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In observational studies of survival time featuring a binary time-dependenttreatment, the hazard ratio (an instantaneous measure) is often used torepresent the treatment effect. However, investigators are often moreinterested in the difference in survival functions. We propose semiparametricmethods to estimate the causal effect of treatment among the treated withrespect to survival probability. The objective is to compare post-treatmentsurvival with the survival function that would have been observed in theabsence of treatment. For each patient, we compute a prognostic score (based onthe pre-treatment death hazard) and a propensity score (based on the treatmenthazard). Each treated patient is then matched with an alive, uncensored andnot-yet-treated patient with similar prognostic and/or propensity scores. Theexperience of each treated and matched patient is weighted using a variant ofInverse Probability of Censoring Weighting to account for the impact ofcensoring. We propose estimators of the treatment-specific survival functions(and their difference), computed through weighted Nelson-Aalen estimators.Closed-form variance estimators are proposed which take into consideration thepotential replication of subjects across matched sets. The proposed methods areevaluated through simulation, then applied to estimate the effect of kidneytransplantation on survival among end-stage renal disease patients using datafrom a national organ failure registry.

Matching methods for obtaining survival functions to estimate the effect of a time-dependent treatment