# Time-independent variables in survival analysis

In any non-cross-sectional, prospective (whether it be longitudinal, survival, etc) study there are baseline variables which contain the status of the variable at the beginning of the study, and these remain fixed for the duration of observation. But these are distinct from other time-invariant predictors which may contain information (usually some form of summary) about the value of the variable during the study. What comes to mind here is mainly a survival-type analysis and considering smoking as an example of exposure. Am I correct in stating how one could define smoking as a time-invariant exposure?

1. Baseline - is the person currently a smoker / have they ever smoked / etc: yes/no. This is the value of smoking status in the study start.
2. Time-invariant - did the person ever smoke during the study: yes/no. This is a summary of smoking status over the person's observation time.
3. Time-invariant. Even though probably not the most appropriate summary in this particular example, you could also calculate the proportion/percentage of the total observation time that the person was a smoker.

The issue with using time-invariant measures for variables that change status during observation is that you run the risk of immortal-time bias, which is why you might consider using a time-varying covariate.

What I mainly want to get at here is that there aren't any 'rules' specifically for survival analysis that say you shouldn't use post-baseline data for formulating time-invariant predictors. I think I have conflated baseline and general time-independent variable concepts after reading page 2 of this document that discusses 'not looking into the future'.

https://cran.r-project.org/web/packages/survival/vignettes/timedep.pdf

Thanks.

In a proportional hazards model, the associations of covariates with outcome are evaluated based on the current values among all those still at risk at each event time in the data set.

The first thing to consider is what representation of a covariate is most closely related to the current risk at any time. Although you certainly can't "look into the future," you can represent the past history of a variable in any way that makes sense if you are using time-dependent covariates in your model.

If you want to restrict your model to time-invariant covariates that represent the status at time = 0, however, then neither method 2 or 3 would be appropriate, as both methods involve values of covariates that were only observed after time = 0. Values determined by those methods would not correctly represent the risk at times before the later observations were made.

Method 1 is often appropriate for some characteristics like smoking, as the association with risk typically is a function of long-term exposure. In that case, any exposure change over the few-year course of many survival studies won't make much difference, so the status at time = 0 is a reasonable approximation to current risk throughout the study.

• Thanks @EdM. I think you confirm what I intuited, but have had researchers use methods 2 and 3 and I have been thinking about their validity. So it's really using only baseline or tvc's - any other time-invariant 'summary' (i.e. over the prospective course of the study) covariate representation is really using future data at any event time to predict the current risk. And that's not appropriate. Is that a fair summary? Jun 21, 2023 at 22:03
• @LucaS I think that's a fair summary. Note that even using time-varying covariates in a model can lead to "looking into the future" types of problems if you try to make predictions from it. See this page for some discussion.
– EdM
Jun 22, 2023 at 13:06