Causal Inference for Multilevel Data Through Propensity Score and Prognostic Score Adjustment: The Case of Bernoulli-Distributed Outcomes

• Activity Number: 457
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Bing Yu*+ and Guanglei Hong
• Companies: University of Toronto and The University of Chicago
• Keywords: Bias ; Confidence interval ; Variance ; MSE ; Logistic regression ; Link function

Abstract

For a binary outcome, the treatment effect is often defined as an odds ratio and is estimated through a logistic regression model. The conditional treatment effect is unequal to the marginal treatment effect that is nonzero. In propensity score applications, this inequality leads to a biased estimate of a nonzero marginal treatment effect. Linking the marginal treatment effect with the propensity score-adjusted conditional treatment effect has been a major challenge especially for multilevel data. This paper examines, across a variety of multilevel data structures with a Bernoulli distributed outcome, the effectiveness of alternative variable selection and model specifications for propensity score and prognostic score adjustment. Different link functions are also under investigation. Evaluation criteria include bias, precision, MSE, remaining sample size after stratification, and confidence interval coverage percentage. We use simulated data to evaluate alternative approaches and then illustrate the results with a real data example.