# Estimating expected lifetime from hazard ratio and estimated base hazard function

Apologies if this is a basic question, I am not very familiar with survival analysis ...

I have trained a gradient boosted Cox proportional hazards model in R, and have been able to obtain reasonable hazard function estimates from through the gbm package's basehaz.gbm function.

My goal though is to obtain expected lifetimes. How does one go about obtaining these estimates given an estimated base hazard function and hazard ratios? Would it be best to find a parametric fit to the hazard function (or survival function)? Is this usually handled by a discrete approximation using the estimated survival function (and how would one account for the part of the curve unable to be estimated past a certain time due to sparsity of data)?

I've tried both approaches but have not gotten good results, and the standard parametric survival functions don't seem to fit my estimated curve particularly well.