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There is a growing demand for methods to determine the effects that chemical mixtures have on human health. One statistical challenge is identifying true "bad actors" from a mixture of highly correlated predictors, a setting in which standard approaches such as linear regression become highly variable. Weighted Quantile Sum regression has been proposed to address this problem, through a two-step process where mixture component weights are estimated using bootstrap aggregation in a training dataset and inference on the overall mixture effect occurs in a held-out test set. Weighted Quantile Sum regression is popular in applied papers, but the reliance on data splitting is suboptimal, and analysts who use the same data for both steps risk inflating the Type I error rate. We therefore propose a modification of Weighted Quantile Sum regression that uses a permutation test for inference, which allows for weight estimation using the entire dataset and preserves Type I error. To minimize computational burden, we propose replacing the bootstrap with L1 or L2 penalization and describe how to choose the appropriate penalty given expert knowledge about a mixture of interest. We apply our method to a national pregnancy cohort study of prenatal phthalate exposure and child health outcomes. [ABSTRACT FROM AUTHOR]

Definitive clinical trials are resource intensive, often requiring a large number of participants over several years. One approach to improve the efficiency of clinical trials is to incorporate historical information into the primary trial analysis. This approach has tremendous potential in the areas of pediatric or rare disease trials, where achieving reasonable power is difficult. In this article, we introduce a novel Bayesian group‐sequential trial design based on Multisource Exchangeability Models, which allows for dynamic borrowing of historical information at the interim analyses. Our approach achieves synergy between group sequential and adaptive borrowing methodology to attain improved power and reduced sample size. We explore the frequentist operating characteristics of our design through simulation and compare our method to a traditional group‐sequential design. Our method achieves earlier stopping of the primary study while increasing power under the alternative hypothesis but has a potential for type I error inflation under some null scenarios. We discuss the issues of decision boundary determination, power and sample size calculations, and the issue of information accrual. We present our method for a continuous and binary outcome, as well as in a linear regression setting. [ABSTRACT FROM AUTHOR]

The increasing multiplicity of data sources offers exciting possibilities in estimating the effects of a treatment, intervention, or exposure, particularly if observational and experimental sources could be used simultaneously. Borrowing between sources can potentially result in more efficient estimators, but it must be done in a principled manner to mitigate increased bias and Type I error. Furthermore, when the effect of treatment is confounded, as in observational sources or in clinical trials with noncompliance, causal effect estimators are needed to simultaneously adjust for confounding and to estimate effects across data sources. We consider the problem of estimating causal effects from a primary source and borrowing from any number of supplemental sources. We propose using regression‐based estimators that borrow based on assuming exchangeability of the regression coefficients and parameters between data sources. Borrowing is accomplished with multisource exchangeability models and Bayesian model averaging. We show via simulation that a Bayesian linear model and Bayesian additive regression trees both have desirable properties and borrow under appropriate circumstances. We apply the estimators to recently completed trials of very low nicotine content cigarettes investigating their impact on smoking behavior. [ABSTRACT FROM AUTHOR]

Treatment effect heterogeneity occurs when individual characteristics influence the effect of a treatment. We propose a novel approach that combines prognostic score matching and conditional inference trees to characterize effect heterogeneity of a randomized binary treatment. One key feature that distinguishes our method from alternative approaches is that it controls the Type I error rate, that is, the probability of identifying effect heterogeneity if none exists and retains the underlying subgroups. This feature makes our technique particularly appealing in the context of clinical trials, where there may be significant costs associated with erroneously declaring that effects differ across population subgroups. Treatment effect heterogeneity trees are able to identify heterogeneous subgroups, characterize the relevant subgroups and estimate the associated treatment effects. We demonstrate the efficacy of the proposed method using a comprehensive simulation study and illustrate our method using a nutrition trial dataset to evaluate effect heterogeneity within a patient population. [ABSTRACT FROM AUTHOR]