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I am trying to create a time dependent (covariate) cox regression model for a survival analysis project I am interested in. A brief overview of my dataset:

I have a cohort starting from 2011-01-01, ending in 2016-12-31. The time dependent exposure is bereavement, all people start non-bereaved but eventually some will get exposed.

I have created the dataset using the survival package in R in which an individual who is going to be bereaved gives two rows in the data (one for the non-bereavement period and another for the bereavement period), while a non-bereaved during the follow up has only one row. I am interested in comparing mortality between bereaved and non-bereaved. I can do a survival analysis for that purpose, but I am also interested in seeing if the time since bereavement is also affecting mortality. However, I can't seem to do aforementioned, since I also have non-bereaved ones for which the time since bereavement cannot be computed. Do you happen to have any ideas how can I progress my analysis or happen to know any packages that are relevant to that purpose ? I have also check the following paper, and they seem to have managed something like that :

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2465697/

Kind regards and thank you in advance for any potential ideas!

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What you have done so far seems to match what was done in the paper you cite. You have treated bereavement as a time-varying covariate, using that as a predictor for modeling survival since study start.

I am also interested in seeing if the time since bereavement is also affecting mortality. However, I can't seem to do aforementioned, since I also have non-bereaved ones for which the time since bereavement cannot be computed.

Time since bereavement can't be computed for those who haven't experienced bereavement, but those same individuals also can't have their survival affected by time since bereavement. So you might be overthinking. I have a few suggestions.

First, you could just analyze survival post bereavement separately, with the date of bereavement as time = 0 for that analysis. That would of course be restricted to those who experienced bereavement.

Second, you could add time since bereavement as a predictable time-dependent covariate, with time = 0 kept at your study start date. That value would always be 0 for those who didn't experience bereavement. Section 5 of the R time-dependence vignette shows how to do that with the time-transform feature of the R coxph() function.

Third, you might consider using a multi-state model for this, with transitions possible from non-bereaved to bereaved, from non-bereaved to death, and from bereaved to death. The principles are outlined in the R competing risks vignette. One might think that there would be no significant associations of an individual's characteristics with the risk of experiencing bereavement (e.g., from death of a spouse), but that would give you the opportunity to test that assumption as part of the model.

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