Causal Effect Estimation Using Instrumental Variable Approaches for Log-Linear Structural Nested Mean Models in the Presence of Unmeasured Confounding

• Activity Number: 451
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Chia-Hao Wang*+ and Marshall M. Joffe and Thomas R. Ten Have
• Companies: University of Pennsylvania School of Medicine and University of Pennsylvania and University of Pennsylvania School of Medicine
• Keywords: Bias ; Instrumental variables ; Structural nested mean model ; Unmeasured confounding

Abstract

We extend two common methods for instrumental variable estimation under linear models to a log-linear structural nested mean model (SNMM) to control for unmeasured confounding. The two IV approaches are two-stage predictor substitution (2SPS) and two-stage residual inclusion (2SRI). The theoretical and empirical properties of these IV methods for log-linear SNMM and standard log-linear regression are presented with and without adjustments for violations of the exclusion restriction, which is typically made for IV estimation. When there is no unmeasured confounding, the results show that the standard log-linear regression and 2SRI method yield unbiased estimates while the estimates are biased using the 2SPS method. When unmeasured confounding is present, all three methods yield biased estimates. These results hold regardless of whether the exclusion restriction holds and is adjusted for.