Support for time varying covariates (or, start-stop) survival data

[IyarLin]

Hi,

First, many thanks for writing this package - it is of great value to me.

If I understand correctly the package can only handle survival data of the form Surv(time, status).

Would it be a lot of work to generalize that for Surv(start,stop,status) data?

[RobinDenz1]

Hello there,

thank you for your question!

Yes you are correct, the package currently only works with time-fixed covariates. The best answer to your question on how much work it would be to generalize it to time-varying covariates is: it depends.

First of all, if the variable of interest changes over time this gets very complex instantly, because the causal question to be answered is unclear in those cases. What exactly should the survival curves display? The survival probability given that everyone was exposed from the beginning? Or some mix of treated - untreated times? There is no obvious answer to this. I also suspect that the syntax needed to perform analyses of this kind would be quite different from what I implemented.

If only some confounders change over time, it is less complicated, but still a lot of work. For the "direct" and "direct_pseudo" methods it should work without any fundamental changes to the methodology, but it would require quite some code-refactoring. I am not sure how IPTW or AIPTW based methods could handle this, but there is probably some literature on this somewhere.

What exactly are you trying to do? I might be able to offer a "quick and dirty solution" depending on what your problem is. I am however not going to implement general support for time varying covariates soon, because I am currently working on a second R-package that can handle continuous variables of interest.

[IyarLin]

The use case I have in mind is comparing exposure from the beginning to non exposure from the beginning. I'm using a propensity stratification approach where I divide start-stop intervals to different treatment incidence groups.

I'd like to somehow take weighted combinations of those curves in the control and treatment groups to get ATC and ATT (so if the treatment groups has more tendency to be in one of those groups in certain times it will inherit more of it's survival from that curve).

In binary treatment and continuous/binary outcome it works fine. Survival outcome always has to be so complicated =/

[RobinDenz1]

That sounds like a very interesting problem, but I sadly don't know a solution to it right now.

You said that this is not a problem for binary treatments and continuous/binary outcomes. Could you perhaps cite some of the papers that describe these methods in those scenarios here? I would like to take a look at them. Maybe I can do something similar for the adjustedCurves package in the future.

[IyarLin]

Hi, this is a short summary of the propensity score stratification approach:

Propensity stratification divides the observations into strata that have similar propensity scores, with the objective of balancing the observed variables between treated and control units within each stratum. The treatment effect can then be estimated by combining stratum-specific estimates of treatment effect. Rosenbaum and Rubin (1984, p. 521) show that an adjusted estimate of this type that is based on five strata can remove approximately 90% of the bias in the crude or unadjusted estimate.

You can also see the main reference there

[RobinDenz1]

You could easily use standard propensity stratification with the adjustedCurves R-package. Calculate the propensity score for each person, categorize those into groups and use this categorical variable as adjustment covariate in method="surv_strat_amato". But I am not sure how that would be extended to a time-varying covariate.

[maurosc3ner]

Hi,

I am in the same situation with covariates that varies through time (age or other categorical signal) for recurrent events (disease readmissions in 5 years time period). is there any update about this?

Thanks

[RobinDenz1]

As stated above, extending the adjustedCurves package to allow time-dependent covariates is not a small undertaking. Unfortunately, I had no time to deal with it so far.

Concerning the recurrent events portion of your question: What exactly do you want to estimate? What kind of probability should be displayed? If it's 1 - the causal probability of suffering from the first event (time-to-first-event analysis), you can probably just ignore recurrent events for this analysis.