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I have a question regarding my Time to Event variable. Since I am working with time-varying variables (which can change every year), I use a data structure with one line per individual per year. there are only as many rows as # of years until the event. Each year is indicated whether the event occurs or not. The event can only occur once. Can I work with a modified time-to-event variable here? My idea was to measure the duration anew each year to avoid proportionality problems. That means the time to event is always equal to 1. In fact, I only measure the survival per year. In my analyses, I only want to determine for whom an event occurs and for whom it does not. The advantage of using such an artificial time-to-event variable is that the proportionality assumption can be circumvented in this way. Does this trick seem permissible to you? Thanks a lot... any feedback would be highly appreciated.

EDIT (I thank the commentator for the helpful questions): The events are only recorded as once per year. There is no particular time during the year that the values of time-varying variables change. I only want to know if an event occurred or not. How long the individual survived is basically not important to me. Whether the event happens sooner or later is not important to me. I only want to know which variables have an influence on the occurrence of the event. time since a change in a time-varying variable is more important to me. The effect of certain variables changes over time. That's why i came up with that artificial time to event variable. The survival time / time-to-event is always recalculated after the change of the time-dependent variables.

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  • $\begingroup$ Are the events also only recorded as once per year, or is there a more precise record of event times? Is there some particular time during the year that the values of time-varying variables change? Putting aside any possible issues with "proportionality," which time-to-event do you really want to model: time since entering the study or time since a change in a time-varying variable? Or do you only want to know if an event changed at some time during a particular year, discarding information about prior years? Please edit your question to add that information, as comments can be lost. $\endgroup$
    – EdM
    May 17 at 12:46
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This is probably best modeled with discrete-time survival analysis, which is essentially logistic or another binary-outcome regression that incorporates time as a predictor. That gets around the problems that you face: only knowing the event time to within a year (which otherwise would require specialized interval-censoring analysis), time-varying covariate values updated annually, and a potential lack of proportional hazards. As there is only 1 event per individual you don't have to take into account intra-individual correlations in outcomes (as you would if multiple events were possible per individual).

The third paragraph from the end of this answer outlines discrete-time survival analysis, with a couple of links to further reading. With your data already formatted at 1 row per person per year through the event year, you just have to submit the data to a logistic regression (or possibly use a complementary log-log link for a grouped proportional-hazards model) with the outcome being the event marker (1 for event, 0 for no event) and your set of covariates as predictors.

The question you need to resolve is how to handle time, which should be included in the model as a predictor if for no other reason than to make sure that you don't have an unexpected relationship between time and event probability. Simplest might be to set time = 0 to the study-entry year for each individual. If you think that time since a change in a particular covariate is important, you could consider re-setting time = 0 at each such change. Or if you think that calendar year is important (for example, if the event might have to do with underlying economic conditions), then use the earliest calendar year as the time = 0 reference. You can evaluate multiple such times if you wish; for example, you could include both calendar year and an individual's time since study entry if that makes sense. Those decisions need to be based on your knowledge of the subject matter and the goal of your study.

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  • $\begingroup$ Thank you very much for the quick feedback. I will take a close look at all the links. I had already thought about logistic regressions, but I didn't know how to deal with time. Including it as a predictor in the model is a good approach. The advantage of Cox for me was that I can stratify quite easily, as my data is also clustered. Thank you very much, I was a bit lost.. $\endgroup$
    – Clarissa
    May 17 at 16:21
  • $\begingroup$ @Clarissa you could handle clustered data for example with a mixed-model logistic regression, with random-effect terms for the clusters. $\endgroup$
    – EdM
    May 17 at 17:37

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