In veterinary medicine there is a challenge when assessing prognostic variables for survival. Euthanasia is a competing risk for mortality. The reason for euthanasia may be financial or perhaps to alleviate potential suffering based upon the veterinarians view of the prognosix. Obviously this can bias results. It has been proposed that for these type of studies a committee of veterinarians review the data and construct a counterfactual estimate of the animals chance of survival had it not been euthanized. This seems subjective and since it will be a historical evaluation of the data prone to bias. Are there any suggestions for handling this challenge?
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My two cents about the subject:
You might think about health-outcome as a proxy for quality-life outcome, assuming Euthanasia as a proxy for a state that is worst than death.
If you want to consider a counterfactual you need to adjust for health-condition at the decision point and find some animals with the same propensity for Euthanasia - this way you’ll be able to create IPTW (inverse probability treatment weights) and extract AJ estimates give dependant censoring.
The most straight-forward method would be to do a quick sensitivity analysis handling Euthanasia as competing, censoring and composite event.
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Possibly also consider an ordinal state transition Markov model.