Sensitivity Analysis for Multiple Comparisons in Matched Observational Studies through Quadratically Constrained Linear Programming

A sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding. While sensitivity analyses in matched observational studies have been well addressed when there is a single outcome variable, accounting for multiple comparisons through the existing methods yields overly conservative results when there are multiple outcome variables of interest. This stems from the fact that unmeasured confounding cannot affect the probability of assignment to treatment differently depending on the outcome being analyzed. Existing methods allow this to occur by combining the results of individual sensitivity analyses to assess whether at least one hypothesis is significant, which in turn results in an overly pessimistic assessment of a study's sensitivity to unobserved biases. By solving a quadratically constrained linear program, we are able to perform a sensitivity analysis while enforcing that unmeasured confounding must have the same impact on the treatment assignment probabilities across outcomes for each individual in the study. We show that this allows for uniform improvements in the power of a sensitivity analysis not only for testing the overall null of no effect, but also for null hypotheses on \textit{specific} outcome variables while strongly controlling the familywise error rate. We illustrate our method through an observational study on the effect of smoking on naphthalene exposure

Mediation Analysis Without Sequential Ignorability: Using Baseline Covariates Interacted with Random Assignment as Instrumental Variables

In randomized trials, researchers are often interested in mediation analysis to understand how a treatment works, in particular how much of a treatment's effect is mediated by an intermediated variable and how much the treatment directly affects the outcome not through the mediator. The standard regression approach to mediation analysis assumes sequential ignorability of the mediator, that is that the mediator is effectively randomly assigned given baseline covariates and the randomized treatment. Since the experiment does not randomize the mediator, sequential ignorability is often not plausible. Ten Have et al. (2007, Biometrics), Dunn and Bentall (2007, Statistics in Medicine) and Albert (2008, Statistics in Medicine) presented methods that use baseline covariates interacted with random assignment as instrumental variables, and do not require sequential ignorability. We make two contributions to this approach. First, in previous work on the instrumental variable approach, it has been assumed that the direct effect of treatment and the effect of the mediator are constant across subjects; we allow for variation in effects across subjects and show what assumptions are needed to obtain consistent estimates for this setting. Second, we develop a method of sensitivity analysis for violations of the key assumption that the direct effect of the treatment and the effect of the mediator do not depend on the baseline covariates

Estimation of causal effects using instrumental variables with nonignorable missing covariates: Application to effect of type of delivery NICU on premature infants

Understanding how effective high-level NICUs (neonatal intensive care units that have the capacity for sustained mechanical assisted ventilation and high volume) are compared to low-level NICUs is important and valuable for both individual mothers and for public policy decisions. The goal of this paper is to estimate the effect on mortality of premature babies being delivered in a high-level NICU vs. a low-level NICU through an observational study where there are unmeasured confounders as well as nonignorable missing covariates. We consider the use of excess travel time as an instrumental variable (IV) to control for unmeasured confounders. In order for an IV to be valid, we must condition on confounders of the IV---outcome relationship, for example, month prenatal care started must be conditioned on for excess travel time to be a valid IV. However, sometimes month prenatal care started is missing, and the missingness may be nonignorable because it is related to the not fully measured mother's/infant's risk of complications. We develop a method to estimate the causal effect of a treatment using an IV when there are nonignorable missing covariates as in our data, where we allow the missingness to depend on the fully observed outcome as well as the partially observed compliance class, which is a proxy for the unmeasured risk of complications. A simulation study shows that under our nonignorable missingness assumption, the commonly used estimation methods, complete-case analysis and multiple imputation by chained equations assuming missingness at random, provide biased estimates, while our method provides approximately unbiased estimates. We apply our method to the NICU study and find evidence that high-level NICUs significantly reduce deaths for babies of small gestational age, whereas for almost mature babies like 37 weeks, the level of NICUs makes little difference. A sensitivity analysis is conducted to assess the sensitivity of our conclusions to key assumptions about the missing covariates. The method we develop in this paper may be useful for many observational studies facing similar issues of unmeasured confounders and nonignorable missing data as ours.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS699 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org