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A stepped-wedge cluster randomized trial (CRT) is a unidirectional crossover study in which timings of treatment initiation for clusters are randomized. Because the timing of treatment initiation is different for each cluster, an emerging question is whether the treatment effect depends on the exposure time, namely, the time duration since the initiation of treatment. Existing approaches for assessing exposure-time treatment effect heterogeneity either assume a parametric functional form of exposure time or model the exposure time as a categorical variable, in which case the number of parameters increases with the number of exposure-time periods, leading to a potential loss in efficiency. In this article, we propose a new model formulation for assessing treatment effect heterogeneity over exposure time. Rather than a categorical term for each level of exposure time, the proposed model includes a random effect to represent varying treatment effects by exposure time. This allows for pooling information across exposure-time periods and may result in more precise average and exposure-time-specific treatment effect estimates. In addition, we develop an accompanying permutation test for the variance component of the heterogeneous treatment effect parameters. We conduct simulation studies to compare the proposed model and permutation test to alternative methods to elucidate their finite-sample operating characteristics, and to generate practical guidance on model choices for assessing exposure-time treatment effect heterogeneity in stepped-wedge CRTs.

As individuals age, death is a competing risk for Alzheimer's disease (AD) but the reverse is not the case. As such, studies of AD can be placed within the semi-competing risks framework. Central to semi-competing risks, and in contrast to standard competing risks , is that one can learn about the dependence structure between the two events. To-date, however, most methods for semi-competing risks treat dependence as a nuisance and not a potential source of new clinical knowledge. We propose a novel regression-based framework that views the two time-to-event outcomes through the lens of a longitudinal bivariate process on a partition of the time scales of the two events. A key innovation of the framework is that dependence is represented in two distinct forms, local and global dependence, both of which have intuitive clinical interpretations. Estimation and inference are performed via penalized maximum likelihood, and can accommodate right censoring, left truncation, and time-varying covariates. An important consequence of the partitioning of the time scale is that an ambiguity regarding the specific form of the likelihood contribution may arise; a strategy for sensitivity analyses regarding this issue is described. The framework is then used to investigate the role of gender and having ≥1 apolipoprotein E (APOE) ε4 allele on the joint risk of AD and death using data from the Adult Changes in Thought study.

The neonatal mortality rate in Rwanda remains above the United Nations Sustainable Development Goal 3 target of 12 deaths per 1,000 live births. As part of a larger effort to reduce preventable neonatal deaths in the country, we conducted a study to examine risk factors for low birthweight. The data was collected via a cost-efficient cluster-based outcome-dependent sampling scheme wherein clusters of individuals (health centers) were selected on the basis of, in part, the outcome rate of the individuals. For a given dataset collected via a cluster-based outcome-dependent sampling scheme, estimation for a marginal model may proceed via inverse-probability-weighted generalized estimating equations, where the cluster-specific weights are the inverse probability of the health center's inclusion in the sample. In this paper, we provide a detailed treatment of the asymptotic properties of this estimator, together with an explicit expression for the asymptotic variance and a corresponding estimator. Furthermore, motivated by the study we conducted in Rwanda, we propose a number of small-sample bias corrections to both the point estimates and the standard error estimates. Through simulation, we show that applying these corrections when the number of clusters is small generally reduces the bias in the point estimates, and results in closer to nominal coverage. The proposed methods are applied to data from 18 health centers and 1 district hospital in Rwanda.

Summary. Statistical analyses that investigate risk factors for Alzheimer’s disease (AD) are often subject to a number of challenges. Some of these challenges arise due to practical considerations regarding data collection such that the observation of AD events is subject to complex censoring including left-truncation and either interval or right-censoring. Additional challenges arise due to the fact that study participants under investigation are often subject to competing forces, most notably death, that may not be independent of AD. Towards resolving the latter, researchers may choose to embed the study of AD within the “semi-competing risks” framework for which the recent statistical literature has seen a number of advances including for the so-called illness-death model. To the best of our knowledge, however, the semi-competing risks literature has not fully considered analyses in contexts with complex censoring, as in studies of AD. This is particularly the case when interest lies with the accelerated failure time (AFT) model, an alternative to the traditional multiplicative Cox model that places emphasis away from the hazard function. In this article, we outline a new Bayesian framework for estimation/inference of an AFT illness-death model for semi-competing risks data subject to complex censoring. An efficient computational algorithm that gives researchers the flexibility to adopt either a fully parametric or a semi-parametric model specification is developed and implemented. The proposed methods are motivated by and illustrated with an analysis of data from the Adult Changes in Thought study, an on-going community-based prospective study of incident AD in western Washington State.

Ecological studies that make use of data on groups of individuals, rather than on the individuals themselves, are subject to numerous biases that cannot be resolved without some individual-level data. In the context of a rare outcome, the hybrid design for ecological inference efficiently combines group-level data with individual-level case-control data. Unfortunately, except in relatively simple settings, use of the design in practice is limited since evaluation of the hybrid likelihood is computationally prohibitively expensive. In this article we first propose and develop an alternative representation of the hybrid likelihood. Second, based on this new representation, a series of approximations are proposed that drastically reduce computational burden. A comprehensive simulation shows that, in a broad range of scenarios, estimators based on the approximate hybrid likelihood exhibit the same operating characteristics as the exact hybrid likelihood, without any penalty in terms of increased bias or reduced efficiency. Third, in settings where the approximations may not hold, a pragmatic estimation and inference strategy is developed that uses the approximate form for some likelihood contributions and the exact form for others. The strategy gives researchers the ability to balance computational tractability with accuracy in their own settings. Finally, as a by-product of the development, we provide the first explicit characterization of the hybrid aggregate data design which combines data from an aggregate data study (Prentice and Sheppard, 1995, Biometrika 82, 113-125) with case-control samples. The methods are illustrated using data from North Carolina on births between 2007 and 2009.

Summary A recently funded study of the impact of oral contraceptive use on the risk of bone fracture employed the randomized recruitment scheme of Weinberg and Wacholder (1990, Biometrics 46, 963–975). One potential complication in the bone fracture study is the potential for differential response rates between cases and controls; participation rates in previous, related studies have been around 70%. Although data from randomized recruitment schemes may be analyzed within the two-phase study framework, ignoring potential differential participation may lead to biased estimates of association. To overcome this, we build on the two-phase framework and propose an extension by introducing an additional stage of data collection aimed specifically at addressing potential differential participation. Four estimators that correct for both sampling and participation bias are proposed; two are general purpose and two are for the special case where covariates underlying the participation mechanism are discrete. Because the fracture study is ongoing, we illustrate the methods using infant mortality data from North Carolina.

The ecological study design suffers from a broad range of biases that result from the loss of information regarding the joint distribution of individual-level outcomes, exposures, and confounders. The consequent nonidentifiability of individual-level models cannot be overcome without additional information; we combine ecological data with a sample of individual-level case-control data. The focus of this article is hierarchical models to account for between-group heterogeneity. Estimation and inference pose serious computational challenges. We present a Bayesian implementation based on a data augmentation scheme where the unobserved data are treated as auxiliary variables. The methods are illustrated with a dataset of county-specific infant mortality data from the state of North Carolina.