Shrinkage Priors for Isotonic Probability Vectors and Binary Data Modeling

This paper outlines a new class of shrinkage priors for Bayesian isotonic regression modeling a binary outcome against a predictor, where the probability of the outcome is assumed to be monotonically non-decreasing with the predictor. The predictor is categorized into a large number of groups, and the set of differences between outcome probabilities in consecutive categories is equipped with a multivariate prior having support over the set of simplexes. The Dirichlet distribution, which can be derived from a normalized cumulative sum of gamma-distributed random variables, is a natural choice of prior, but using mathematical and simulation-based arguments, we show that the resulting posterior can be numerically unstable, even under simple data configurations. We propose an alternative prior motivated by horseshoe-type shrinkage that is numerically more stable. We show that this horseshoe-based prior is not subject to the numerical instability seen in the Dirichlet/gamma-based prior and that the posterior can estimate the underlying true curve more efficiently than the Dirichlet distribution. We demonstrate the use of this prior in a model predicting the occurrence of radiation-induced lung toxicity in lung cancer patients as a function of dose delivered to normal lung tissue

Estimating Marginal Hazard Ratios by Simultaneously Using A Set of Propensity Score Models: A Multiply Robust Approach

The inverse probability weighted Cox model is frequently used to estimate marginal hazard ratios. Its validity requires a crucial condition that the propensity score model is correctly specified. To provide protection against misspecification of the propensity score model, we propose a weighted estimation method rooted in empirical likelihood theory. The proposed estimator is multiply robust in that it is guaranteed to be consistent when a set of postulated propensity score models contains a correctly specified model. Our simulation studies demonstrate satisfactory finite sample performance of the proposed method in terms of consistency and efficiency. We apply the proposed method to compare the risk of postoperative hospitalization between sleeve gastrectomy and Roux-en-Y gastric bypass using data from a large medical claims and billing database.We further extend the development to multi-site studies to enable each site to postulate multiple site-specific propensity score models

Power calculation for cross-sectional stepped-wedge cluster randomized trials with binary outcomes

Power calculation for stepped-wedge cluster randomized trials (SW-CRTs) presents unique challenges, beyond those of standard cluster randomized trials (CRTs), due to the need to consider temporal within cluster correlations and background period effects. To date, power calculation methods specific to SW-CRTs have primarily been developed under a linear model. When the outcome is binary, the use of a linear model corresponds to assessing a prevalence difference; yet trial analysis often employs a non-linear link function. We assess power for cross-sectional SW-CRTs under a logistic model fitted by generalized estimating equations. Firstly, under an exchangeable correlation structure, we show the power based on a logistic model is lower than that from assuming a linear model in the absence of period effects. We then evaluate the impact of background prevalence changes over time on power. To allow the correlation among outcomes in the same cluster to change over time and with treatment status, we generalize the methods to more complex correlation structures. Our simulation studies demonstrate that the proposed power calculation methods perform well with the model-based variance under the true correlation structure and reveal that a working independence structure can result in substantial efficiency loss, while a working exchangeable structure performs well even when the underlying correlation structure deviates from exchangeable. An extension to our methods accounts for variable cluster sizes and reveals unequal cluster sizes have a modest impact on power. We illustrate the approaches by application to a quality of care improvement trial for acute coronary syndrome

Survival mediation analysis with the death-truncated mediator: The completeness of the survival mediation parameter

In medical research, the development of mediation analysis with a survival outcome has facilitated investigation into causal mechanisms. However, studies have not discussed the death-truncation problem for mediators, the problem being that conventional mediation parameters cannot be well-defined in the presence of a truncated mediator. In the present study, we systematically defined the completeness of causal effects to uncover the gap, in conventional causal definitions, between the survival and nonsurvival settings. We proposed three approaches to redefining the natural direct and indirect effects, which are generalized forms of the conventional causal effects for survival outcomes. Furthermore, we developed three statistical methods for the binary outcome of the survival status and formulated a Cox model for survival time. We performed simulations to demonstrate that the proposed methods are unbiased and robust. We also applied the proposed method to explore the effect of hepatitis C virus infection on mortality, as mediated through hepatitis B viral load

Randomization-Based Confidence Intervals for Cluster Randomized Trials

In a cluster randomized trial (CRT), groups of people are randomly assigned to different interventions. Existing parametric and semiparametric methods for CRTs rely on distributional assumptions or a large number of clusters to maintain nominal confidence interval (CI) coverage. Randomization-based inference is an alternative approach that is distribution-free and does not require a large number of clusters to be valid. Although it is well-known that a CI can be obtained by inverting a randomization test, this requires randomization testing a non-zero null hypothesis, which is challenging with non-continuous and survival outcomes. In this paper, we propose a general method for randomization-based CIs using individual-level data from a CRT. This fast and flexible approach accommodates various outcome types, can account for design features such as matching or stratification, and employs a computationally efficient algorithm. We evaluate this method\u27s performance through simulations and apply it to the Botswana Combination Prevention Project, a large HIV prevention trial with an interval-censored time-to-event outcome

Integrated multiple mediation analysis: A robustness–specificity trade-off in causal structure

Recent methodological developments in causal mediation analysis have addressed several issues regarding multiple mediators. However, these developed methods differ in their definitions of causal parameters, assumptions for identification, and interpretations of causal effects, making it unclear which method ought to be selected when investigating a given causal effect. Thus, in this study, we construct an integrated framework, which unifies all existing methodologies, as a standard for mediation analysis with multiple mediators. To clarify the relationship between existing methods, we propose four strategies for effect decomposition: two-way, partially forward, partially backward, and complete decompositions. This study reveals how the direct and indirect effects of each strategy are explicitly and correctly interpreted as path-specific effects under different causal mediation structures. In the integrated framework, we further verify the utility of the interventional analogues of direct and indirect effects, especially when natural direct and indirect effects cannot be identified or when cross-world exchangeability is invalid. Consequently, this study yields a robustness–specificity trade-off in the choice of strategies. Inverse probability weighting is considered for estimation. The four strategies are further applied to a simulation study for performance evaluation and for analyzing the Risk Evaluation of Viral Load Elevation and Associated Liver Disease/Cancer data set from Taiwan to investigate the causal effect of hepatitis C virus infection on mortality

A modular framework for early-phase seamless oncology trials

Background: As our understanding of the etiology and mechanisms of cancer becomes more sophisticated and the number of therapeutic options increases, phase I oncology trials today have multiple primary objectives. Many such designs are now \u27seamless\u27, meaning that the trial estimates both the maximum tolerated dose and the efficacy at this dose level. Sponsors often proceed with further study only with this additional efficacy evidence. However, with this increasing complexity in trial design, it becomes challenging to articulate fundamental operating characteristics of these trials, such as (i) what is the probability that the design will identify an acceptable, i.e. safe and efficacious, dose level? or (ii) how many patients will be assigned to an acceptable dose level on average? Methods: In this manuscript, we propose a new modular framework for designing and evaluating seamless oncology trials. Each module is comprised of either a dose assignment step or a dose-response evaluation, and multiple such modules can be implemented sequentially. We develop modules from existing phase I/II designs as well as a novel module for evaluating dose-response using a Bayesian isotonic regression scheme. Results: We also demonstrate a freely available R package called seamlesssim to numerically estimate, by means of simulation, the operating characteristics of these modular trials. Conclusions: Together, this design framework and its accompanying simulator allow the clinical trialist to compare multiple different candidate designs, more rigorously assess performance, better justify sample sizes, and ultimately select a higher quality design

Estimation of Conditional Power for Cluster-Randomized Trials with Interval-Censored Endpoints

Cluster-randomized trials (CRTs) of infectious disease preventions often yield correlated, interval-censored data: dependencies may exist between observations from the same cluster, and event occurrence may be assessed only at intermittent clinic visits. This data structure must be accounted for when conducting interim monitoring and futility assessment for CRTs. In this article, we propose a flexible framework for conditional power estimation when outcomes are correlated and interval-censored. Under the assumption that the survival times follow a shared frailty model, we first characterize the correspondence between the marginal and cluster-conditional survival functions, and then use this relationship to semiparametrically estimate the cluster-specific survival distributions from the available interim data. We incorporate assumptions about changes to the event process over the remainder of the trial---as well as estimates of the dependency among observations in the same cluster---to extend these survival curves through the end of the study. Based on these projected survival functions we generate correlated interval-censored observations, and then calculate the conditional power as the proportion of times (across multiple full-data generation steps) that the null hypothesis of no treatment effect is rejected. We evaluate the performance of the proposed method through extensive simulation studies, and illustrate its use on a large cluster-randomized HIV prevention trial

Robust inference on effects attributable to mediators: A controlled-direct-effect-based approach for causal effect decomposition with multiple mediators

Effect decomposition is a critical technique for mechanism investigation in settings with multiple causally ordered mediators. Causal mediation analysis is a standard method for effect decomposition, but the assumptions required for the identification process are extremely strong. By extending the framework of controlled direct effects, this study proposes the effect attributable to mediators (EAM) as a novel measure for effect decomposition. For policy making, EAM represents how much an effect can be eliminated by setting mediators to certain values. From the perspective of mechanism investigation, EAM contains information about how much a particular mediator or set of mediators is involved in the causal mechanism through mediation, interaction, or both. The assumptions of EAM for identification are considerably weaker than the those of causal mediation analysis. We develop a semiparametric estimator of EAM with robustness to model misspecification. The asymptotic property is fully realized. We applied EAM to assess the magnitude of the effect of hepatitis C virus infection on mortality, which was eliminated by controlling alanine aminotransferase and treating hepatocellular carcinoma

Potential health risks linked to emerging contaminants in major rivers and treated waters

The presence of endocrine-disrupting chemicals (EDCs) in our local waterways is becoming an increasing threat to the surrounding population. These compounds and their degradation products (found in pesticides, herbicides, and plastic waste) are known to interfere with a range of biological functions from reproduction to differentiation. To better understand these effects, we used an in silico ontological pathway analysis to identify the genes affected by the most commonly detected EDCs in large river water supplies, which we grouped together based on four common functions: Organismal injuries, cell death, cancer, and behavior. In addition to EDCs, we included the opioid buprenorphine in our study, as this similar ecological threat has become increasingly detected in river water supplies. Through the identification of the pleiotropic biological effects associated with both the acute and chronic exposure to EDCs and opioids in local water supplies, our results highlight a serious health threat worthy of additional investigations with a potential emphasis on the effects linked to increased DNA damage