My question is:
What is the appropriate estimate of mean survival in a target population defined by a health care provider?
The context is:
Typically, evidence about the relative effects of treatments comes from one or more RCTs and mean survival for each treatment is estimated from some parametric model fitted to the data i.e. with extrapolation to patients lifetimes and without an assumption of proportional hazards. When there is only one RCT it is common to use only the study data and to fit models separately to the data from each treatment arm or with an effect for treatment included for each parameter in the models.
When there are multiple RCTs the studies are typically used to estimate relative effects (e.g. using a network meta-analysis of fractional polynomials for the hazard function) which are “added” to a baseline hazard function in order to generate treatment specific survival functions and mean survival.
A common feature of both situations is that the analysis is of marginal models with no account taken of the sampling scheme or known prognostic factors or treatment effect modifiers. Accepting the principle that clinical trials should be analysed as randomised then we should include any stratification factors and also any known prognostic factors.
My questions are:
How should mean survival for the target population be estimated from a conditional model?
What is the relevance of the joint distribution of the covariates in the target population and how might this be estimated?
What can be said about the interpretation of the estimates of mean survival from marginal and conditional means and the extent to which estimates from a marginal model are biased with invalid estimates of error?