Kaplan-Meier Survival Estimates using "sts graph" and time-varying covariates: any problems?

[Andrea Berni]

Hello everyone.

As the title says, I am involved in producing some KMSE graphs using time-varying covariates (such as being unemployed or employed). My question is this: is there any problem when using time-varying covariates in such graphs? I correctly used "stset" before, setting "failure" and "id". My outcome is transition to the first child, analysed through ages 20-39. Finally, I also wonder what are the differences in interpretation... (differences compared to using normal non-TV covariates).

Thanks in advance.

[Andrea Berni]

Update: I've just read this article: https://www.jstor.org/stable/27643698?seq=1#, which says KMSE can be made through "extended KMSE" (no idea how that works in STATA) where basically individuals "can contribute to different curves at different times during follow-up. (...) these curves represent hypothetical cohorts whose covariate values remain constant during follow-up."

Now, I am not sure of how that is to be interpreted, and of course I have no idea about how to do that either. Thought it could help.

[Marcos Almeida]

Welcome to the Stata Forum/ Statalist,

You may wish to take a close look at two options of - sts graph - command: strata() and adjustfor().

[Steve Samuels]

Time-varying covariates and Survival curves don't go well together, and the proposed "extended" Kaplan-Meier curves don't help ( covariates in the extended curves do not vary!).

The best studied case of portraying survival with time-varying covariates is that of a single binary covariate:. For example: an individual starts out in one of two groups then at some time t* after the start of follow-up switches to another group; or an event occurs at t* which is expected to influence survival. In that case, the cohort shifts from that at baseline to those still alive at t*, including those who experience the switch or event. The new survival curve starts at t* with a value of S(t*) = 1. This method was proposed by Anderson et. al (1983) who called it a Landmark Analsysis and by Simon and Makuch (1984). This post shows how to estimate the new curve. I proposed a different curve with time-varying strata membership here. Now throw in covariates that change continuously in time and there is not good way (that I can see) to portray a "survival" curve which reflects the shifts.

By the way, analyses with time-varying covariates may easily suffer from reverse causation if one is not careful. See this article by Jay Goodliffe.


References:

Anderson, James R, Kevin C Cain, and Richard D Gelber. 1983. Analysis of survival by tumor response. Journal of Clinical Oncology 1, no. 11: 710-719, downloaded from: http://jco.publicaciones.saludcastil...1/710.full.pdf

Simon, Richard, and Robert W Makuch. 1984. A non‐parametric graphical representation of the relationship between survival and the occurrence of an event: Application to responder versus non‐responder bias. Statistics in Medicine 3, no. 1: 35-44.

Goodliffe, Jay "The Hazards of Time-Varying Covariates".

[Andrea Berni]

Thanks both of you, especially Steve for the article of Goodliffe. Anyway, I have chosen to use a constant variable with Kaplan-Meier graphs, since I only needed to make some descriptive statistics, after all.

Have a nice day.

[Mahmoud Slim]

Time-varying covariates and Survival curves don't go well together, and the proposed "extended" Kaplan-Meier curves don't help ( covariates in the extended curves do not vary!).

The best studied case of portraying survival with time-varying covariates is that of a single binary covariate:. For example: an individual starts out in one of two groups then at some time t* after the start of follow-up switches to another group; or an event occurs at t* which is expected to influence survival. In that case, the cohort shifts from that at baseline to those still alive at t*, including those who experience the switch or event. The new survival curve starts at t* with a value of S(t*) = 1. This method was proposed by Anderson et. al (1983) who called it a Landmark Analsysis and by Simon and Makuch (1984). This post shows how to estimate the new curve. I proposed a different curve with time-varying strata membership here. Now throw in covariates that change continuously in time and there is not good way (that I can see) to portray a "survival" curve which reflects the shifts.

By the way, analyses with time-varying covariates may easily suffer from reverse causation if one is not careful. See this article by Jay Goodliffe.


References:

Anderson, James R, Kevin C Cain, and Richard D Gelber. 1983. Analysis of survival by tumor response. Journal of Clinical Oncology 1, no. 11: 710-719, downloaded from: http://jco.publicaciones.saludcastil...1/710.full.pdf

Simon, Richard, and Robert W Makuch. 1984. A non‐parametric graphical representation of the relationship between survival and the occurrence of an event: Application to responder versus non‐responder bias. Statistics in Medicine 3, no. 1: 35-44.

Goodliffe, Jay "The Hazards of Time-Varying Covariates".

Hi Steve,

I have a quick question concerning the Simon-Makuch curves. Do these curves work only when the time-varying covariate is interventional/irreversible? So if a covariate like smoking is the one we are going to analyze, do they still work taking into consideration that some subjects will move from smokers to non smokers and vice versa?

Thanks and sorry for coming across so late,
Mahmoud

[Steve Samuels]

The methods I described apply to a one-time change. For reversals, check out the multistate package (SSC), a "module to perform multi-state survival analysis", by Michael Crowther and Paul Lambert.

[Christophe Corpechot]

@Steve,

Hi Steve,

I'm interested in evaluating 'Kaplan Meier' estimates based on a binary time-varying covariate.
I came across your post a little by chance
and your following codes come at the right time:
***********CODE BEGINS***************** webuse stan3, clear stset t1, fail(died) id(id) gen dummy=1 local lm = 18 /* landmark */ stcox dummy, strata(posttran), if _t>=`lm' predict surv, basesurv separate surv, by(posttran) tempvar t`lm' gen `t`lm'' = _t-`lm' twoway connect surv0 surv1 `t`lm'' if _t>=`lm', /// sort lp(dash solid) /// saving(g`"`lm'"', replace) /// title("Landmark = `lm' Days") *********CODE ENDS************* Is there a simple way to calculate 95% confidence interval of surv0 and surv01?

Hope you can read me and many thanks in advance for your reply.

Christophe (a beginner with Stata)