A Unifying Framework for Assessing Bias in Two-Stage Instrumental Variable Models

• Activity Number: 10
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Nandita Mitra* and Fei Wan and Dylan Small
• Companies: University of Pennsylvania and University of Pennsylvania and University of Pennsylvania
• Keywords: instrumental variables ; bias ; dissimilarity metric ; observational study ; two-stage models ; non-linear models

Abstract

Two stage instrumental variable methods are often used to compare treatment effects in observational studies. Specifically, for non-linear outcomes, two stage residual inclusion (2SRI) has been the method of choice over two stage predictor substitution (2SPS). We propose a unifying regression-based framework to understanding the bias in these two approaches when the outcome is binary, counts or time to event. Under this framework, we demonstrate that only if the influence of the unmeasured covariates on the treatment is proportional to their effect on the outcome, then 2SRI estimates will be unbiased. We propose a novel dissimilarity metric to quantify the difference in these effects and demonstrate that with increasing dissimilarity, the bias increases in magnitude. Using extensive Monte-Carlo simulations we show that this bias is greatest when the outcome is time to event and binary compared to count data. We demonstrate the sensitivity of results to increasing dissimilarity between the effects of the unmeasured covariate on the treatment versus outcome using data from a study of the effect of hospital volume on mortality rates of premature babies.