INFLUENCE FUNCTION BASED COVARIANCE MATRIX FOR SUMMARY STATISTICS OF SURVIVAL DATA

When multiple survival summaries are reported from the same clinical trial, joint uncertainty and agreement between estimators depend on their within-trial covariance structure. This note revisits covariance estimation for a vector comprising a fixed-time survival difference, an RMST difference, and a Cox log-hazard ratio under proportional hazards. Using asymptotic linearity and influence functions, we derive plug-in covariance estimators as empirical second moments of estimated influence values and express them in standard event-time (Greenwood-type) form. We then map these expressions to the stochastic-integral representation used by Ristl et al. and show that the resulting plug-in estimators coincide after matching notation and conventions, with remaining differences attributable to implementation choices such as tie handling and numerical integration of RMST.