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The survival package in R appears to focus on continuous time survival models. I am interested in estimating a discrete time version of a proportional hazard model, the complementary log-log model. I have a fairly straightforward survival model, with simple right censoring.

I know that one way to estimate this model is to create a data set that has a separate row for each observation for each period in which it isn't "dead." Then, a glm model with the cloglog link can be used.

This approach seems very memory inefficient; indeed, it would likely produce a data set that is too large for the memory on my machine.

A second approach would be to code up the MLE myself. That would be simple enough, but I am hoping that there is a package that has this survival model canned. It would just be easier for collaboration and to avoid coding errors to use a package.

Does anyone know of such a package?

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    $\begingroup$ If this is discrete time, you must have a lot of ties, right? I'm under the impression that coxph(ties="exact"), in the standard survival package, makes the model "a conditional logistic model, and is appropriate when the times are a small set of discrete values". Would this not work for you? Is that b/c it wouldn't be using the cloglog link? $\endgroup$ Commented Apr 2, 2013 at 22:33
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    $\begingroup$ @gung, Thanks for the pointer; I didn't know about that feature. I would prefer to use the cloglog link, though. $\endgroup$
    – Charlie
    Commented Apr 2, 2013 at 23:47

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Having several rows for each observation may seem redundant, but, likely, it's not. If there are any time-varying covariates in the model, then each observation-month will certainly need its own row. One particular example of a time-varying covariate is the elapsed time. Since this variable should almost certainly be included in the model, it makes sense to have a separate row for each observation-period. Thus, the first approach suggested is likely the best one.

Note that this is different from a continuous time proportional hazards model with a Weibull distribution. There, the survival model can be simplified to a single line for each observation if time elapsed is the only time-varying covariate (see here, for example). A similar result holds for the Cox proportional hazard model.

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