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I am using a longitudinal survey panel as my data source to run a Cox regression. The survey is administered biannually. Based on some previous research, the number of children in the household is seen as an important factor in whether the event occurs or not, and this, of course, is a time varying covariate. In the case of uncensored observations, it seems fairly logical to pull that data point from the most recent survey--that is if the event occurred in 2020, I could use the children present in 2018.

In the case of censored observations, however, I'm not entirely sure from which time point to pull the data. For observations that have not experienced the event, should the data be pulled from the most recent wave of the survey (2020)? For censored observations that were lost due to drop out, do I use the data most recently available?

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If you have time-varying covariates you need to "pull" the covariate values for all cases still at risk at all times at which any case has an event.

The Cox model assumes that the instantaneous value of a covariate is associated with the risk of an event at that time. So you have to know the covariate values for all cases still at risk at each event time whether they ultimately have events or are censored. Otherwise you can't estimate the true instantaneous risk of the case(s) with the event at that time from the risks of those that continue at risk thereafter, as the Cox regression requires.

I understand that the survival package in R has ways to reshape such data into the correct form.

With this type of data, evidently with only a small number of discrete time points, a Cox model might not be appropriate. There are techniques for discrete-time survival analysis. I'm not very familiar with them, but there are questions about them on this site to get you started.

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  • $\begingroup$ Hmm.. That would seem to involve a ton more covariates. Isn't that accounted for by the length of time and censorship? And just to clarify, I assume you're saying that if the survey is given at t_1, t_2, I need to measure it at all those times. $\endgroup$
    – Ryan
    May 27, 2020 at 21:39
  • $\begingroup$ @Ryan yes, it is a lot more covariate values. See this document for more discussion. To fit the model, you must compare the covariate values of a case with an event to the covariate values of all the other cases still at risk at that time. Length of time and censoring don't get around the need for those event-time-specific comparisons. So yes, you have to know the covariate values at each survey time for this type of study. And you should look into discrete-time survival analysis as a Cox model probably isn't best. $\endgroup$
    – EdM
    May 28, 2020 at 12:04

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