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I have daily survival estimates from a nest survival model, and I would like to extrapolate these estimates to encompass the full incubation period for a few specific values of a continuous covariate. I see how to use the Delta method to calculate this by hand for a simple model with maybe two levels of a grouping factor, but it gets more complicated for models with more predictors. I understand that covariate.predictions uses the delta method, but I haven't found any clear examples of how to implement my formula S^23. I assume there is an easy way to do this that I just haven't discovered?

My apologies if this should have been added to an existing topic.

If S is constant over time then calculation for variance is straightforward application of delta method. See deltamethod function in package. S can be a function of a time constant covariate but you just need to compute for each covariate value. If S varies by time then look at deltamethod.special in RMark. Use prod and provide a vector of 23 values of S and their vcv matrix which you can get from covariate.predictions.

Assuming you meant deltamethod in the msm package, that was exactly what I needed! Thanks!

Yes. The deltamethod.special function uses delta method in MSM and just makes it easier to do for particular functions like sums and products.