Instrumental variable estimation of causal odds ratios using structural nested mean models

Abstract

We consider estimating causal odds ratios using an instrumental variable under a logistic structural nested mean model (LSNMM). Current methods for LSNMMs either rely heavily on possible "uncongenial" modeling assumptions or involve intricate numerical challenges, which have impeded their use. In this article, we present an alternative method that ensures a congenial parametrization, circumvents computational complexity of existing methods, and is easy to implement. We illustrate the proposed method to (1) estimate the causal effect of years of education on earnings using data from the NLSYM and (2) assess the impact of moving families from high to low-poverty neighborhoods had on lifetime major depressive disorder among adolescents in the "Moving to Opportunity (MTO) for Fair Housing Demonstration Project" from the Department of Housing and Urban Development.

Keywords: Causality; Confounding; Instrumental variable; Non-compliance; Odds ratio; Structural model.