- sum(wt[event]*log(h[event])) - sum(wt*H) if (delayed) { eta0 <- as.vector(X0 %*% beta) ## etaD0 <- as.vector(XD0 %*% beta) ll <- ll + sum(wt0*link$H(eta0))
}
return(ll)
}
if (no.sp && !is.null(sp.init)) {
if(!is.null(gam.obj$full.sp)) gam.obj$sp <- gam.obj$full.sp value <- NULL while(is.na(value <- negllsp(init,gam.obj$sp)) || !attr(value,"feasible")) {
gam.call$sp <- gam.obj$sp * 5
if (no.sp) sp <- gam.call$sp ## Unresolved: should we change sp.init if the initial values are not feasible? gam.obj <- eval(gam.call) if(!is.null(gam.obj$full.sp)) gam.obj$sp <- gam.obj$full.sp
init <- coef(gam.obj)
if (frailty)
init <- c(init,logtheta=logtheta)
if (all(gam.obj$sp > 1e5)) break ## stop("Initial values not valid and revised sp>1e5") } args$sp <- gam.obj$sp } else args$sp <- sp
#     ### Using exterior penalty method for nonlinear constraints: h(t)>=0 or increasing logH(t)
#     ### Some initial values should be outside the feasible region
#     while(all(XD%*%init>=0)){
#       init <- init+0.001
#     }
#     ### Check initial value
#     if(any(XD%*%init<=0)) {
#       cat("Some initial values are exactly outside the feasible region of this problem","\n")
#     }
## MLE
args$return_type <- if (!no.sp) { # fixed sp as specified args$return_type <- "optim_fixed"
} else if (length(sp)>1) {
"optim_multivariate"
} else {
"optim_first"
}
if (frailty) { # first fit without the frailty
args2 <- args
args2$frailty <- FALSE args2$cluster <- NULL
args2$type <- "pstpm2" localIndex <- 1:(length(args2$init)-1)
args2$init <- args2$init[localIndex]
args2$parscale <- args2$parscale[localIndex]
fit <- .Call("model_output", args2, PACKAGE="rstpm2")
rm(args2)
args$init <- c(fit$coef,logtheta)
}
fit <- .Call("model_output", args, PACKAGE = "rstpm2")
fit$coef <- as.vector(fit$coef)
fit$sp <- as.vector(fit$sp)
names(fit$coef) <- names(init) args$init <- init <- fit$coef args$sp <- sp <- fit$sp edf <- fit$edf
edf_var<- as.vector(fit$edf_var) names(edf_var) <- sapply(gam.obj$smooth,"[[","label")
names(fit$coef) <- rownames(fit$hessian) <- colnames(fit$hessian) <- names(init) args$kappa.final <- fit$kappa negll <- function(beta) negllsp(beta,sp) gradnegll <- function(beta) gradnegllsp(beta,sp) parnames(negll) <- parnames(gradnegll) <- names(init) mle2 <- if (use.gr) { mle2(negll,init,vecpar=TRUE, control=control, gr=gradnegll, eval.only=TRUE, ...) } else mle2(negll,init,vecpar=TRUE, control=control, eval.only=TRUE, ...) hessian <- mle2@details$hessian <- fit$hessian ## mle2@vcov <- solve(optimHess(coef(mle2),negll,gradnegll)) mle2@details$convergence <- 0
if (inherits(vcov <- try(solve(hessian)), "try-error")) {
warning("Non-invertible Hessian")
mle2@vcov <- matrix(NA,length(coef), length(coef))
}
warning("Non-invertible Hessian - refitting with Nelder-Mead")
args$optimiser <- "NelderMead" fit <- .Call("model_output", args, PACKAGE="rstpm2") args$init <- coef <- as.vector(fit$coef) args$kappa.final <- fit$kappa hessian <- fit$hessian
names(coef) <- rownames(hessian) <- colnames(hessian) <- names(init)
mle2 <- mle2(negll, coef, vecpar=TRUE, control=control, ..., eval.only=TRUE)
mle2@vcov <- if (!inherits(vcov <- try(solve(hessian)), "try-error")) vcov else matrix(NA,length(coef), length(coef))
mle2@details$convergence <- fit$fail # fit$itrmcd if (inherits(vcov, "try-error")) warning("Non-invertible Hessian - refitting failed") } } else { mle2@vcov <- vcov } out <- new("pstpm2", call = mle2@call, call.orig = mle2@call, coef = mle2@coef, fullcoef = mle2@fullcoef, vcov = mle2@vcov, min = mle2@min, details = mle2@details, minuslogl = mle2@minuslogl, method = mle2@method, optimizer = "optim", # mle2@optimizer data = data, # mle2@data, which uses as.list() formula = mle2@formula, xlevels = .getXlevels(mt, mf), ##contrasts = attr(X, "contrasts"), contrasts = NULL, # wrong! logli = logli, ##weights = weights, Call = Call, terms = mt, model.frame = mf, gam = gam.obj, timeVar = timeVar, time0Var = time0Var, timeExpr = timeExpr, time0Expr = time0Expr, like = like, fullformula = fullformula, delayed=delayed, frailty = frailty, x = X, xd = XD, termsd = mt, # wrong! y = y, sp = sp, nevent=nevent, link=link, edf=edf, edf_var=edf_var, df=edf, args=args) # if (robust) # kludge # out@vcov <- sandwich.stpm2(out, cluster=cluster) if (robust && !frailty) { ## Bread matrix bread.mat <- solve(fit$hessian)
## Meat matirx calculated with individual penalized score functions
beta.est <- fit$coef sp.opt <- fit$sp
eta <- as.vector(args$X %*% beta.est) etaD <- as.vector(XD %*% beta.est) h <- link$h(eta,etaD) + bhazard
H <- link$H(eta) gradh <- link$gradh(eta,etaD,args)
gradH <- link$gradH(eta,args) ## right censored data score.ind <- t(wt*(gradH - ifelse(event,1/h,0)*gradh)) + dpfun(beta.est, sp.opt)/nrow(gradH) meat.mat <- var(t(score.ind))*nrow(gradH) out@vcov <- bread.mat %*% meat.mat %*% t(bread.mat) } return(out) } ## Could this inherit from summary.stpm2? setClass("summary.pstpm2", representation(pstpm2="pstpm2",frailty="logical",theta="list",wald="matrix"), contains="summary.mle2") setMethod("summary", "pstpm2", function(object) { newobj <- as(summary(as(object,"mle2")),"summary.pstpm2") newobj@pstpm2 <- object newobj@frailty <- object@frailty newobj@call <- object@Call if (object@frailty) { coef <- coef(newobj) theta <- exp(coef[nrow(coef),1]) se.logtheta <- coef[nrow(coef),2] se.theta <- theta*se.logtheta test.statistic <- (1/se.logtheta)^2 p.value <- pchisq(test.statistic,df=1,lower.tail=FALSE)/2 newobj@theta <- list(theta=theta, se.theta=se.theta, p.value=p.value) } else newobj@theta <- list() vcov1 <- vcov(object) coef1 <- coef(object) ## Wald test for the smoothers wald <- t(sapply(names(object@edf_var), function(name) { i <- grep(name,colnames(vcov1),fixed=TRUE) statistic <- as.vector(coef1[i] %*% solve(vcov1[i,i]) %*% coef1[i]) edf <- object@edf_var[name] c(statistic=statistic,ncoef=length(i),edf=edf,p.value=pchisq(statistic, edf, lower.tail=FALSE)) })) colnames(wald) <- c("Wald statistic","Number of coef","Effective df","P value") newobj@wald <- wald newobj }) setMethod("show", "summary.pstpm2", function(object) { show(as(object,"summary.mle2")) cat(sprintf("\nEffective df=%g\n",object@pstpm2@edf)) printCoefmat(object@wald) if (object@frailty) cat(sprintf("\ntheta=%g\tse=%g\tp=%g\n", object@theta$theta,object@theta$se.theta,object@theta$p.value))
})
setMethod("AICc", "pstpm2",
function (object, ..., nobs=NULL, k=2)  {
L <- list(...)
if (length(L)) {
L <- c(list(object),L)
if (is.null(nobs)) {
nobs <- sapply(L,nobs)
}
if (length(unique(nobs))>1)
stop("nobs different: must have identical data for all objects")
val <- sapply(L, AICc, nobs=nobs, k=k)
df <- sapply(L,attr,"edf")
data.frame(AICc=val,df=df)
} else {
df <- attr(object,"edf")
if (is.null(nobs)) nobs <- object@nevent
c(-2*logLik(object)+k*df+k*df*(df+1)/(nobs-df-1))
}
})
setMethod("qAICc", "pstpm2",
function (object, ..., nobs = NULL, dispersion = 1, k = 2)  {
L <- list(...)
if (length(L)) {
L <- c(list(object),L)
if (is.null(nobs)) {
nobs <- sapply(L,nobs)
}
if (length(unique(nobs))>1)
stop("nobs different: must have identical data for all objects")
val <- sapply(L, qAICc, nobs=nobs,dispersion=dispersion,k=k)
df <- sapply(L,attr,"edf")
data.frame(qAICc=val,df=df)
} else {
df <- attr(object,"edf")
if (is.null(nobs)) nobs <- object@nevent
c(-2*logLik(object)/dispersion+k*df+k*df*(df+1)/(nobs-df-1))
}
})
setMethod("qAIC", "pstpm2",
function (object, ..., dispersion = 1, k = 2)  {
L <- list(...)
if (length(L)) {
L <- c(list(object),L)
if (is.null(nobs)) {
nobs <- sapply(L,nobs)
}
if (length(unique(nobs))>1)
stop("nobs different: must have identical data for all objects")
val <- sapply(L, qAIC, dispersion=dispersion, k=k)
df <- sapply(L,attr,"edf")
data.frame(qAICc=val,df=df)
} else {
df <- attr(object,"edf")
c(-2*logLik(object)/dispersion+k*df)
}
})
setMethod("AIC", "pstpm2",
function (object, ..., k = 2) {
L <- list(...)
if (length(L)) {
L <- c(list(object),L)
if (!all(sapply(L,class)=="pstpm2")) stop("all objects in list must be class pstpm2")
val <- sapply(L,AIC,k=k)
df <- sapply(L,attr,"edf")
data.frame(AIC=val,df=df)
} else -2 * as.numeric(logLik(object)) + k * attr(object, "edf")
})
setMethod("BIC", "pstpm2",
function (object, ..., nobs = NULL) {
L <- list(...)
if (length(L)) {
L <- c(list(object),L)
if (!all(sapply(L,class)=="pstpm2")) stop("all objects in list must be class pstpm2")
val <- sapply(L,BIC,nobs=nobs)
df <- sapply(L,attr,"edf")
data.frame(BIC=val,df=df)
} else {
if (is.null(nobs)) nobs <- object@nevent
-2 * as.numeric(logLik(object)) + log(nobs) * attr(object, "edf")
}
})
setMethod("eform", signature(object="pstpm2"),
function (object, parm, level = 0.95, method = c("Profile"),
name = "exp(beta)")
{
method <- match.arg(method)
if (missing(parm))
parm <- TRUE
estfun <- switch(method, Profile = confint)
val <- exp(cbind(coef = coef(object), estfun(object, level = level)))
colnames(val) <- c(name, colnames(val)[-1])
val[parm, ]
})
setMethod("show", "pstpm2",
function(object) {
object@call.orig <- object@Call
show(as(object,"mle2"))
})

## Revised from bbmle:
## changed the calculation of the degrees of freedom in the third statement of the .local function
setMethod("anova", signature(object="pstpm2"),
function (object, ..., width = getOption("width"),
exdent = 10)
{
mlist <- c(list(object), list(...))
mnames <- sapply(sys.call(sys.parent())[-1], deparse)
ltab <- as.matrix(do.call("rbind", lapply(mlist, function(x) {
c(Tot Df = x@edf, Deviance = -2 * logLik(x)) # changed to x@edf
})))
terms = sapply(mlist, function(obj) {
if (is.null(obj@formula) || obj@formula == "") {
mfun <- obj@call$minuslogl mfun <- paste("[", if (is.name(mfun)) { as.character(mfun) } else { "..." }, "]", sep = "") paste(mfun, ": ", paste(names(obj@coef), collapse = "+"), sep = "") } else { as.character(obj@formula) } }) mterms <- paste("Model ", 1:length(mnames), ": ", mnames, ", ", terms, sep = "") mterms <- strwrapx(mterms, width = width, exdent = exdent, wordsplit = "[ \n\t]") heading <- paste("Likelihood Ratio Tests", paste(mterms, collapse = "\n"), sep = "\n") ltab <- cbind(ltab, Chisq = abs(c(NA, diff(ltab[, "Deviance"]))), Df = abs(c(NA, diff(ltab[, "Tot Df"])))) ltab <- cbind(ltab, Pr(>Chisq) = c(NA, pchisq(ltab[, "Chisq"][-1], ltab[, "Df"][-1], lower.tail = FALSE))) rownames(ltab) <- 1:nrow(ltab) attr(ltab, "heading") <- heading class(ltab) <- "anova" ltab }) setMethod("predictnl", "pstpm2", function(object,fun,newdata=NULL,link=c("I","log","cloglog","logit"), gd=NULL, ...) { ## should gd be passed as argument to numDeltaMethod? link <- match.arg(link) linkf <- eval(parse(text=link)) if (is.null(newdata) && !is.null(object@data)) newdata <- object@data localf <- function(coef,...) { object@fullcoef = coef linkf(fun(object,...)) } numDeltaMethod(object,localf,newdata=newdata,gd=gd,...) }) ## setMethod("predict", "pstpm2", function(object,newdata=NULL, type=c("surv","cumhaz","hazard","density","hr","sdiff","hdiff","loghazard","link","meansurv","meansurvdiff","meanhr","odds","or","margsurv","marghaz","marghr","meanhaz","af","fail","margfail","meanmargsurv","rmst"), grid=FALSE,seqLength=300, se.fit=FALSE,link=NULL,exposed=incrVar(var),var=NULL,keep.attributes=FALSE,use.gr=TRUE,level=0.95, n.gauss.quad=100, full=FALSE, ...) { type <- match.arg(type) predict.stpm2.base(object=object, newdata=newdata, type=type, grid=grid, seqLength=seqLength, se.fit=se.fit, link=link, exposed=exposed, var=var, keep.attributes=keep.attributes, use.gr=use.gr, level=level, n.gauss.quad=n.gauss.quad, full=full, ...) }) setMethod("residuals", "pstpm2", function(object, type=c("li","gradli")) residuals.stpm2.base(object=object, type=match.arg(type))) ##%c% <- function(f,g) function(...) g(f(...)) # function composition ## to do: ## (*) Stata-compatible knots setMethod("plot", signature(x="pstpm2", y="missing"), function(x,y,newdata=NULL,type="surv", xlab=NULL,ylab=NULL,line.col=1,ci.col="grey",lty=par("lty"), add=FALSE,ci=!add,rug=!add, var=NULL,exposed=incrVar(var),times=NULL,...) plot.stpm2.base(x=x, y=y, newdata=newdata, type=type, xlab=xlab, ylab=ylab, line.col=line.col, lty=lty, add=add, ci=ci, rug=rug, var=var, exposed=exposed, times=times, ...) ) lines.pstpm2 <- function(x,newdata=NULL,type="surv", col=1,ci.col="grey",lty=par("lty"), ci=FALSE,rug=FALSE, var=NULL,exposed=incrVar(var),times=NULL,...) plot.stpm2.base(x=x, newdata=newdata, type=type, line.col=col, ci.col=ci.col, lty=lty, add=TRUE, ci=ci, rug=rug, var=var, exposed=exposed, times=times, ...) setMethod("lines", signature(x="pstpm2"), lines.pstpm2) ## sandwich variance estimator (from the sandwich package) ## coeftest.stpm2 <- ## function (x, vcov. = NULL, df = NULL, ...) ## { ## est <- coef(x) ## if (is.null(vcov.)) ## se <- vcov(x) ## else { ## if (is.function(vcov.)) ## se <- vcov.(x) ## else se <- vcov. ## } ## se <- sqrt(diag(se)) ## if (!is.null(names(est)) && !is.null(names(se))) { ## anames <- names(est)[names(est) %in% names(se)] ## est <- est[anames] ## se <- se[anames] ## } ## tval <- as.vector(est)/se ## pval <- 2 * pnorm(abs(tval), lower.tail = FALSE) ## cnames <- c("Estimate", "Std. Error", "z value", "Pr(>|z|)") ## mthd <- "z" ## rval <- cbind(est, se, tval, pval) ## colnames(rval) <- cnames ## class(rval) <- "coeftest" ## attr(rval, "method") <- paste(mthd, "test of coefficients") ## return(rval) ## } ## weights.stpm2 <- ## function (object, ...) ## { ## wts <- object@weights ## if (is.null(wts)) ## wts ## else napredict(object@na.action, wts) ## } ## copy of bbmle:::strwrapx strwrapx <- function (x, width = 0.9 * getOption("width"), indent = 0, exdent = 0, prefix = "", simplify = TRUE, parsplit = "\n[ \t\n]*\n", wordsplit = "[ \t\n]") { if (!is.character(x)) x <- as.character(x) indentString <- paste(rep.int(" ", indent), collapse = "") exdentString <- paste(rep.int(" ", exdent), collapse = "") y <- list() plussplit = function(w) { lapply(w, function(z) { plusloc = which(strsplit(z, "")[[1]] == "+") plussplit = apply(cbind(c(1, plusloc + 1), c(plusloc, nchar(z, type = "width"))), 1, function(b) substr(z, b[1], b[2])) plussplit }) } z <- lapply(strsplit(x, parsplit), function(z) { lapply(strsplit(z, wordsplit), function(x) unlist(plussplit(x))) }) for (i in seq_along(z)) { yi <- character(0) for (j in seq_along(z[[i]])) { words <- z[[i]][[j]] nc <- nchar(words, type = "w") if (any(is.na(nc))) { nc0 <- nchar(words) nc[is.na(nc)] <- nc0[is.na(nc)] } if (any(nc == 0)) { zLenInd <- which(nc == 0) zLenInd <- zLenInd[!(zLenInd %in% (grep("\\.$",
words) + 1))]
if (length(zLenInd) > 0) {
words <- words[-zLenInd]
nc <- nc[-zLenInd]
}
}
if (length(words) == 0) {
yi <- c(yi, "", prefix)
next
}
currentIndex <- 0
lowerBlockIndex <- 1
upperBlockIndex <- integer(0)
lens <- cumsum(nc + 1)
first <- TRUE
maxLength <- width - nchar(prefix, type = "w") -
indent
while (length(lens) > 0) {
k <- max(sum(lens <= maxLength), 1)
if (first) {
first <- FALSE
maxLength <- maxLength + indent - exdent
}
currentIndex <- currentIndex + k
if (nc[currentIndex] == 0)
upperBlockIndex <- c(upperBlockIndex, currentIndex -
1)
else upperBlockIndex <- c(upperBlockIndex, currentIndex)
if (length(lens) > k) {
if (nc[currentIndex + 1] == 0) {
currentIndex <- currentIndex + 1
k <- k + 1
}
lowerBlockIndex <- c(lowerBlockIndex, currentIndex +
1)
}
if (length(lens) > k)
lens <- lens[-(1:k)] - lens[k]
else lens <- NULL
}
nBlocks <- length(upperBlockIndex)
s <- paste(prefix, c(indentString, rep.int(exdentString,
nBlocks - 1)), sep = "")
for (k in (1:nBlocks)) {
s[k] <- paste(s[k], paste(words[lowerBlockIndex[k]:upperBlockIndex[k]],
collapse = " "), sep = "")
}
s = gsub("\\+ ", "+", s)
yi <- c(yi, s, prefix)
}
y <- if (length(yi))
c(y, list(yi[-length(yi)]))
else c(y, "")
}
if (simplify)
y <- unlist(y)
y
}

## S3 methods
coef.pstpm2 <- coef.stpm2 <- coef
vcov.pstpm2 <- vcov.stpm2 <- vcov



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