survfit() functions don't seem to return estimates of coefficients and coefficient-covariance matrices in a form that the
pool() function in
mice can readily use. You can apply Rubin's rules to get pooled estimates including variances, following the principles in Stef van Buuren's book.
An object returned by the
survdiff() function with the default log-rank test contains the numbers of observed and expected (under the null hypothesis) events for each stratum, in the
exp slots respectively. The
var slot contains the corresponding covariance matrix. If there are N strata there are only N-1 independent contributions to
obs-exp, so one stratum needs to be removed for the statistical test, which is a multi-parameter Wald test of the null hypothesis that all of the remaining
obs-exp values are 0.
Section 5.3.1 of van Buuren's book shows how to pool such estimates. A Wald statistic is calculated from the imputation-adjusted pooled covariance matrix (see Section 2.3.2), then evaluated in an F-test having degrees of freedom based on the number of imputations, the number of coefficients, and the fraction of missing information.
D1() function in
mice implements this. I'm not sure how to get the
survdiff() output into the needed form. "Any R expression produced by
expression() can be evaluated on the multiply imputed data," however (Section 5.1.4). One might write an expression to put the needed (linearly independent)
obs-exp and covariance estimates from the
survdiff() models into a format that the broom package can interpret to extract model components for
pool(). (See the documentation for
pool().) I don't have any experience with that, however.
The pooled Kaplan-Meier curves would be the averages of the individual curves, by stratum. The object returned by
survfit() contains standard errors for each event time point, of the type that was specified in the function call. To get closer to the normality assumed by Rubin's rules, choose the
log (default) or the
log-log type, apply Rubin's rules to pool at each time point, then re-transform back to the survival scale.