Flexible estimation of multiple conditional quantiles is of interest in numerous applications, such as studying the effect of pregnancy-related factors on low and high birth weight. We propose a Bayesian nonparametric method to simultaneously estimate noncrossing, nonlinear quantile curves. We expand the conditional distribution function of the response in I-spline basis functions where the covariate-dependent coefficients are modeled using neural networks. By leveraging the approximation power of splines and neural networks, our model can approximate any continuous quantile function. Compared to existing models, our model estimates all rather than a finite subset of quantiles, scales well to high dimensions, and accounts for estimation uncertainty. While the model is arbitrarily flexible, interpretable marginal quantile effects are estimated using accumulative local effect plots and variable importance measures. A simulation study shows that our model can better recover quantiles of the response distribution when the data are sparse, and an analysis of birth weight data is presented.

We propose inference procedures for general factorial designs with time-to-event endpoints. Similar to additive Aalen models, null hypotheses are formulated in terms of cumulative hazards. Deviations are measured in terms of quadratic forms in Nelson-Aalen-type integrals. Different from existing approaches, this allows to work without restrictive model assumptions as proportional hazards. In particular, crossing survival or hazard curves can be detected without a significant loss of power. For a distribution-free application of the method, a permutation strategy is suggested. The resulting procedures' asymptotic validity is proven and small sample performances are analyzed in extensive simulations. The analysis of a data set on asthma illustrates the applicability.

In this paper, we propose a frequentist model averaging method for quantile regression with high-dimensional covariates. Although research on these subjects has proliferated as separate approaches, no study has considered them in conjunction. Our method entails reducing the covariate dimensions through ranking the covariates based on marginal quantile utilities. The second step of our method implements model averaging on the models containing the covariates that survive the screening of the first step. We use a delete-one cross-validation method to select the model weights, and prove that the resultant estimator possesses an optimal asymptotic property uniformly over any compact (0,1) subset of the quantile indices. Our proof, which relies on empirical process theory, is arguably more challenging than proofs of similar results in other contexts owing to the high-dimensional nature of the problem and our relaxation of the conventional assumption of the weights summing to one. Our investigation of finite-sample performance demonstrates that the proposed method exhibits very favorable properties compared to the least absolute shrinkage and selection operator (LASSO) and smoothly clipped absolute deviation (SCAD) penalized regression methods. The method is applied to a microarray gene expression data set.

The time-varying frequency characteristics of many biomedical time series contain important scientific information. However, the high-dimensional nature of the time-varying power spectrum as a surface in time and frequency limits its direct use by applied researchers and clinicians for elucidating complex mechanisms. In this article, we introduce a new approach to time-frequency analysis that decomposes the time-varying power spectrum in to orthogonal rank-one layers in time and frequency to provide a parsimonious representation that illustrates relationships between power at different times and frequencies. The approach can be used in fully nonparametric analyses or in semiparametric analyses that account for exogenous information and time-varying covariates. An estimation procedure is formulated within a penalized reduced-rank regression framework that provides estimates of layers that are interpretable as power localized within time blocks and frequency bands. Empirical properties of the procedure are illustrated in simulation studies and its practical use is demonstrated through an analysis of heart rate variability during sleep.

The stepped wedge cluster randomized trial (SW-CRT) is an increasingly popular design for evaluating health service delivery or policy interventions. An essential consideration of this design is the need to account for both within-period and between-period correlations in sample size calculations. Especially when embedded in health care delivery systems, many SW-CRTs may have subclusters nested in clusters, within which outcomes are collected longitudinally. However, existing sample size methods that account for between-period correlations have not allowed for multiple levels of clustering. We present computationally efficient sample size procedures that properly differentiate within-period and between-period intracluster correlation coefficients in SW-CRTs in the presence of subclusters. We introduce an extended block exchangeable correlation matrix to characterize the complex dependencies of outcomes within clusters. For Gaussian outcomes, we derive a closed-form sample size expression that depends on the correlation structure only through two eigenvalues of the extended block exchangeable correlation structure. For non-Gaussian outcomes, we present a generic sample size algorithm based on linearization and elucidate simplifications under canonical link functions. For example, we show that the approximate sample size formula under a logistic linear mixed model depends on three eigenvalues of the extended block exchangeable correlation matrix. We provide an extension to accommodate unequal cluster sizes and validate the proposed methods via simulations. Finally, we illustrate our methods in two real SW-CRTs with subclusters.

A novel functional additive model is proposed, which is uniquely modified and constrained to model nonlinear interactions between a treatment indicator and a potentially large number of functional and/or scalar pretreatment covariates. The primary motivation for this approach is to optimize individualized treatment rules based on data from a randomized clinical trial. We generalize functional additive regression models by incorporating treatment-specific components into additive effect components. A structural constraint is imposed on the treatment-specific components in order to provide a class of additive models with main effects and interaction effects that are orthogonal to each other. If primary interest is in the interaction between treatment and the covariates, as is generally the case when optimizing individualized treatment rules, we can thereby circumvent the need to estimate the main effects of the covariates, obviating the need to specify their form and thus avoiding the issue of model misspecification. The methods are illustrated with data from a depression clinical trial with electroencephalogram functional data as patients' pretreatment covariates.

Prediction modeling for clinical decision making is of great importance and needed to be updated frequently with the changes of patient population and clinical practice. Existing methods are either done in an ad hoc fashion, such as model recalibration or focus on studying the relationship between predictors and outcome and less so for the purpose of prediction. In this article, we propose a dynamic logistic state space model to continuously update the parameters whenever new information becomes available. The proposed model allows for both time-varying and time-invariant coefficients. The varying coefficients are modeled using smoothing splines to account for their smooth trends over time. The smoothing parameters are objectively chosen by maximum likelihood. The model is updated using batch data accumulated at prespecified time intervals, which allows for better approximation of the underlying binomial density function. In the simulation, we show that the new model has significantly higher prediction accuracy compared to existing methods. We apply the method to predict 1 year survival after lung transplantation using the United Network for Organ Sharing data.

The Corona Virus Disease (COVID-19) pandemic has increased mortality in countries worldwide. To evaluate the impact of the pandemic on mortality, the use of excess mortality rather than reported COVID-19 deaths has been suggested. Excess mortality, however, requires estimation of mortality under nonpandemic conditions. Although many methods exist to forecast mortality, they are either complex to apply, require many sources of information, ignore serial correlation, and/or are influenced by historical excess mortality. We propose a linear mixed model that is easy to apply, requires only historical mortality data, allows for serial correlation, and down-weighs the influence of historical excess mortality. Appropriateness of the linear mixed model is evaluated with fit statistics and forecasting accuracy measures for Belgium and the Netherlands. Unlike the commonly used 5-year weekly average, the linear mixed model is forecasting the year-specific mortality, and as a result improves the estimation of excess mortality for Belgium and the Netherlands.

Disease registries, surveillance data, and other datasets with extremely large sample sizes become increasingly available in providing population-based information on disease incidence, survival probability, or other important public health characteristics. Such information can be leveraged in studies that collect detailed measurements but with smaller sample sizes. In contrast to recent proposals that formulate additional information as constraints in optimization problems, we develop a general framework to construct simple estimators that update the usual regression estimators with some functionals of data that incorporate the additional information. We consider general settings that incorporate nuisance parameters in the auxiliary information, non-i.i.d. data such as those from case-control studies, and semiparametric models with infinite-dimensional parameters common in survival analysis. Details of several important data and sampling settings are provided with numerical examples.

Suppose we are interested in the effect of a treatment in a clinical trial. The efficiency of inference may be limited due to small sample size. However, external control data are often available from historical studies. Motivated by an application to Helicobacter pylori infection, we show how to borrow strength from such data to improve efficiency of inference in the clinical trial. Under an exchangeability assumption about the potential outcome mean, we show that the semiparametric efficiency bound for estimating the average treatment effect can be reduced by incorporating both the clinical trial data and external controls. We then derive a doubly robust and locally efficient estimator. The improvement in efficiency is prominent especially when the external control data set has a large sample size and small variability. Our method allows for a relaxed overlap assumption, and we illustrate with the case where the clinical trial only contains a treated group. We also develop doubly robust and locally efficient approaches that extrapolate the causal effect in the clinical trial to the external population and the overall population. Our results also offer a meaningful implication for trial design and data collection. We evaluate the finite-sample performance of the proposed estimators via simulation. In the Helicobacter pylori infection application, our approach shows that the combination treatment has potential efficacy advantages over the triple therapy.

Modeling and drawing inference on the joint associations between single-nucleotide polymorphisms and a disease has sparked interest in genome-wide associations studies. In the motivating Boston Lung Cancer Survival Cohort (BLCSC) data, the presence of a large number of single nucleotide polymorphisms of interest, though smaller than the sample size, challenges inference on their joint associations with the disease outcome. In similar settings, we find that neither the debiased lasso approach (van de Geer et al., 2014), which assumes sparsity on the inverse information matrix, nor the standard maximum likelihood method can yield confidence intervals with satisfactory coverage probabilities for generalized linear models. Under this "large n, diverging p" scenario, we propose an alternative debiased lasso approach by directly inverting the Hessian matrix without imposing the matrix sparsity assumption, which further reduces bias compared to the original debiased lasso and ensures valid confidence intervals with nominal coverage probabilities. We establish the asymptotic distributions of any linear combinations of the parameter estimates, which lays the theoretical ground for drawing inference. Simulations show that the proposed refined debiased estimating method performs well in removing bias and yields honest confidence interval coverage. We use the proposed method to analyze the aforementioned BLCSC data, a large-scale hospital-based epidemiology cohort study investigating the joint effects of genetic variants on lung cancer risks.

We consider the proportional hazards model in which the covariates include the discretized categories of a continuous time-dependent exposure variable measured with error. Naively ignoring the measurement error in the analysis may cause biased estimation and erroneous inference. Although various approaches have been proposed to deal with measurement error when the hazard depends linearly on the time-dependent variable, it has not yet been investigated how to correct when the hazard depends on the discretized categories of the time-dependent variable. To fill this gap in the literature, we propose a smoothed corrected score approach based on approximation of the discretized categories after smoothing the indicator function. The consistency and asymptotic normality of the proposed estimator are established. The observation times of the time-dependent variable are allowed to be informative. For comparison, we also extend to this setting two approximate approaches, the regression calibration and the risk-set regression calibration. The methods are assessed by simulation studies and by application to data from an HIV clinical trial.

Two-phase designs can reduce the cost of epidemiological studies by limiting the ascertainment of expensive covariates or/and exposures to an efficiently selected subset (phase-II) of a larger (phase-I) study. Efficient analysis of the resulting data set combining disparate information from phase-I and phase-II, however, can be complex. Most of the existing methods, including semiparametric maximum-likelihood estimator, require the information in phase-I to be summarized into a fixed number of strata. In this paper, we describe a novel method for the analysis of two-phase studies where information from phase-I is summarized by parameters associated with a reduced logistic regression model of the disease outcome on available covariates. We then setup estimating equations for parameters associated with the desired extended logistic regression model, based on information on the reduced model parameters from phase-I and complete data available at phase-II after accounting for nonrandom sampling design. We use generalized method of moments to solve overly identified estimating equations and develop the resulting asymptotic theory for the proposed estimator. Simulation studies show that the use of reduced parametric models, as opposed to summarizing data into strata, can lead to more efficient utilization of phase-I data. An application of the proposed method is illustrated using the data from the U.S. National Wilms Tumor Study.

A common assumption of data analysis in clinical trials is that the patient population, as well as treatment effects, do not vary during the course of the study. However, when trials enroll patients over several years, this hypothesis may be violated. Ignoring variations of the outcome distributions over time, under the control and experimental treatments, can lead to biased treatment effect estimates and poor control of false positive results. We propose and compare two procedures that account for possible variations of the outcome distributions over time, to correct treatment effect estimates, and to control type-I error rates. The first procedure models trends of patient outcomes with splines. The second leverages conditional inference principles, which have been introduced to analyze randomized trials when patient prognostic profiles are unbalanced across arms. These two procedures are applicable in response-adaptive clinical trials. We illustrate the consequences of trends in the outcome distributions in response-adaptive designs and in platform trials, and investigate the proposed methods in the analysis of a glioblastoma study.

The most common objective for response-adaptive clinical trials is to seek to ensure that patients within a trial have a high chance of receiving the best treatment available by altering the chance of allocation on the basis of accumulating data. Approaches that yield good patient benefit properties suffer from low power from a frequentist perspective when testing for a treatment difference at the end of the study due to the high imbalance in treatment allocations. In this work we develop an alternative pairwise test for treatment difference on the basis of allocation probabilities of the covariate-adjusted response-adaptive randomization with forward-looking Gittins Index (CARA-FLGI) Rule for binary responses. The performance of the novel test is evaluated in simulations for two-armed studies and then its applications to multiarmed studies are illustrated. The proposed test has markedly improved power over the traditional Fisher exact test when this class of nonmyopic response adaptation is used. We also find that the test's power is close to the power of a Fisher exact test under equal randomization.

This paper is concerned with using multivariate binary observations to estimate the probabilities of unobserved classes with scientific meanings. We focus on the setting where additional information about sample similarities is available and represented by a rooted weighted tree. Every leaf in the given tree contains multiple samples. Shorter distances over the tree between the leaves indicate a priori higher similarity in class probability vectors. We propose a novel data integrative extension to classical latent class models with tree-structured shrinkage. The proposed approach enables (1) borrowing of information across leaves, (2) estimating data-driven leaf groups with distinct vectors of class probabilities, and (3) individual-level probabilistic class assignment given the observed multivariate binary measurements. We derive and implement a scalable posterior inference algorithm in a variational Bayes framework. Extensive simulations show more accurate estimation of class probabilities than alternatives that suboptimally use the additional sample similarity information. A zoonotic infectious disease application is used to illustrate the proposed approach. The paper concludes by a brief discussion on model limitations and extensions.

Bayesian compartmental infectious disease models yield important inference on disease transmission by appropriately accounting for the dynamics and uncertainty of infection processes. In addition to estimating transition probabilities and reproductive numbers, these statistical models allow researchers to assess the probability of disease risk and quantify the effectiveness of interventions. These infectious disease models rely on data collected from all individuals classified as positive based on various diagnostic tests. In infectious disease testing, however, such procedures produce both false-positives and false-negatives at varying rates depending on the sensitivity and specificity of the diagnostic tests being used. We propose a novel Bayesian spatio-temporal infectious disease modeling framework that accounts for the additional uncertainty in the diagnostic testing and classification process that provides estimates of the important transmission dynamics of interest to researchers. The method is applied to data on the 2006 mumps epidemic in Iowa, in which over 6,000 suspected mumps cases were tested using a buccal or oral swab specimen, a urine specimen, and/or a blood specimen. Although all procedures are believed to have high specificities, the sensitivities can be low and vary depending on the timing of the test as well as the vaccination status of the individual being tested.