Propensity Score Subclassification and Its Applications to Social Work Research

Purpose: Propensity score matching (PSM) has been increasingly applied to social work research to address challenging questions concerning causality. Relatively speaking, propensity score subclassification (PSS) has not been widely applied. The PSS method was originally developed by Rosenbaum and Rubin in their seminal paper (1983) and serves similar functions as PSM. Recent studies show numerous advantages of PSS, including its ability to retain observations from the original sample, easy application, and versatility to accommodate various outcome analyses (e.g., survival analysis, categorical outcome analysis, HLM, SEM, and more). In their recent review of econometric methods of program evaluation, Imbens and Wooldridge (2009) recommend three propensity score approaches, and PSS is one of them. This workshop employs the panel data of the National Survey of Child Adolescent Well-being (NSCAW) to demonstrate the application of PSS to a child welfare study.

Methods: The key feature of subclassificaiton is to make participants within a stratum as homogeneous as possible in terms of estimated propensity scores. Comparing to the classic covariate subclassificaiton, it overcomes the dimensionality problem by using a summary “propensity score”. Cochran (1968) shows that a subclassification of five groups effectively removes bias of 90%. Rosenbaum and Rubin (1983, 1984) prove that the propensity score is an efficient balancing score that corrects for overt selection bias. After subclassification using quintiles or deciles of propensity scores, researchers conduct a multivariate outcome analysis for each stratum; aggregating treatment effects over all five or ten subclasses, researchers can make an estimate of treatment effect for the entire sample and discern whether or not the overall treatment effect is statistically significant.

Contents: The workshop will focus on the following topics: (1) review of the PSS procedure, (2) the dimensionality problem in covariate subclssification, (3) the overlap assumption and approaches to address its violation, and (4) presentation of an illustrating example.

Findings: Using the NSCAW data, the illustration shows that the PSS sufficiently removes selection bias created by 16 observed covariates, retains more observations than PSM, and permits an outcome analysis using Cox regression. By controlling for selection bias, the study shows that children whose caregivers used substance abuse treatment are more likely to receive a maltreatment rereport, and the hazard of having rereport for these children is 45.52% higher than that of children whose caregivers did not use the treatment. The treatment effect estimated by PSS is not statistically significant, while the same effect estimated by the Cox regression without controlling for selection bias is significant at the .001 level. The significant finding from the uncontrolled model may be biased due to the failure of controlling for selectivity.

 Implications: The workshop is a step-by-step demonstration of the PSS method. Participants will learn effective and efficient methods of causal inference from the workshop to address challenging problems of selectivity when PSM is infeasible.

 Pedagogical Techniques:  Teaching methods include lecture, PowerPoint presentation, and computer demonstration of running the Stata software.