Sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures

Abstract

Robins introduced marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators for the causal effect of a time-varying treatment on the mean of repeated measures. We investigate the sensitivity of IPTW estimators to unmeasured confounding. We examine a new framework for sensitivity analyses based on a nonidentifiable model that quantifies unmeasured confounding in terms of a sensitivity parameter and a user-specified function. We present augmented IPTW estimators of MSM parameters and prove their consistency for the causal effect of an MSM, assuming a correct confounding bias function for unmeasured confounding. We apply the methods to assess sensitivity of the analysis of Hernán et al., who used an MSM to estimate the causal effect of zidovudine therapy on repeated CD4 counts among HIV-infected men in the Multicenter AIDS Cohort Study. Under the assumption of no unmeasured confounders, a 95 per cent confidence interval for the treatment effect includes zero. We show that under the assumption of a moderate amount of unmeasured confounding, a 95 per cent confidence interval for the treatment effect no longer includes zero. Thus, the analysis of Hernán et al. is somewhat sensitive to unmeasured confounding. We hope that our research will encourage and facilitate analyses of sensitivity to unmeasured confounding in other applications.

Missing Confounding Data in Marginal Structural Models: A Comparison of Inverse Probability Weighting and Multiple Imputation

“…Specifically, we require no unmeasured confounding (sequential randomization), time ordering (exposure precedes outcome) and consistency (Mortimer et al, 2005;Brumback et al, 2004). Also, we require that all treatments are possible (i.e., the probability of receiving treatment is neither zero nor one) given the covariates (the experimental treatment assumption) Mortimer et al, 2005).…”

“…MSMs are particularly useful for the analysis of observational drug data Hernán et al, 2000). However, more commonly than not, some individuals in longitudinal studies have missing covariate information, and omission of an important variable from the probability of treatment model can lead to biased inference (Brumback et al, 2004). In general, inappropriate handling of the missing data in the analysis can lead to incorrect conclusions, either because of biased treatment effect estimates or reduced power (or both).…”

The Impact of Academic Patenting on the Rate, Quality, and Direction of (Public) Research Output

“…We present a sensitivity analysis for unmeasured confounding, following Robins (1999a) and Brumback et al (2004). The basic approach is similar to that adopted by other researchers who have evaluated the robustness of non-experimental estimators in the presence of selectivity (see for example Altonji et al (2005) for the case of Heckman two-step estimators and Rosenbaum (2002, chap.…”

Graphical Causal Models

“…See Wodtke et al (2011) for a sociological application to the joint effects of time-varying neighborhood conditions on education. See Sharkey and Elwert (2011) for an example of a formal sensitivity analysis for model violations (Robins 1999;Brumback et al 2004).…”