Confidence intervals of harmful function of the mukhaz package

Question

muhaz evaluates the hazard function from right-hand censorship using kernel smoothing techniques. My question is, is there a way to get confidence intervals for the hazard function that muhaz calculates?

 options(scipen=999) library(muhaz) data(ovarian, package="survival") attach(ovarian) fit1 <- muhaz(futime, fustat) plot(fit1, lwd=3, ylim=c(0,0.002)) 

In the above example, muhaz.object fit has several records fit1$msemin , fit1$var.min , fit1$haz.est , however their length is half fit1$haz.est .

Any ideas if you can extract confidence intervals for the hazard function?

EDIT: I tried the following based on what @ user20650 suggested

 options(scipen=999) library(muhaz) data(ovarian, package="survival") fit1 <- muhaz(ovarian$futime, ovarian$fustat,min.time=0, max.time=744) h.df<-data.frame(est=fit1$est.grid, h.orig=fit1$haz.est) for (i in 1:10000){ dsonarian<-ovarian[sample(1:nrow(ovarian), nrow(ovarian), replace = T),] dsmuhaz<-muhaz(dsonarian$futime, dsonarian$fustat, min.time=0, max.time=744 ) h.df<-cbind(h.df, dsmuhaz$haz.est) } h.df$upper.ci<-apply(h.df[,c(-1,-2)], 1, FUN=function(x) quantile(x, probs = 0.975)) h.df$lower.ci<-apply(h.df[,c(-1,-2)], 1, FUN=function(x) quantile(x, probs = 0.025)) plot(h.df$est, h.df$h.orig, type="l", ylim=c(0,0.003), lwd=3) lines(h.df$est, h.df$upper.ci, lty=3, lwd=3) lines(h.df$est, h.df$lower.ci, lty=3, lwd=3) 

Setting max.time seems to work, each bootstrap sample has the same grid points. However, CI got little point. Normally, I would expect that the intervals are narrow at t = 0 and will expand with time (less information, more uncertainty), but the intervals obtained seem more or less constant over time.

Answer 1

The boot answer gives the answer as the commentator suggested. Your intuition is right that you should expect CI to expand as risk decreases. However, this effect will be reduced by the smoothing process, and the longer the interval over which smoothing is applied, the less you should notice a change in CI size. Try to smooth out for a fairly short period of time, and you should notice that CI expand more noticeably.

As you may find, these smoothed hazard areas can be very limited and very sensitive to how smoothing is done. As an exercise, it is instructive to model survival times from a series of Weibull distributions with a shape parameter set to 0.8, 1.0, 1.2, and then look at these smoothed hazard areas and try to classify them. To the extent that these graphs are informative, it is simple enough to determine the difference between these three curves based on the trend rate of the hazard function. YMMV, but I was not very impressed with the results when I conducted these tests with reasonable sample sizes according to clinical trials in oncology.

As an alternative to smoothed hazardous areas, you can try to establish piecewise-exponential curves using the method of Han et al. ( http://www.ncbi.nlm.nih.gov/pubmed/23900779 ) and download it. Their algorithm will determine the breakpoints at which there is a statistically significant change in the degree of danger, and can give you a better idea of ​​the trend towards the speed of danger than smoothed danger sections. This also avoids the arbitrary but consistent selection of smoothing parameters.