aft.cpp
#include <RcppArmadillo.h>
#include <c_optim.h>
#include <splines.h>
#include <aft.h>
namespace rstpm2 {
using namespace arma;
using namespace Rcpp;
aft::aft(SEXP list) : args(as<List>(list)) {
init = as<vec>(args["init"]);
X = as<mat>(args["X"]);
XD = as<mat>(args["XD"]);
XD0 = as<mat>(args["XD0"]);
event = as<vec>(args["event"]);
time = as<vec>(args["time"]);
boundaryKnots = as<vec>(args["boundaryKnots"]);
interiorKnots = as<vec>(args["interiorKnots"]);
q_matrix = as<mat>(args["q.const"]);
cure = as<int>(args["cure"]);
s = ns(boundaryKnots, interiorKnots, q_matrix, 1, cure);
delayed = as<bool>(args["delayed"]);
if (delayed) {
time0 = as<vec>(args["time0"]);
X0 = as<mat>(args["X0"]);
}
kappa = 1.0e3;
}
mat aft::rmult(mat m, vec v) {
mat out(m);
out.each_col() %= v;
return out;
}
mat aft::rmult(mat m, uvec v) {
mat out(m);
out.each_col() %= conv_to<vec>::from(v);
return out;
}
double aft::objective(vec betafull)
{
vec beta = betafull.subvec(0,X.n_cols-1);
vec betas = betafull.subvec(X.n_cols,betafull.size()-1);
vec eta = X * beta;
vec etaD = XD * beta;
vec logtstar = log(time) - eta;
vec etas = s.basis(logtstar) * betas;
vec etaDs = s.basis(logtstar,1) * betas;
// fix bounds on etaDs
vec eps = etaDs*0. + 1e-8;
double pen = dot(min(etaDs,eps), min(etaDs,eps));
etaDs = max(etaDs, eps);
// fix bounds on etaD
pen += dot(min(1-etaD, eps), min(1-etaD,eps));
etaD = 1 - max(1-etaD, eps);
// add penalty for monotone splines
vec betasStar = s.q_matrix.t() * betas;
for (size_t i=1; i<betasStar.size(); i++) {
double delta = betasStar(i)-betasStar(i-1);
if (delta<0.0)
pen += kappa*delta*delta;
}
vec logh = etas + log(etaDs) + log(1/time - etaD/time);
vec H = exp(etas);
double f = pen - (dot(logh,event) - sum(H));
if (delayed) {
vec eta0 = X0 * beta;
vec logtstar0 = log(time0) - eta0;
vec etas0 = s.basis(logtstar0) * betas;
vec etaDs0 = s.basis(logtstar0,1) * betas;
vec H0 = exp(etas0);
vec eps0 = etaDs0*0. + 1e-16;
f += dot(min(etaDs0,eps0), min(etaDs0,eps0));
f -= sum(H0);
}
return f;
}
vec aft::gradientPenalty(mat Q, vec beta) { // Q: (nbeta+2) x nbeta
size_t n = Q.n_rows;
mat D = join_rows(zeros(n-1,1),eye(n-1,n-1)) - join_rows(eye(n-1,n-1),zeros(n-1,1)); // (nbeta+1) x (nbeta+2)
vec delta = D * Q * beta; // nbeta+1
mat M = Q.t() * D.row(0).t() * D.row(0) * Q * (delta(0)<0.0); // nbeta x nbeta
for(size_t j=1; j<delta.size(); j++) {
if (delta(j)<0.0)
M += Q.t() * D.row(j).t() * D.row(j) * Q;
}
return 2*M*beta*kappa;
}
vec aft::gradient(vec betafull)
{
vec beta = betafull.subvec(0,X.n_cols-1);
vec betas = betafull.subvec(X.n_cols,betafull.size()-1);
vec eta = X * beta;
vec etaD = XD * beta;
vec logtstar = log(time) - eta;
mat Xs = s.basis(logtstar);
mat XDs = s.basis(logtstar,1);
mat XDDs = s.basis(logtstar,2);
vec etas = Xs * betas;
vec etaDs = XDs * betas;
vec etaDDs = XDDs * betas;
// H calculations
vec H = exp(etas);
mat dHdbetas = rmult(Xs,H);
mat dHdbeta = -rmult(X,H % etaDs);
// penalties
vec eps = etaDs*0. + 1e-8;
uvec pindexs = (etaDs < eps);
uvec pindex = ((1.0 - etaD) < eps);
// fix bounds on etaDs
// mat pgrads = join_rows(-2*rmult(X,etaDs % etaDDs),2*rmult(XDs,etaDs));
mat pgrads = join_rows(X*0.0,2*rmult(XDs,etaDs));
etaDs = max(etaDs, eps);
// fix bounds on etaD
// mat pgrad = join_rows(-2*rmult(XD,1/time-etaD),XDs*0.0);
//
mat pgrad = join_rows(-2.0*rmult(X,etaDs % etaDDs)-2.0*rmult(XD,1-etaD),Xs*0.0);
etaD = 1 - max(1-etaD, eps);
vec logh = etas + log(etaDs) + log(1/time - etaD/time);
vec h = exp(logh);
mat dloghdbetas = Xs+rmult(XDs,1/etaDs % (1-pindexs));
mat dloghdbeta = -rmult(X,etaDs % (1-pindexs)) - rmult(X,etaDDs/etaDs % (1-pindexs)) - rmult(XD, (1-pindex)/time/(1-etaD));
mat gradi = join_rows(-rmult(dloghdbeta,event)+dHdbeta, -rmult(dloghdbetas,event)+dHdbetas) + rmult(pgrad,pindex) + rmult(pgrads,pindexs);
// mat gradi = join_rows(-rmult(dloghdbeta,event)+dHdbeta, -rmult(dloghdbetas,event)+dHdbetas);
vec out = sum(gradi,0).t();
out += join_cols(beta*0.0, gradientPenalty(s.q_matrix.t(), betas));
if (delayed) {
vec eta0 = X0 * beta;
vec etaD0 = XD0 * beta;
vec logtstar0 = log(time0) - eta0;
mat Xs0 = s.basis(logtstar0);
mat XDs0 = s.basis(logtstar0,1);
mat XDDs0 = s.basis(logtstar0,2);
vec etas0 = Xs0 * betas;
vec etaDs0 = XDs0 * betas;
vec etaDDs0 = XDDs0 * betas;
vec H0 = exp(etas0);
mat dHdbetas0 = rmult(Xs0,H0);
mat dHdbeta0 = -rmult(X0,H0 % etaDs0);
vec eps0 = etaDs0*0. + 1e-8;
uvec pindex0 = ((1.0 - etaD0) < eps0);
uvec pindexs0 = (etaDs0 < eps0);
etaDs0 = max(etaDs0, eps0);
// mat pgrad0 = join_rows(-2*rmult(XD0,1-etaD0),XDs0*0.0);
// mat pgrads0 = join_rows(-2*rmult(X0,etaDs0 % etaDDs0),2*rmult(XDs0,etaDs0));
mat pgrad0 = join_rows(-2.0*rmult(X0,etaDs0 % etaDDs0)-2.0*rmult(XD0,1-etaD0),Xs0*0.0);
mat pgrads0 = join_rows(X0*0.0,2*rmult(XDs0,etaDs0));
// out += sum(join_rows(-dHdbeta0, -dHdbetas0), 0).t();
out += sum(join_rows(-dHdbeta0, -dHdbetas0) + rmult(pgrads0,pindexs0) +
rmult(pgrad0,pindex0), 0).t();
}
return out;
}
double aft::objective(NumericVector betafull) {
return objective(as<vec>(wrap(betafull)));
}
NumericVector aft::gradient(NumericVector betafull) {
vec value = gradient(as<vec>(wrap(betafull)));
return as<NumericVector>(wrap(value));
}
vec aft::survival(vec time, mat X) {
vec beta = init.subvec(0,X.n_cols-1);
vec betas = init.subvec(X.n_cols,init.size()-1);
vec eta = X * beta;
vec logtstar = log(time) - eta;
vec etas = s.basis(logtstar) * betas;
vec S = exp(-exp(etas));
return S;
}
vec aft::haz(vec time, mat X, mat XD)
{
vec beta = init.subvec(0,X.n_cols-1);
vec betas = init.subvec(X.n_cols,init.size()-1);
vec eta = X * beta;
vec etaD = XD * beta;
vec logtstar = log(time) - eta;
mat Xs = s.basis(logtstar);
mat XDs = s.basis(logtstar,1);
mat XDDs = s.basis(logtstar,2);
vec etas = Xs * betas;
vec etaDs = XDs * betas;
vec etaDDs = XDDs * betas;
// penalties
vec eps = etaDs*0. + 1e-8;
uvec pindexs = (etaDs < eps);
uvec pindex = ((1.0/time - etaD) < eps);
// fix bounds on etaDs
etaDs = max(etaDs, eps);
// fix bounds on etaD
etaD = 1/time - max(1/time-etaD, eps);
vec logh = etas + log(etaDs) + log(1/time -etaD);
vec h = exp(logh);
return h;
}
mat aft::gradh(vec time, mat X, mat XD)
{
vec beta = init.subvec(0,X.n_cols-1);
vec betas = init.subvec(X.n_cols,init.size()-1);
vec eta = X * beta;
vec etaD = XD * beta;
vec logtstar = log(time) - eta;
mat Xs = s.basis(logtstar);
mat XDs = s.basis(logtstar,1);
mat XDDs = s.basis(logtstar,2);
vec etas = Xs * betas;
vec etaDs = XDs * betas;
vec etaDDs = XDDs * betas;
// penalties
vec eps = etaDs*0. + 1e-8;
uvec pindexs = (etaDs < eps);
uvec pindex = ((1.0/time - etaD) < eps);
// fix bounds on etaDs
etaDs = max(etaDs, eps);
// fix bounds on etaD
etaD = 1/time - max(1/time-etaD, eps);
vec logh = etas + log(etaDs) + log(1/time -etaD);
vec h = exp(logh);
mat dloghdbetas = Xs+rmult(XDs,1/etaDs % (1-pindexs));
mat dloghdbeta = -rmult(X,etaDs % (1-pindexs) % (1-pindex)) - rmult(X,etaDDs/etaDs % (1-pindexs) % (1-pindex)) - rmult(XD, (1-pindexs) % (1-pindex)/(1/time-etaD));
mat gradh = join_rows(rmult(dloghdbeta,h), rmult(dloghdbetas,h));
return gradh;
}
RcppExport SEXP aft_model_output(SEXP args) {
aft model(args);
List list = as<List>(args);
std::string return_type = as<std::string>(list["return_type"]);
if (return_type == "nmmin") {
// model.pre_process();
NelderMead nm;
nm.trace = as<int>(list["trace"]);
nm.maxit = as<int>(list["maxit"]);
NumericVector betafull = as<NumericVector>(wrap(model.init));
nm.optim<aft>(betafull,model);
// model.post_process();
return List::create(_("fail")=nm.fail,
_("coef")=wrap(nm.coef),
_("hessian")=wrap(nm.hessian));
}
else if (return_type == "vmmin") {
// model.pre_process();
BFGS bfgs;
bfgs.trace = as<int>(list["trace"]);
bfgs.maxit = as<int>(list["maxit"]);
NumericVector betafull = as<NumericVector>(wrap(model.init));
bfgs.optim<aft>(betafull,model);
// model.post_process();
return List::create(_("fail")=bfgs.fail,
_("coef")=wrap(bfgs.coef),
_("hessian")=wrap(bfgs.hessian));
}
else if (return_type == "objective")
return wrap(model.objective(model.init));
else if (return_type == "gradient")
return wrap(model.gradient(model.init));
else if (return_type == "survival")
return wrap(model.survival(as<vec>(list["time"]),as<mat>(list["X"])));
else if (return_type == "haz")
return wrap(model.haz(as<vec>(list["time"]),as<mat>(list["X"]),as<mat>(list["XD"])));
else if (return_type == "gradh")
return wrap(model.gradh(as<vec>(list["time"]),as<mat>(list["X"]),as<mat>(list["XD"])));
else {
REprintf("Unknown return_type.\n");
return wrap(-1);
}
}
// RcppExport SEXP aft_objective_function(SEXP args)
// {
// List list = as<List>(args);
// vec beta = as<vec>(list["beta"]);
// vec betas = as<vec>(list["betas"]);
// mat X = as<mat>(list["X"]);
// mat XD = as<mat>(list["XD"]);
// vec event = as<vec>(list["event"]);
// vec time = as<vec>(list["time"]);
// vec boundaryKnots = as<vec>(list["boundaryKnots"]);
// vec interiorKnots = as<vec>(list["interiorKnots"]);
// ns s(boundaryKnots, interiorKnots, 1);
// vec eta = X * beta;
// vec etaD = XD * beta;
// vec logtstar = log(time) - eta;
// vec etas = s.basis(logtstar) * betas;
// vec etaDs = s.basis(logtstar,1) * betas;
// vec eps = etaDs*0. + 1e-8;
// double pen = dot(min(etaDs,eps), min(etaDs,eps));
// etaDs = max(etaDs, eps);
// vec logh = etas + log(etaDs) + log(etaD+1.) - log(time);
// vec H = exp(etas);
// double f = pen - (dot(logh,event) - sum(H));
// return wrap(f);
// }
} // namespace rstpm2
