Propensity stratification divides the observations into strata that have similar propensity scores, with the objective of balancing the observed variables between treated and control units within each stratum. The treatment effect can then be estimated by combining stratum-specific estimates of treatment effect. Rosenbaum and Rubin (1984, p. 521) show that an adjusted estimate of this type that is based on five strata can remove approximately 90% of the bias in the crude or unadjusted estimate.
The PSMATCH procedure performs stratification when you specify the STRATA statement, which divides the observations contained in the support region into strata (you specify the support region in the REGION= option in the PROC PSMATCH statement).
In general, when observations are stratified, it is common to require the same number of observations in each stratum. However, in the context of propensity score analysis, the number of units in the control group tends to be much larger than the number of units in the treated group. Consequently, this requirement can produce strata for which the number of units in the treated group is insufficient to compute reliable stratum-specific estimates of the treatment effect.
The KEY=TREATED option (which is the default) in the STRATA statement avoids this problem by allocating approximately the same number of treated units to each stratum. Alternatively, you can specify the KEY=TOTAL option to allocate approximately the same number of observations (for either treated or control units) to each stratum. Regardless of the method of allocation, you should ensure that the number of treated units and the number of control units in each stratum are sufficient to estimate the treatment effect.
To assess the variable balance after stratification, you can use the STRATUMWGT= option in the STRATA statement to specify the stratum weights, compute the weighted averages of stratum-specific variable averages in the treated group and in the control group, and then compare the resulting weighted averages between the treated and control groups.
In the outcome analysis, you can use the weighted average of the stratum-specific treatment estimates to estimate the treatment effect. You can estimate the ATT if you weight by the stratum-specific number of treated units, and you can estimate the ATE if you weight by the stratum-specific number of units (treated and control units combined) (Stuart 2010, p. 13; Guo and Fraser 2015, pp. 76–77).
The STRATUMWGT=TOTAL option uses the proportional size of the stratum as the stratum weight. The proportional size is the number of total units (treated and control) in the stratum divided by the total number of units. Stratum weights of this type are appropriate for estimating the ATE. The STRATUMWGT=TREATED option uses the proportional number of treated units as the stratum weight. This number is the number of treated units in the stratum divided by the total number of treated units. Stratum weights of this type are appropriate for estimating the ATT. The following section provides more details about weighting after stratification.