# Which models are available to estimate relative life expectancy (in years, not in hazard ratios)?

I have a well-phenotyped survival dataset (i.e. it has a high number of relevant covariates for a study of mortality) for which I estimate how certain conditions influence life expectancy (LE). It would be much more informative to compute this in lost or gained years of life rather than stating a hazard ratio from a Cox model.

I wonder what people thoughts or experience are on

1. comparing easily available median life expectancy from Cox model instead of LE

2. fitting parametric survival model within PH assumption (Weibull or Cox–Gompertz model as in https://www.sciencedirect.com/science/article/pii/S0167668720300500#fig1) and computing LEs

3. using Aalen's additive hazard model

4. Anyone tried any machine learning for that? It seems many deep learning are still with Cox-PH at its heart as FastCPH. And survival random forest is predicting from Kaplan-Meier in the final leaves so again median will be estimated better than anything extrapolated)

5. Some other option?

Similar questions were asked before, What is the minimum information required to calculate life expectancy from a cox regression model? https://stackoverflow.com/questions/28491796/how-to-predict-survival-time-in-coxs-regression-model-in-r, which are mostly about getting life expectancy from Cox-PH with the advice of taking the 1st or the 2nd option, so I am mostly curious of other non-Cox model options.

Median estimates from Cox models are of course fine in that sense, as long as $$>> 50\%$$ have had the event and the number with an even is large enough. Otherwise the estimate has a large sampling variability and you might be better off using an appropriate parametric model, if you know which one would be adequate for the problem at hand. A problem, again is that when we do not see events for everyone, we make assumptions about what distributions could describe their survival times. If we see times of death for everyone, then we can look whether e.g. a Weibull distribution seems to fit. One difficult in interpretation is that you could get something that looks like Weibull distributed event times in multiple ways (and it's pretty hard to tell the difference): 1) changing hazard rate over time for everyone (conditional on covariates), 2) actually the event rate is constant for everyone, but varies between individuals.