R package for estimating the hazard discrimination summary (HDS). HDS is a measure of time-varying prognostic performance. It can be thought of as an incident, time-varying extension of the discrimination slope (Yates 1982), which is perhaps better known as an important part of the integrated discrimination improvement (IDI; Pencina et al. 2008). Alternatively, HDS is a risk-based complement to the incident/dynamic time-dependent AUC (Heagerty and Zheng 2005). Under some circumstances, HDS also has interesting connections to the Cox model partial likelihood. For a detailed overview of HDS, see Liang and Heagerty (2016) and the related discussions and rejoinder.
To install through CRAN, use
install.packages("hds")To install the latest (though not necessarily stable) GitHub version,
make sure you have devtools installed and use
devtools::install_github("liangcj/hds")A simple example using the Mayo PBC data from the
survival package demonstrating both hds
(estimator based on the Cox model) and hdslc (more flexible
estimator based on the local-in-time Cox model):
head(hds(times = survival::pbc[1:312, 2],
status = (survival::pbc[1:312, 3]==2)*1,
m = survival::pbc[1:312, 5]))
hdsres <- hds(times=pbc5[,1], status=pbc5[,2], m=pbc5[,3:7])
hdslcres <- hdslc(times = pbc5[,1], status=pbc5[,2], m = pbc5[,3:7], h = 730)
Survt <- summary(survival::survfit(survival::Surv(pbc5[,1], pbc5[,2])~1))
Survtd <- cbind(Survt$time, c(0,diff(1-Survt$surv)))
tden <- density(x=Survtd[,1], weights=Survtd[,2], bw=100, kernel="epanechnikov")
par(mar=c(2.25,2.25,0,0)+0.1, mgp=c(1.25,0.5,0))
plot(c(hdslcres[,1], hdslcres[,1]), c(hdslcres[,2] - 1.96*hdslcres[,3],
hdslcres[,2] + 1.96*hdslcres[,3]),
type="n", xlab="days", ylab="HDS(t)", cex.lab=.75, cex.axis=.75,
ylim=c(-3,15), xlim=c(0,3650))
polygon(x=c(hdsres[,1], hdsres[312:1,1]), col=rgb(1,0,0,.25), border=NA,
fillOddEven=TRUE, y=c(hdsres[,2]+1.96*hdsres[,3],
(hdsres[,2]-1.96*hdsres[,3])[312:1]))
polygon(x=c(hdslcres[,1], hdslcres[312:1, 1]), col=rgb(0,0,1,.25), border=NA,
fillOddEven=TRUE, y=c(hdslcres[,2] + 1.96*hdslcres[,3],
(hdslcres[,2] - 1.96*hdslcres[,3])[312:1]))
lines(hdsres[,1], hdsres[,2], lwd=2, col="red")
lines(hdslcres[,1], hdslcres[,2], lwd=2, col="blue")
abline(h=1, lty=3)
legend(x=1200, y=14, legend=c("Proportional hazards",
"Local-in-time proportional hazards",
"Time density"), col=c("red", "blue", "gray"),
lwd=2, bty="n", cex=0.75)
with(tden, polygon(c(x, x[length(x):1]),
c(y*3/max(y)-3.5, rep(-3.5, length(x))),
col="gray", border=NA, fillOddEven=TRUE))Liang CJ and Heagerty PJ (2016). A risk-based measure of time-varying prognostic discrimination for survival models. Biometrics. doi:10.1111/biom.12628
Gerds TA and Schumacher M (2016). Discussion of “A risk-based measure of time-varying prognostic discrimination for survival models,” by C. Jason Liang and Patrick J. Heagerty. Biometrics. doi:10.1111/biom.12629
Parast L and Rutter CM (2016). Discussion of “A risk-based measure of time-varying prognostic discrimination for survival models,” by C. Jason Liang and Patrick J. Heagerty. Biometrics. doi:10.1111/biom.12630
Michael H and Tian L (2016). Discussion of “a risk-based measure of time-varying prognostic discrimination for survival models,” by C. Jason Liang and Patrick J. Heagerty. Biometrics. doi:10.1111/biom.12631
Liang CJ and Heagerty PJ (2016). Rejoinder to discussions on: A risk-based measure of time-varying prognostic discrimination for survival models. Biometrics. doi:10.1111/biom.12632
Saha-Chaudhuri P and Heagerty PJ (2013). Non-parametric estimation of a time-dependent predictive accuracy curve. Biostatistics, 14(1), 42-59. doi: 10.1093/biostatistics/kxs021
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