We consider covariate selection and the ensuing model uncertainty aspects in the context of Cox regression. The perspective we take is probabilistic, and we handle it within a Bayesian framework. One of the critical elements in variable/model selection is choosing a suitable prior for model parameters. Here, we derive the so-called conventional prior approach and propose a comprehensive implementation that results in an automatic procedure. Our simulation studies and real applications show improvements over existing literature. For the sake of reproducibility but also for its intrinsic interest for practitioners, a web application requiring minimum statistical knowledge implements the proposed approach.

In survival data analysis, a competing risk is an event whose occurrence precludes or alters the chance of the occurrence of the primary event of interest. In large cohort studies with long-term follow-up, there are often competing risks. Further, if the event of interest is rare in such large studies, the case-cohort study design is widely used to reduce the cost and achieve the same efficiency as a cohort study. The conventional additive hazards modeling for competing risks data in case-cohort studies involves the cause-specific hazard function, under which direct assessment of covariate effects on the cumulative incidence function, or the subdistribution, is not possible. In this paper, we consider an additive hazard model for the subdistribution of a competing risk in case-cohort studies. We propose estimating equations based on inverse probability weighting methods for the estimation of the model parameters. Consistency and asymptotic normality of the proposed estimators are established. The performance of the proposed methods in finite samples is examined through simulation studies and the proposed approach is applied to a case-cohort dataset from the Sister Study.

Publication bias is a major concern in conducting systematic reviews and meta-analyses. Various sensitivity analysis or bias-correction methods have been developed based on selection models, and they have some advantages over the widely used trim-and-fill bias-correction method. However, likelihood methods based on selection models may have difficulty in obtaining precise estimates and reasonable confidence intervals, or require a rather complicated sensitivity analysis process. Herein, we develop a simple publication bias adjustment method by utilizing the information on conducted but still unpublished trials from clinical trial registries. We introduce an estimating equation for parameter estimation in the selection function by regarding the publication bias issue as a missing data problem under the missing not at random assumption. With the estimated selection function, we introduce the inverse probability weighting (IPW) method to estimate the overall mean across studies. Furthermore, the IPW versions of heterogeneity measures such as the between-study variance and the I2 measure are proposed. We propose methods to construct confidence intervals based on asymptotic normal approximation as well as on parametric bootstrap. Through numerical experiments, we observed that the estimators successfully eliminated bias, and the confidence intervals had empirical coverage probabilities close to the nominal level. On the other hand, the confidence interval based on asymptotic normal approximation is much wider in some scenarios than the bootstrap confidence interval. Therefore, the latter is recommended for practical use.

Analysis of observational studies increasingly confronts the challenge of determining which of a possibly high-dimensional set of available covariates are required to satisfy the assumption of ignorable treatment assignment for estimation of causal effects. We propose a Bayesian nonparametric approach that simultaneously 1) prioritizes inclusion of adjustment variables in accordance with existing principles of confounder selection; 2) estimates causal effects in a manner that permits complex relationships among confounders, exposures, and outcomes; and 3) provides causal estimates that account for uncertainty in the nature of confounding. The proposal relies on specification of multiple Bayesian Additive Regression Trees models, linked together with a common prior distribution that accrues posterior selection probability to covariates on the basis of association with both the exposure and the outcome of interest. A set of extensive simulation studies demonstrates that the proposed method performs well relative to similarly-motivated methodologies in a variety of scenarios. We deploy the method to investigate the causal effect of emissions from coal-fired power plants on ambient air pollution concentrations, where the prospect of confounding due to local and regional meteorological factors introduces uncertainty around the confounding role of a high-dimensional set of measured variables. Ultimately, we show that the proposed method produces more efficient and more consistent results across adjacent years than alternative methods, lending strength to the evidence of the causal relationship between SO2 emissions and ambient particulate pollution. This article is protected by copyright. All rights reserved.

The Alaskan landscape has undergone substantial changes in recent decades, most notably the expansion of shrubs and trees across the Arctic. We developed a Bayesian hierarchical model to quantify the impact of climate change on the structural transformation of ecosystems using remotely sensed imagery. We used latent trajectory processes to model dynamic state probabilities that evolve annually, from which we derived transition probabilities between ecotypes. Our latent trajectory model accommodates temporal irregularity in survey intervals and uses spatio-temporally heterogeneous climate drivers to infer rates of land cover transitions. We characterized multi-scale spatial correlation induced by plot and subplot arrangements in our study system. We also developed a Pólya-Gamma sampling strategy to improve computation. Our model facilitates inference on the response of ecosystems to shifts in the climate and can be used to predict future land cover transitions under various climate scenarios. This article is protected by copyright. All rights reserved.

Sponsors often rely on multi-regional clinical trials (MRCTs) to introduce new treatments more rapidly into the global market. Many commonly used statistical methods do not account for regional differences, and small regional sample sizes frequently result in lower estimation quality of region-specific treatment effects. The International Council for Harmonization E17 guidelines suggest consideration of methods that allow for information borrowing across regions to improve estimation. In response to these guidelines, we develop a novel methodology to estimate global and region-specific treatment effects from MRCTs with time-to-event endpoints using Bayesian model averaging (BMA). This approach accounts for the possibility of heterogeneous treatment effects between regions, and we discuss how to assess the consistency of these effects using posterior model probabilities. We obtain posterior samples of the treatment effects using a Laplace approximation, and we show through simulation studies that the proposed modeling approach estimates region-specific treatment effects with lower mean squared error than a Cox proportional hazards model while resulting in a similar rejection rate of the global treatment effect. We then apply the BMA approach to data from the LEADER trial, an MRCT designed to evaluate the cardiovascular safety of an anti-diabetic treatment.

The Taiwan air quality monitoring network (TAQMN) and the AirBox network both monitor PM2.5 in Taiwan. The TAQMN, managed by Taiwan's Environmental Protection Administration (EPA), provides high-quality PM2.5 measurements at 77 monitoring stations. The AirBox network launched more recently consists of low-cost, small internet-of-things (IoT) microsensors (i.e., AirBoxes) at thousands of locations. While the AirBox network provides broad spatial coverage, its measurements are unreliable and require calibrations. However, applying a universal calibration procedure to all AirBoxes does not work well because the calibration line varies with local factors, including the chemical compositions of PM2.5 , which are not homogeneous in space. Therefore, different calibrations are needed at different locations to adapt to their local environments. Unfortunately, AirBoxes and EPA locations are misaligned, challenging the calibration task. In this paper, we propose a spatial model with spatially varying coefficients to account for the heterogeneity in the data. Our method gives spatially adaptive calibrations of AirBoxes and produces accurate PM2.5 concentration estimates with their error bars at any location, incorporating two types of measurements. In addition, the proposed method is robust to outliers, requires no colocated data, and provides calibration formulas for new AirBoxes once they are added to the network. We illustrate our approach using hourly PM2.5 data in 2020. After the calibration, the results show that the PM2.5 prediction improves by about 38%-68% in root-mean-squared prediction error. Once the calibration formulas are established, we can obtain reliable PM2.5 values even if we ignore EPA data.

Recently, Barber and Candès laid the theoretical foundation for a general framework for false discovery rate (FDR) control based on the notion of "knockoffs." A closely related FDR control methodology has long been employed in the analysis of mass spectrometry data, referred to there as "target-decoy competition" (TDC). However, any approach that aims to control the FDR, which is defined as the expected value of the false discovery proportion (FDP), suffers from a problem. Specifically, even when successfully controlling the FDR at level α, the FDP in the list of discoveries can significantly exceed α. We offer FDP-SD, a new procedure that rigorously controls the FDP in the knockoff/TDC competition setup by guaranteeing that the FDP is bounded by α at a desired confidence level. Compared with the recently published framework of Katsevich and Ramdas, FDP-SD generally delivers more power and often substantially so in simulated and real data.

We consider estimator and model choice when estimating abundance from capture-recapture data. Our work is motivated by a mark-recapture distance sampling example where model and estimator choice led to unexpectedly large disparities in the estimates. To understand these differences we look at three estimation strategies (maximum likelihood estimation, conditional maximum likelihood estimation, and Bayesian estimation) for both binomial and Poisson models. We show that assuming the data have a binomial or multinomial distribution introduces implicit and unnoticed assumptions that are not addressed when fitting with maximum likelihood estimation. This can have an important effect in finite samples, particularly if our data arise from multiple populations. We relate these results to those of restricted maximum likelihood in linear mixed effects models. This article is protected by copyright. All rights reserved.

Recurrent events are often important endpoints in randomized clinical trials. For example, the number of recurrent disease-related hospitalizations may be considered as a clinically meaningful endpoint in cardiovascular studies. In some settings, the recurrent event process may be terminated by an event such as death, which makes it more challenging to define and estimate a causal treatment effect on recurrent event endpoints. In this paper, we focus on the principal stratum estimand, where the treatment effect of interest on recurrent events is defined among subjects who would be alive regardless of the assigned treatment. For the estimation of the principal stratum effect in randomized clinical trials, we propose a Bayesian approach based on a joint model of the recurrent event and death processes with a frailty term accounting for within-subject correlation. We also present Bayesian posterior predictive check procedures for assessing the model fit. The proposed approaches are demonstrated in the randomized Phase III chronic heart failure trial PARAGON-HF (NCT01920711).

When there are resource constraints, it may be necessary to rank individualized treatment benefits to facilitate the prioritization of assigning different treatments. Most existing literature on individualized treatment rules targets absolute conditional treatment effect differences as a metric for the benefit. However, there can be settings where relative differences may better represent such benefit. In this paper, we consider modeling such relative differences formed as scale-invariant contrasts between the conditional treatment effects. By showing that all scale-invariant contrasts are monotonic transformations of each other, we posit a single index model for a particular relative contrast. We then characterize semiparametric estimating equations, including the efficient score, to estimate index parameters. To achieve semiparametric efficiency, we propose a two-step approach that minimizes a doubly robust loss function for initial estimation and then performs a one-step efficiency augmentation procedure. Careful theoretical and numerical studies are provided to show the superiority of our proposed approach.

Post-market active safety monitoring is important for the timely capture of safety signals associated with exposure to a new vaccine or drug. The group sequential analysis is a common method employed in safety surveillance. Specifically, it compares the post-vaccination incidence of adverse event (AE) in a vaccinated population with a pre-specified reference level by sequentially conducting hypothesis testing during the surveillance. When the number of AEs is "too high", a safety signal is identified. If the null hypothesis is never rejected, the vaccine is considered safe. Such an approach does not account for either the variation in determining the reference risk from a control population or the seasonality effect. Furthermore, not rejecting the null could be due to a lack of power and cannot always be interpreted as proof of safety. In this paper, we proposed a new group sequential test procedure fully accounting for both seasonality and variation from the historical controls. More importantly, we proposed to construct a confidence interval for the relative AE risk between the exposed and control groups at the end of the study, which can be used to quantify the safety of the vaccine. The proposed method is illustrated via real-data examples on anaphylaxis and examined by extensive simulation studies.

In this paper, we focus on estimating the average treatment effect (ATE) of a target population when individual-level data from a source population and summary-level data (e.g., first or second moments of certain covariates) from the target population are available. In the presence of the heterogeneous treatment effect, the ATE of the target population can be different from that of the source population when distributions of treatment effect modifiers are dissimilar in these two populations, a phenomenon also known as covariate shift. Many methods have been developed to adjust for covariate shift, but most require individual covariates from a representative target sample. We develop a weighting approach based on the summary-level information from the target sample to adjust for possible covariate shift in effect modifiers. In particular, weights of the treated and control groups within a source sample are calibrated by the summary-level information of the target sample. Our approach also seeks additional covariate balance between the treated and control groups in the source sample. We study the asymptotic behavior of the corresponding weighted estimator for the target population ATE under a wide range of conditions. The theoretical implications are confirmed in simulation studies and a real-data application.

We consider the problem of combining data from observational and experimental sources to draw causal conclusions. To derive combined estimators with desirable properties, we extend results from the Stein shrinkage literature. Our contributions are threefold. First, we propose a generic procedure for deriving shrinkage estimators in this setting, making use of a generalized unbiased risk estimate. Second, we develop two new estimators, prove finite sample conditions under which they have lower risk than an estimator using only experimental data, and show that each achieves a notion of asymptotic optimality. Third, we draw connections between our approach and results in sensitivity analysis, including proposing a method for evaluating the feasibility of our estimators.

Identifying a patient's disease/health status from electronic medical records is a frequently encountered task in electronic health records (EHR) related research, and estimation of a classification model often requires a benchmark training data with patients' known phenotype statuses. However, assessing a patient's phenotype is costly and labor intensive, hence a proper selection of EHR records as a training set is desired. We propose a procedure to tailor the best training subsample with limited sample size for a classification model, minimizing its mean-squared phenotyping/classification error (MSE). Our approach incorporates "positive only" information, an approximation of the true disease status without false alarm, when it is available. In addition, our sampling procedure is applicable for training a chosen classification model which can be misspecified. We provide theoretical justification on its optimality in terms of MSE. The performance gain from our method is illustrated through simulation and a real-data example, and is found often satisfactory under criteria beyond MSE.