A Test for the Correct Specification of Marginal Structural Models

• Activity Number: 160 - Novel Perspectives on the Estimation of Longitudinal Effects
• Type: Topic Contributed
• Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 11:50 AM
• Sponsor: SSC (Statistical Society of Canada)
• Author(s): Denis Talbot* and Alioune Sall and Karine Aube and Xavier Trudel and Chantal Brisson
• Companies: Universite Laval and Universite Laval and Universite Laval and Universite Laval and Universite Laval
• Keywords: Causal inference; Marginal structural models; Model specification; Longitudinal Data

Abstract

Marginal structural models allow estimating causal contrasts between different treatment regimes in the presence of time-dependent confounding. One key assumption for unbiasedly estimating these contrasts is that the structural model, which relates the counterfactual outcome to the time-varying treatment, is correctly specified. We introduce a test for verifying if a given proposed specification for the structural outcome model is correct. This test takes advantage of the fact that there exist various inverse probability weighting estimators of the parameters of a marginal structural model that converge toward the true parameters when the structural model is correctly specified. However, when the structural model is incorrectly specified, these estimators can converge to different values. To verify if a proposed specification is correct, we thus propose a Wald test based on the difference between the estimates obtained with different weighting estimators. The theoretical distribution of the test will be discussed and simulation studies are used to investigate and compare the performance of different versions of the test.