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I'm using coyote telemetry data to understand the impacts of various environmental characteristics on their survival. The data I have includes the locations of a few hundred animals throughout their tracking period, mortality data for the animals who were recovered postmortem, and the birth year of some individuals.

I originally subset the data to those animals with known birth year so that the model would estimate hazard functions based on age (surv_age in data frame ex. below). It turns out that severely biases the sample to one region of the study area.

Is it theoretically sound to using the first location as the baseline for entry, i.e. the first entry for tstart, instead of estimated birth date?

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From your data sample, it seems that all of your survival times will be since the time of first locating an animal, with the first tstart value of 0. You then evidently will use age at that time as a covariate in the model. To that extent, you already are "using the first location as the baseline for entry, i.e. the first entry for tstart."

That's not the same thing as modeling survival since birth, which you could do by adding the the age at first locating the animal to all the tstart and tstop values relative to first location time. That would model survival since birth, conditional upon an animal's having already lived long enough to be located in your study.

I'm not sure which type of survival time would be expected in a study like yours. Check with colleagues who understand this particular subject matter.

In either type of model, consider multiple imputation of missing birth dates, based on whatever additional data you have, instead of subsetting the data to those with known birth dates. That's a well respected way of dealing with missing data, with over 500 related questions on this site, a freely available text by Stef van Buuren explaining the principles and application, and tools for implementation available for example in the mice and rms packages in R.

One warning: a Cox model only uses the current values of time-varying covariates in its calculations. It doesn't take into account the history of those time-varying covariates unless you construct some predictor that incorporates that history. That might be important for this type of study.

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