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  1. Summary

    Comparative effectiveness research often involves evaluating the differences in the risks of an event of interest between two or more treatments using observational data. Often, the post‐treatment outcome of interest is whether the event happens within a pre‐specified time window, which leads to a binary outcome. One source of bias for estimating the causal treatment effect is the presence of confounders, which are usually controlled using propensity score‐based methods. An additional source of bias is right‐censoring, which occurs when the information on the outcome of interest is not completely available due to dropout, study termination, or treatment switch before the event of interest. We propose an inverse probability weighted regression‐based estimator that can simultaneously handle both confounding and right‐censoring, calling the method CIPWR, with the letter C highlighting the censoring component. CIPWR estimates the average treatment effects by averaging the predicted outcomes obtained from a logistic regression model that is fitted using a weighted score function. The CIPWR estimator has a double robustness property such that estimation consistency can be achieved when either the model for the outcome or the models for both treatment and censoring are correctly specified. We establish the asymptotic properties of the CIPWR estimator for conducting inference, and compare its finite sample performance with that of several alternatives through simulation studies. The methods under comparison are applied to a cohort of prostate cancer patients from an insurance claims database for comparing the adverse effects of four candidate drugs for advanced stage prostate cancer.

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  2. The statistical practice of modeling interaction with two linear main effects and a product term is ubiquitous in the statistical and epidemiological literature. Most data modelers are aware that the misspecification of main effects can potentially cause severe type I error inflation in tests for interactions, leading to spurious detection of interactions. However, modeling practice has not changed. In this article, we focus on the specific situation where the main effects in the model are misspecified as linear terms and characterize its impact on common tests for statistical interaction. We then propose some simple alternatives that fix the issue of potential type I error inflation in testing interaction due to main effect misspecification. We show that when using the sandwich variance estimator for a linear regression model with a quantitative outcome and two independent factors, both the Wald and score tests asymptotically maintain the correct type I error rate. However, if the independence assumption does not hold or the outcome is binary, using the sandwich estimator does not fix the problem. We further demonstrate that flexibly modeling the main effect under a generalized additive model can largely reduce or often remove bias in the estimates and maintain the correct type I error rate for both quantitative and binary outcomes regardless of the independence assumption. We show, under the independence assumption and for a continuous outcome, overfitting and flexibly modeling the main effects does not lead to power loss asymptotically relative to a correctly specified main effect model. Our simulation study further demonstrates the empirical fact that using flexible models for the main effects does not result in a significant loss of power for testing interaction in general. Our results provide an improved understanding of the strengths and limitations for tests of interaction in the presence of main effect misspecification. Using data from a large biobank study “The Michigan Genomics Initiative”, we present two examples of interaction analysis in support of our results.

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  3. We consider comparative effectiveness research (CER) from observational data with two or more treatments. In observational studies, the estimation of causal effects is prone to bias due to confounders related to both treatment and outcome. Methods based on propensity scores are routinely used to correct for such confounding biases. A large fraction of propensity score methods in the current literature consider the case of either two treatments or continuous outcome. There has been extensive literature with multiple treatment and binary outcome, but interest often lies in the intersection, for which the literature is still evolving. The contribution of this article is to focus on this intersection and compare across methods, some of which are fairly recent. We describe propensity‐based methods when more than two treatments are being compared, and the outcome is binary. We assess the relative performance of these methods through a set of simulation studies. The methods are applied to assess the effect of four common therapies for castration‐resistant advanced‐stage prostate cancer. The data consist of medical and pharmacy claims from a large national private health insurance network, with the adverse outcome being admission to the emergency room within a short time window of treatment initiation.

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