Stratification on the propensity score and covariate adjustment using the propensity score are the two other propensity score methods19 . With covariate adjustment using the propensity score, one regresses the outcome on the propensity score and an indicator variable denoting treatment selection. With time-to-event outcomes, a Cox proportional hazards model would be used to regress the hazard of the occurrence of the outcome on the propensity score and an indicator variable denoting treatment status. This approach has been shown to result in biased estimation of marginal hazard ratios30 . Furthermore, it has also been shown to result in a biased estimate of the conditional hazard ratio that would result from adjusting for all the prognostically important covariates in a multivariable Cox regression model46 (link).
Stratification on the propensity score involves stratifying subjects into mutually exclusive subsets based on their estimated propensity score. In practice, analysts often use five subclasses on the basis of the quintiles of the estimated propensity score. When estimating linear treatment effects, stratum-specific estimates of effect are obtained. These stratum-specific estimates are then pooled to obtain an overall estimate of treatment effect. There are three ways in which one could estimate a hazard ratio using stratification on the propensity score. First, one can estimate stratum-specific Cox regression models in which survival is regressed on treatment selection. The stratum-specific log-hazard ratios are then pooled or averaged to obtain a pooled hazard ratio. Second, one can regress survival on an indicator variable denoting treatment status and a categorical variable denoting the propensity score strata. Third, one can regress survival on an indicator variable denoting treatment status and stratify on the propensity score strata, thereby allowing the baseline hazard to vary across strata. While stratification performs well for estimating linear treatment effects19 , it results in biased estimation of marginal hazard ratios30 . Furthermore, one implementation of stratification has also been shown to result in a biased estimate of the conditional hazard ratio that would result from adjusting for all the prognostically important covariates in a multivariable Cox regression model46 (link). It appears that each of these approaches results in an estimate of a conditional hazard ratio, rather than a marginal hazard ratio. Further research is required to determine how these conditional hazard ratios differ from that obtained by adjusting for the prognostically important covariates in a conventional Cox regression model.
Because our focus is on methods that allow estimation of both marginal survival curves and marginal hazard ratios, we do not consider these two propensity score methods further in this study.
Stratification on the propensity score involves stratifying subjects into mutually exclusive subsets based on their estimated propensity score. In practice, analysts often use five subclasses on the basis of the quintiles of the estimated propensity score. When estimating linear treatment effects, stratum-specific estimates of effect are obtained. These stratum-specific estimates are then pooled to obtain an overall estimate of treatment effect. There are three ways in which one could estimate a hazard ratio using stratification on the propensity score. First, one can estimate stratum-specific Cox regression models in which survival is regressed on treatment selection. The stratum-specific log-hazard ratios are then pooled or averaged to obtain a pooled hazard ratio. Second, one can regress survival on an indicator variable denoting treatment status and a categorical variable denoting the propensity score strata. Third, one can regress survival on an indicator variable denoting treatment status and stratify on the propensity score strata, thereby allowing the baseline hazard to vary across strata. While stratification performs well for estimating linear treatment effects19 , it results in biased estimation of marginal hazard ratios30 . Furthermore, one implementation of stratification has also been shown to result in a biased estimate of the conditional hazard ratio that would result from adjusting for all the prognostically important covariates in a multivariable Cox regression model46 (link). It appears that each of these approaches results in an estimate of a conditional hazard ratio, rather than a marginal hazard ratio. Further research is required to determine how these conditional hazard ratios differ from that obtained by adjusting for the prognostically important covariates in a conventional Cox regression model.
Because our focus is on methods that allow estimation of both marginal survival curves and marginal hazard ratios, we do not consider these two propensity score methods further in this study.
