How to obtain an unbiased post-stratified estimator for survival probabilities?

Suppose I have estimated the survival probabilities $\hat{S(t)}_1, \hat{S(t)}_2, \ldots, \hat{S(t)}_H$ from $H$ strata. Now I want to get an unbiased estimate of population survival probability $S(t)$ using these stratum-specific estimates. Then what should be the estimator?

Should it be $\hat{S(t)}_{pst} = \sum_{i=1}^h \dfrac{N_h}{N} \times \hat{S(t)}_h$?

If I want to adjust for under or over representation in the sample, then what should be the estimator (suppose I know the population and sample proportions)?

Thanks for your kind guidance.
No easy way to adjust. At any time horizon T, the event of survival up to T is co-dependent with the stratum membership. Not only do conditional probabilities differ from the unconditional probabilities but they change with T.

The easiest way out is simulating a representative sample of the whole population out of your strata multiple times. For each simulated sample, run survival analysis and get the survival curve. Use the survival curves from multiple simulations to draw the confidence band for the true survival curve.
i want do stratified cox model in R :
but it shows this error :

Error in Surv(t, status) : Time variable is not numeric
pleas help me how can numeric time and whats your idea ?


Omega Contributor
Not a regular R user, but have you looked to see how time is formatted in the dataset?