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I have fitted a cox regression in R and I am wondering how I can know if a specific time period is associated with more or less death (death is my event in my survival model). I can see it on my figures that there seems to be a drop in survival in 2004 (see here):

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Furthermore, I have calculated mortality rates seperately, and there also seems to be an increase in mortality in 2004, but I want to confirm this with my cox regression. Should I add time as a covariate in my model? How do I interpret this?

Thanks.

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  • $\begingroup$ Did everyone enter the study at the same time (e.g., in 1995 or thereabout, as the plot would seem to imply)? $\endgroup$
    – EdM
    Aug 17, 2018 at 15:07
  • $\begingroup$ Yes, all individuals entered the study in 1996. $\endgroup$ Aug 17, 2018 at 15:09

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I don't know that a Cox proportional hazards (PH) regression can accomplish what you want.

Cox PH regression is semi-parametric, in that it takes the empirical baseline survival curve as given and of the same shape for all groups. It then determines whether any of the groups or other covariates affect the slope of that shared baseline survival-curve shape. So if there were an increase in mortality in 2004 shared among all groups, then that would be subsumed as part of the baseline hazard over time.

In any event, make sure that your eye is not being deceived somewhat by the 2 groups with the lowest survival. Drops in survival in small groups can appear very large on this type of plot even if they just represent the luck of the draw with a small number of cases. Those 2 groups seem to have very few members compared to the other groups, which don't have such a dramatic drop in survival in 2004.

Also, I'm a bit troubled by the apparent restriction of deaths to just a few years (apparently 1998, 1999, 2000, 2004, 2011, 2018). That seems like you might have interval-censored data in which vital status was only followed up in those years but the deaths could have occurred at any time since the prior follow-up time. That requires special care for which you should get expert local help.

It might be better to approach these data with discrete time survival analysis, which is essentially a set of logistic regressions. That might allow for testing of additional hazards associated with particular years, but I don't have any personal experience with that type of analysis.

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