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My dataset (example here) represents a long-term capture-mark-recapture study, approximately 20 years duration. I am interested in looking at how the survival of animals is influenced by their sex and exposure to viral pathogens. I have data on the age of animals at each capture, but do not technically have data on their time of death, rather if an animal is not captured at a one particular time/consecutive time points they have either evaded capture or have died.

The mean age of animals is <1 year, but some individuals live for up to 7 years. Hence over the 20 year study period several thousand animals enter and exit the population (and enter/exit the study) at very different times.

Question: Can such data be used in survival analysis using a Cox proportional-hazards model, Kaplan-Meier survival curves or similar? If not, does anyone have any recommendations as to how one might approach the analysis of such data? (Considering the question(s) of interest - italic text above). Note that I do not have information on the specific time of event/death.

To date I have modelled this data using mixed models with a gamma distribution, age as the outcome and sex and pathogen exposure as predictors. However, I'm not confident that this is the correct approach. Whilst this compares the time that animals were alive (age) it does not consider the rate at which they may have died - I understand that survival analysis compares both the median time of survival and the rate at which death might have occurred.

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  • $\begingroup$ Are you interested in time-varying covariates, like the influence of their weight-changes over time affecting survival? $\endgroup$ – Cam.Davidson.Pilon Nov 20 '20 at 3:58
  • $\begingroup$ This would be interesting, but only be a side interest and not a main interest. Thanks @Cam.Davidson.Pilon $\endgroup$ – Pat Taggart Nov 20 '20 at 5:30
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Even though you have no recorded death events (i.e. all your data is censored), you can still make inferences using survival analysis. However, there is a tradeoff: you won't be able to use any non-parametric or semi-parametric models. These include Kaplan Meier model and the Cox model. You are resigned to use a fully parametric model (not a bad thing!). For example, a Weibull, or a Gamma, or spline model. All these handle censoring of death events, even 100% censoring, and will provide coefficient estimates of your covariates, produce median survival times, etc.

Software:

  • in R, there is flexsurvreg
  • in Stata, there is merlin
  • in Python, there is lifelines (I'm the author)

If you'd like, you can go one step further and include the prior information you have about lifespans - "mean is < 1 year, but sometimes as high as 7 years" - by using a Bayesian parametric model. Basically, you choose priors on the unknown parameters that reflect your current knowledge about lifespans.

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  • $\begingroup$ Thanks @Cam.Davidson.Pilon. If I understand correctly, my model essentially just becomes a GLMM or GAMM then? Where the outcome is Age, fixed effects are Sex, Pathogen exposure and Weight, and a random intercept for Individual animal. In which case, such a model could also be implemented in lme4 or glmmTMB? $\endgroup$ – Pat Taggart Nov 22 '20 at 21:54
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    $\begingroup$ It's a GLM with censoring - so you might need to specifically use a survival analysis library if lme4, etc., don't support censoring. $\endgroup$ – Cam.Davidson.Pilon Nov 23 '20 at 2:51

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