Probability of future survival for extended cox model I have fit an extended cox model in R (i.e., some of the covariates change with time), and am now interested in predicting, for the censored observations, the probability that they will survive an additional year. I am fine with kaplan-meier survival curve estimates, and if needed, smoothed estimates for the hazard. 
How would I go about getting these probability predictions? Tools for doing this and/or a theoretical understanding of how to do it would be helpful to me.  
 A: Perhaps the Cox-predicted survival curve could help you. Example follows. It does work with the extended Cox model.
install.packages("survMisc"); library(survMisc); library(survival)

# Fit a model, stratified by the variable you wish to predict upon
fits <- coxph(Surv(time, status==2) ~ age + strata(sex), data=lung)

# What is the age-adjusted survival for each sex? A prediction...
autoplot(autoplot(survfit(fits, newdata=data.frame(age=mean(lung$age, na.rm=T), legTextSize = 14, legLabSize = 14, legTitle='', axisLabSize = 14, tabTitle = "Number at risk", title="Adjusted survival by sex", xlab="Time (years)", ylab="Probability of survival", nRiskSize=5, censSize=0))))


A: Say a person you want to predict for is censored at time $c_1$. You are interested in the predicted survival from that point on, so on  $S(w) = P(T>c_1+w| T>c_1)$. Then denote $c_1$ as a landmark time and:


*

*create a landmark data set, where time point $c_1$ becomes the new time $0$. In this data set you want to keep only the persons who are still at risk at $c_1$, and discard all information on the past. 

*Fit the same (Cox) model on this data set. The predicted survival curve from this data set, for the subject that you are interested in (the one censored at $c_1$), is the quantity of interest (you can select the value at 1 year after that). Having a time-dependent covariate should not be a problem. For this subject you can use the last observed value.

*Then repeat the procedure for all the censoring time points. 


There are two packages in R which can do the splitting of the data set (dynpred and mstate) but it wouldn't be very complicated to implement a function like that yourself. 
For more theoretical explanations about this, a reference book is Dynamic Prediction in Clinical Survival Analysis by Hans van Houwelingen and Hein Putter, in this paper or there are a bunch of presentations that I just found online with Google, such as this one.
