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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 dataset 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., Accepted for publication in Biometrics; 1 figure, 3 tables

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.

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.

Latent class analysis is an intuitive tool to characterize disease phenotype heterogeneity. With data more frequently collected on multiple phenotypes in chronic disease studies, it is of rising interest to investigate how the latent classes embedded in one phenotype are related to another phenotype. Motivated by a cohort with mild cognitive impairment (MCI) from the Uniform Data Set (UDS), we propose and study a time-dependent structural model to evaluate the association between latent classes and competing risk outcomes that are subject to missing failure types. We develop a two-step estimation procedure which circumvents latent class membership assignment and is rigorously justified in terms of accounting for the uncertainty in classifying latent classes. The new method also properly addresses the realistic complications for competing risks outcomes, including random censoring and missing failure types. The asymptotic properties of the resulting estimator are established. Given that the standard bootstrapping inference is not feasible in the current problem setting, we develop analytical inference procedures, which are easy to implement. Our simulation studies demonstrate the advantages of the proposed method over benchmark approaches. We present an application to the MCI data from UDS, which uncovers a detailed picture of the neuropathological relevance of the baseline MCI subgroups. This article is protected by copyright. All rights reserved.

Accurate risk assessment is critical in clinical decision-making. It entails the projected risk based on a risk prediction model agreeing with the observed risk in the target cohort. However, the model often over- or under-estimates the risk. Building a new model for the target cohort would be ideal but costly. It is therefore of great interest to recalibrate an existing model for the target cohort. Existing methods have been proposed to recalibrate the model by leveraging the disease incidence rates from the target cohort. However, they assume the same covariate distribution across cohorts and when the assumption is violated, the recalibrated model can be substantially biased. Further, recalibration is also complicated by the two-phase sampling design that is commonly used for developing risk prediction models. In this paper, we develop a weighted estimating-equation approach accounting for the two-phase design and combine it with a weighted empirical likelihood that leverages the summary information on both disease incidence rates and covariates from the target cohort. We provide a resampling-based inference procedure. Our extensive simulation results show that using the summary information from the target population, the proposed recalibration method yields nearly unbiased risk estimates under a wide range of scenarios. An application to a colorectal cancer study also illustrates that the proposed method yields a well-calibrated model in the target cohort.

Mendelian randomization (MR) utilizes genetic variants as instrumental variables (IVs) to estimate the causal effect of an exposure variable on an outcome of interest even in the presence of unmeasured confounders. However, many MR methods including the most popular inverse-variance weighted (IVW) estimator could be biased by the weak IVs that are weakly associated with the exposure. In this article, we develop a novel method called penalized inverse-variance weighted (pIVW) estimator, where we adjust the IVW estimator to account for the weak IVs by a proposed penalization method to prevent the denominator of the pIVW estimator from being close to zero. Moreover, we account for the horizontal pleiotropy—a widespread phenomenon in human genome that could bias the inference for the causal effect—by adjusting the variance estimation of the pIVW estimator. The proposed pIVW estimator can reduce to the debiased IVW (dIVW) estimator—another extension of the the IVW estimator—when the number of IVs and the IV strength increase. More generally, we prove that the pIVW estimator can achieve smaller bias and variance than the dIVW estimator under some regularity conditions. We also illustrate the improved performance of the proposed pIVW estimator over competing MR methods through a comprehensive simulation study. Further, we analyze the causal effects of the obesity-related traits and diseases on the Coronavirus disease 2019 (COVID-19). Notably, we find that hypertensive disease is associated with increased risk of hospitalized COVID-19, while peripheral vascular disease and higher body mass index are associated with increased risks of COVID-19 infection, hospitalized COVID-19 and critically ill COVID-19. The R package for the pIVW method is publicly available at https://github.com/siqixu/mr.pivw.

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 presence of protein aggregates in cells is a known feature of many human age-related diseases, such as Huntington's disease. Simulations using fixed parameter values in a model of the dynamic evolution of expanded polyglutamine (PolyQ) proteins in cells have been used to gain a better understanding of the biological system, how to focus drug development and how to construct more efficient designs of future laboratory-based in vitro experiments. However, there is considerable uncertainty about the values of some of the parameters governing the system. Currently, appropriate values are chosen by ad hoc attempts to tune the parameters so that the model output matches experimental data. The problem is further complicated by the fact that the data only offer a partial insight into the underlying biological process: the data consist only of the proportions of cell death and of cells with inclusion bodies at a few time points, corrupted by measurement error. Developing inference procedures to estimate the model parameters in this scenario is a significant task. The model probabilities corresponding to the observed proportions cannot be evaluated exactly and so they are estimated within the inference algorithm by repeatedly simulating realisations from the model. In general such an approach is computationally very expensive and we therefore construct Gaussian process emulators for the key quantities and reformulate our algorithm around these fast stochastic approximations. We conclude by examining the fit of our model and highlight appropriate values of the model parameters leading to new insights into the underlying biological processes such as the kinetics of aggregation., 21 pages

Changepoint detection methods are used in many areas of science and engineering, for example, in the analysis of copy number variation data to detect abnormalities in copy numbers along the genome. Despite the broad array of available tools, methodology for quantifying our uncertainty in the strength (or the presence) of given changepoints post-selection are lacking. Post-selection inference offers a framework to fill this gap, but the most straightforward application of these methods results in low-powered hypothesis tests and leaves open several important questions about practical usability. In this work, we carefully tailor post-selection inference methods toward changepoint detection, focusing on copy number variation data. To accomplish this, we study commonly used changepoint algorithms: binary segmentation, as well as two of its most popular variants, wild and circular, and the fused lasso. We implement some of the latest developments in post-selection inference theory, mainly auxiliary randomization. This improves the power, which requires implementations of Markov chain Monte Carlo algorithms (importance sampling and hit-and-run sampling) to carry out our tests. We also provide recommendations for improving practical useability, detailed simulations, and example analyses on array comparative genomic hybridization as well as sequencing data.

Multivariate spatial data, where multiple responses are simultaneously recorded across spatially indexed observational units, are routinely collected in a wide variety of disciplines. For example, the Southern Ocean Continuous Plankton Recorder survey collects records of zooplankton communities in the Indian sector of the Southern Ocean, with the aim of identifying and quantifying spatial patterns in biodiversity in response to environmental change. One increasingly popular method for modeling such data is spatial generalized linear latent variable models (GLLVMs), where the correlation across sites is captured by a spatial covariance function in the latent variables. However, little is known about the impact of misspecifying the latent variable correlation structure on inference of various parameters in such models. To address this gap in the literature, we investigate how misspecifying and assuming independence for the latent variables' correlation structure impacts estimation and inference in spatial GLLVMs. Through both theory and numerical studies, we show that performance of maximum likelihood estimation and inference on regression coefficients under misspecification depends on a combination of the response type, the magnitude of true regression coefficient, and the corresponding loadings, and, most importantly, whether the corresponding covariate is (also) spatially correlated. On the other hand, estimation and inference of truly nonzero loadings and prediction of latent variables is consistently not robust to misspecification of the latent variable correlation structure.

Health research using electronic health records (EHR) has gained popularity, but misclassification of EHR-derived disease status and lack of representativeness of the study sample can result in substantial bias in effect estimates and can impact power and type I error. In this paper, we develop new strategies for handling disease status misclassification and selection bias in EHR-based association studies. We first focus on each type of bias separately. For misclassification, we propose three novel likelihood-based bias correction strategies. A distinguishing feature of the EHR setting is that misclassification may berelated to patient-specific factors, and the proposed methods leverage data in the EHR to estimate misclassification rateswithout gold standard labels. For addressing selection bias, we describe how calibration and inverse probability weighting methods from the survey sampling literature can be extended and applied to the EHR setting.Addressing misclassification and selection biases simultaneously is a more challenging problem than dealing with each on its own, and we propose several new strategies to address this situation. For all methods proposed, we derive valid standard errors and provide software for implementation. We provide a new suite of statistical estimation and inference strategies for addressing misclassification and selection bias simultaneously that is tailored to problems arising in EHR data analysis. We apply these methods to data from The Michigan Genomics Initiative (MGI), a longitudinal EHR-linked biorepository.

This paper presents a model-based method for clustering multivariate binary observations that incorporates constraints consistent with the scientific context. The approach is motivated by the precision medicine problem of identifying autoimmune disease patient subsets or classes who may require different treatments. We start with a family of restricted latent class models or RLCMs (e.g., Xu and Shang, 2018). However, in the motivating example and many others like it, the unknown number of classes and the definition of classes using binary states are among the targets of inference. We use a Bayesian approach to RCLMs in order to use informative prior assumptions on the number and definitions of latent classes to be consistent with scientific knowledge so that the posterior distribution tends to concentrate on smaller numbers of clusters and sparser binary patterns. The paper derives a posterior sampling algorithm based on Markov chain Monte Carlo with split-merge updates to efficiently explore the space of clustering allocations. Through simulations under the assumed model and realistic deviations from it, we demonstrate greater interpretability of results and superior finite-sample clustering performance for our method compared to common alternatives. The methods are illustrated with an analysis of protein data to detect clusters representing autoantibody classes among scleroderma patients. This article is protected by copyright. All rights reserved.

We consider a novel problem, bi-level graphical modeling, in which multiple individual graphical models can be considered as variants of a common group-level graphical model and inference of both the group- and individual-level graphical models is of interest. Such a problem arises from many applications, including multi-subject neuro-imaging and genomics data analysis. We propose a novel and efficient statistical method, the random covariance model, to learn the group- and individual-level graphical models simultaneously. The proposed method can be nicely interpreted as a random covariance model that mimics the random effects model for mean structures in linear regression. It accounts for similarity between individual graphical models, identifies group-level connections that are shared by individuals, and simultaneously infers multiple individual-level networks. Compared to existing multiple graphical modeling methods that only focus on individual-level graphical modeling, our model learns the group-level structure underlying the multiple individual graphical models and enjoys computational efficiency that is particularly attractive for practical use. We further define a measure of degrees-of-freedom for the complexity of the model useful for model selection. We demonstrate the asymptotic properties of our method and show its finite-sample performance through simulation studies. Finally, we apply the method to our motivating clinical data, a multi-subject resting-state functional magnetic resonance imaging dataset collected from participants diagnosed with schizophrenia, identifying both individual- and group-level graphical models of functional connectivity.

Researchers are increasingly interested in using sensor technology to collect accurate activity information and make individualized inference about treatments, exposures, and policies. How to optimally combine population data with data from an individual remains an open question. Multisource exchangeability models (MEMs) are a Bayesian approach for increasing precision by combining potentially heterogeneous supplemental data sources into analysis of a primary source. MEMs are a potentially powerful tool for individualized inference but can integrate only a few sources; their model space grows exponentially, making them intractable for high-dimensional applications. We propose iterated MEMs (iMEMs), which identify a subset of the most exchangeable sources prior to fitting a MEM model. iMEM complexity scales linearly with the number of sources, and iMEMs greatly increase precision while maintaining desirable asymptotic and small sample properties. We apply iMEMs to individual-level behavior and emotion data from a smartphone app and show that they achieve individualized inference with up to 99% efficiency gain relative to standard analyses that do not borrow information.

State‐space models (SSMs) are a popular tool for modeling animal abundances. Inference difficulties for simple linear SSMs are well known, particularly in relation to simultaneous estimation of process and observation variances. Several remedies to overcome estimation problems have been studied for relatively simple SSMs, but whether these challenges and proposed remedies apply for nonlinear stage‐structured SSMs, an important class of ecological models, is less well understood. Here we identify improvements for inference about nonlinear stage‐structured SSMs fit with biased sequential life stage data. Theoretical analyses indicate parameter identifiability requires covariates in the state processes. Simulation studies show that plugging in externally estimated observation variances, as opposed to jointly estimating them with other parameters, reduces bias and standard error of estimates. In contrast to previous results for simple linear SSMs, strong confounding between jointly estimated process and observation variance parameters was not found in the models explored here. However, when observation variance was also estimated in the motivating case study, the resulting process variance estimates were implausibly low (near‐zero). As SSMs are used in increasingly complex ways, understanding when inference can be expected to be successful, and what aids it, becomes more important. Our study illustrates (a) the need for relevant process covariates and (b) the benefits of using externally estimated observation variances for inference about nonlinear stage‐structured SSMs.

After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is exacerbated in high-dimensional settings, where variable selection becomes unavoidable. This has prompted a flurry of activity in developing uniformly valid hypothesis tests for a low-dimensional regression parameter (e.g. the causal effect of an exposure A on an outcome Y) in high-dimensional models. So far there has been limited focus on model misspecification, although this is inevitable in high-dimensional settings. We propose tests of the null that are uniformly valid under sparsity conditions weaker than those typically invoked in the literature, assuming working models for the exposure and outcome are both correctly specified. When one of the models is misspecified, by amending the procedure for estimating the nuisance parameters, our tests continue to be valid; hence they are doubly robust. Our proposals are straightforward to implement using existing software for penalized maximum likelihood estimation and do not require sample-splitting. We illustrate them in simulations and an analysis of data obtained from the Ghent University Intensive Care Unit., Comment: 53 pages, 5 tables

Cohort studies provide information on relative hazards and pure risks of disease. For rare outcomes, large cohorts are needed to have sufficient numbers of events, making it costly to obtain covariate information on all cohort members. We focus on nested case-control designs that are used to estimate relative hazard in the Cox regression model. In 1997, Langholz and Borgan showed that pure risk can also be estimated from nested case-control data. However, these approaches do not take advantage of some covariates that may be available on all cohort members. Researchers have used weight calibration to increase the efficiency of relative hazard estimates from case-cohort studies and nested cased-control studies. Our objective is to extend weight calibration approaches to nested case-control designs to improve precision of estimates of relative hazards and pure risks. We show that calibrating sample weights additionally against follow-up times multiplied by relative hazards during the risk projection period improves estimates of pure risk. Efficiency improvements for relative hazards for variables that are available on the entire cohort also contribute to improved efficiency for pure risks. We develop explicit variance formulas for the weight-calibrated estimates. Simulations show how much precision is improved by calibration and confirm the validity of inference based on asymptotic normality. Examples are provided using data from the American Association of Retired Persons Diet and Health Cohort Study.

Studies of social networks provide unique opportunities to assess the causal effects of interventions that may impact more of the population than just those intervened on directly. Such effects are sometimes called peer or spillover effects, and may exist in the presence of interference, i.e., when one individual's treatment affects another individual's outcome. Randomization-based inference (RI) methods provide a theoretical basis for causal inference in randomized studies, even in the presence of interference. In this article, we consider RI of the intervention effect in the eX-FLU trial, a randomized study designed to assess the effect of a social distancing intervention on influenza-like-illness transmission in a connected network of college students. The approach considered enables inference about the effect of the social distancing intervention on the per-contact probability of influenza-like-illness transmission in the observed network. The methods allow for interference between connected individuals and for heterogeneous treatment effects. The proposed methods are evaluated empirically via simulation studies, and then applied to data from the eX-FLU trial. This article is protected by copyright. All rights reserved.

A generalized case-control (GCC) study, like the standard case-control study, leverages outcome-dependent sampling (ODS) to extend to nonbinary responses. We develop a novel, unifying approach for analyzing GCC study data using the recently developed semiparametric extension of the generalized linear model (GLM), which is substantially more robust to model misspecification than existing approaches based on parametric GLMs. For valid estimation and inference, we use a conditional likelihood to account for the biased sampling design. We describe analysis procedures for estimation and inference for the semiparametric GLM under a conditional likelihood, and we discuss problems with estimation and inference under a conditional likelihood when the response distribution is misspecified. We demonstrate the flexibility of our approach over existing ones through extensive simulation studies, and we apply the methodology to an analysis of the Asset and Health Dynamics Among the Oldest Old study, which motives our research. The proposed approach yields a simple yet versatile solution for handling ODS in a wide variety of possible response distributions and sampling schemes encountered in practice.

Experiments that longitudinally collect RNA sequencing (RNA-seq) data can provide transformative insights in biology research by revealing the dynamic patterns of genes. Such experiments create a great demand for new analytic approaches to identify differentially expressed (DE) genes based on large-scale time-course count data. Existing methods, however, are suboptimal with respect to power and may lack theoretical justification. Furthermore, most existing tests are designed to distinguish among conditions based on overall differential patterns across time, though in practice, a variety of composite hypotheses are of more scientific interest. Finally, some current methods may fail to control the false discovery rate. In this paper, we propose a new model and testing procedure to address the above issues simultaneously. Specifically, conditional on a latent Gaussian mixture with evolving means, we model the data by negative binomial distributions. Motivated by Storey (2007) and Hwang and Liu (2010), we introduce a general testing framework based on the proposed model and show that the proposed test enjoys the optimality property of maximum average power. The test allows not only identification of traditional DE genes but also testing of a variety of composite hypotheses of biological interest. We establish the identifiability of the proposed model, implement the proposed method via efficient algorithms, and demonstrate its good performance via simulation studies. The procedure reveals interesting biological insights, when applied to data from an experiment that examines the effect of varying light environments on the fundamental physiology of the marine diatom Phaeodactylum tricornutum.

Researchers often use a two-step process to analyze multivariate data. First, dimensionality is reduced using a technique such as principal component analysis, followed by a group comparison using a t -test or analysis of variance. Although this practice is often discouraged, the statistical properties of this procedure are not well understood, starting with the hypothesis being tested. We suggest that this approach might be considering two distinct hypotheses, one of which is a global test of no differences in the mean vectors, and the other being a focused test of a specific linear combination where the coefficients have been estimated from the data. We study the asymptotic properties of the two-sample t -statistic for these two scenarios, assuming a nonsparse setting. We show that the size of the global test agrees with the presumed level but that the test has poor power. In contrast, the size of the focused test can be arbitrarily distorted with certain mean and covariance structures. A simple method is provided to correct the size of the focused test. Data analyses and simulations are used to illustrate the results. Recommendations on the use of this two-step method and the related use of principal components for prediction are provided.

This paper focuses on analysis of spatiotemporal binary data with absorbing states. The research was motivated by a clinical study on amyotrophic lateral sclerosis (ALS), a neurological disease marked by gradual loss of muscle strength over time in multiple body regions. We propose an autologistic regression model to capture complex spatial and temporal dependencies in muscle strength among different muscles. As it is not clear how the disease spreads from one muscle to another, it may not be reasonable to define a neighborhood structure based on spatial proximity. Relaxing the requirement for prespecification of spatial neighborhoods as in existing models, our method identifies an underlying network structure empirically to describe the pattern of spreading disease. The model also allows the network autoregressive effects to vary depending on the muscles’ previous status. Based on the joint distribution derived from this autologistic model, the joint transition probabilities of responses among locations can be estimated and the disease status can be predicted in the next time interval. Model parameters are estimated through maximization of penalized pseudo-likelihood. Postmodel selection inference was conducted via a bias-correction method, for which the asymptotic distributions were derived. Simulation studies were conducted to evaluate the performance of the proposed method. The method was applied to the analysis of muscle strength loss from the ALS clinical study.

The development of methods to identify, validate, and use surrogate markers to test for a treatment effect has been an area of intense research interest given the potential for valid surrogate markers to reduce the required costs and follow-up times of future studies. Several quantities and procedures have been proposed to assess the utility of a surrogate marker. However, few methods have been proposed to address how one might use the surrogate marker information to test for a treatment effect at an earlier time point, especially in settings where the primary outcome and the surrogate marker are subject to censoring. In this paper, we propose a novel test statistic to test for a treatment effect using surrogate marker information measured prior to the end of the study in a time-to-event outcome setting. We propose a robust nonparametric estimation procedure and propose inference procedures. In addition, we evaluate the power for the design of a future study based on surrogate marker information. We illustrate the proposed procedure and relative power of the proposed test compared to a test performed at the end of the study using simulation studies and an application to data from the Diabetes Prevention Program.

In application of diagnostic accuracy, it is possible that a priori information may exist regarding the test score distributions, either between different disease populations for a single test or between multiple correlated tests. Few have considered constrained diagnostic accuracy analysis when the true disease status is binary; almost none when the disease status is ordinal. Motivated by a study on diagnosing endometriosis, we propose an approach to estimating diagnostic accuracy measures that can incorporate different stochastic order constraints on the test scores when an ordinal true disease status is in consideration. We show that the Dirichlet process mixture provides a convenient framework to both flexibly model the test score distributions and embed the a priori ordering constraints. We also utilize the Dirichlet process mixture to model the correlation between multiple tests. In taking a Bayesian perspective to inference, we develop an efficient Markov chain Monte Carlo algorithm to sample from the posterior distribution and provide posterior estimates of the receiver operating characteristic surfaces and the associated summary measures. The proposed approach is evaluated with extensive simulation studies, and is demonstrated with an application to the endometriosis study.

Although many modeling approaches have been developed to jointly analyze longitudinal biomarkers and a time-to-event outcome, most of these methods can only handle one or a few biomarkers. In this article, we propose a novel joint latent class model to deal with high dimensional longitudinal biomarkers. Our model has three components: a class membership model, a survival submodel, and a longitudinal submodel. In our model, we assume that covariates can potentially affect biomarkers and class membership. We adopt a penalized likelihood approach to infer which covariates have random effects and/or fixed effects on biomarkers, and which covariates are informative for the latent classes. Through extensive simulation studies, we show that our proposed method has improved performance in prediction and assigning subjects to the correct classes over other joint modeling methods and that bootstrap can be used to do inference for our model. We then apply our method to a dataset of patients with idiopathic pulmonary fibrosis, for whom gene expression profiles were measured longitudinally.We are able to identify four interesting latent classes with one class being at much higher risk of death compared to the other classes. We also find that each of the latent classes has unique trajectories in some genes, yielding novel biological insights. This article is protected by copyright. All rights reserved.

With rapidly increasing data sources, statistical methods that make use of external information are gradually becoming popular tools in medical research. In this article, we efficiently synthesize the auxiliary survival information and propose a semiparametric estimation method for the combined empirical likelihood in the framework of the nonmixture cure model, to enhance inference about the associations between exposures and disease outcomes. The auxiliary survival probabilities from external sources are first summarized as unbiased estimation equations, which help produce more efficient estimates of the effects of interest and improve the prediction accuracy for the risk of the event. Then we develop a Bernstein-based sieve empirical likelihood method to estimate the parametric and nonparametric components simultaneously. Such an estimation procedure allows us to reduce the computation burden while preserving the shape constraint on the baseline distribution function. The resulting estimators for the true associations are strongly consistent and asymptotically normal. Instead of collecting substantial exposure data, the auxiliary survival information at multiple time points is incorporated, which further reduces the mean squared error of the estimators. This contributes to biomarker evaluation and treatment effect analysis within smaller studies. We show how to choose the number of auxiliary survival probabilities appropriately and provide a guideline for practical applications. Simulation studies demonstrate that the estimators enjoy large gains in efficiency. A melanoma dataset is analyzed for illustrating the methodology. ispartof: BIOMETRICS vol:78 issue:2 pages:448-459 ispartof: location:United States status: published

Studies of Alzheimer's disease (AD) often collect multiple longitudinal clinical outcomes, which are correlated and predictive of AD progression. It is of great scientific interest to investigate the association between the outcomes and time to AD onset. We model the multiple longitudinal outcomes as multivariate sparse functional data and propose a functional joint model linking multivariate functional data to event time data. In particular, we propose a multivariate functional mixed model to identify the shared progression pattern and outcome-specific progression patterns of the outcomes, which enables more interpretable modeling of associations between outcomes and AD onset. The proposed method is applied to the Alzheimer's Disease Neuroimaging Initiative study (ADNI) and the functional joint model sheds new light on inference of five longitudinal outcomes and their associations with AD onset. Simulation studies also confirm the validity of the proposed model. Data used in preparation of this article were obtained from the ADNI database.

We aim to help inform the choice of estimand (i.e., target of inference) and analysis method to be used in future COVID-19 treatment trials. To this end, we describe estimands for outcome types of particular interest in these trials (ordinal and time-to-event). When the outcome is ordinal, the estimands that we consider are the difference between study arms in the mean outcome, the Mann-Whitney (rank--based) estimand, and the average of the cumulative log odds ratios over the levels of the outcome. For time-to-event outcomes, we consider the difference between arms in the restricted mean survival time, the difference between arms in the cumulative incidence, and the relative risk. Advantageously, the interpretability of these estimands does not rely on a proportional odds or proportional hazards assumptions. For each estimand, we evaluate the potential value added by using estimators that leverage information in baseline variables to improve precision and reduce the required sample size to achieve a desired power. These are called covariate adjusted estimators. To evaluate the performance of the covariate adjusted and unadjusted estimators that we present, we simulate two-arm, randomized trials comparing a hypothetical COVID-19 treatment versus standard of care, where the primary outcome is ordinal or time-to-event. Our simulated distributions are derived from two sources: longitudinal data on over 500 patients hospitalized at Weill Cornell Medicine New York Presbyterian Hospital prior to March 28, 2020, and a CDC preliminary description of 2449 cases reported to the CDC from February 12 to March 16, 2020. We focus on hospitalized, COVID-19 positive patients and consider the following outcomes: intubation, ventilator use, and death. We conduct simulations using all three estimands when the outcome is ordinal, but only evaluate the restricted mean survival time when the outcome is time to event. Our simulations showed that, in trials with at least 200 participants, the precision gains due to covariate adjustment are equivalent to requiring 10-20% fewer participants to achieve the same power as a trial that uses the unadjusted estimator; this was the case for each outcome and estimand that we considered.

The outcome in a randomized experiment is sometimes nonnegative with a clump of observations at zero and continuously distributed positive values. One widely used model for a nonnegative outcome with a clump at zero is the Tobit model, which assumes that the treatment has a shift effect on the distribution of a normally distributed latent variable and the observed outcome is the maximum of the latent variable and zero. We develop a class of semiparametric models and inference procedures that extend the Tobit model in two useful directions. First, we consider more flexible models for the treatment effect than the shift effect of the Tobit model; for example, our models allow for the treatment to have a larger in magnitude effect for upper quantiles. Second, we make semiparametric inferences using empirical likelihood that allow the underlying latent variable to have any distribution, unlike the original Tobit model that assumes the latent variable is normally distributed. We apply our approach to data from the RAND Health Insurance Experiment. We also extend our approach to observational studies in which treatment assignment is strongly ignorable.

Longitudinal data are very popular in practice, but they are often missing in either outcomes or time-dependent risk factors, making them highly unbalanced and complex. Missing data may contain various missing patterns or mechanisms, and how to properly handle it for unbiased and valid inference still presents a significant challenge. Here, we propose a novel semiparametric framework for analyzing longitudinal data with both missing responses and covariates that are missing at random and intermittent, a general and widely encountered situation in observational studies. Within this framework, we consider multiple robust estimation procedures based on innovative calibrated propensity scores, which offers additional relaxation of the misspecification of missing data mechanisms and shows more satisfactory numerical performance. Also, the corresponding robust information criterion on consistent variable selection for our proposed model is developed based on empirical likelihood-based methods. These advocated methods are evaluated in both theory and extensive simulation studies in a variety of situations, showing competing properties and advantages compared to the existing approaches. We illustrate the utility of our approach by analyzing the data from the HIV Epidemiology Research Study.

Hub nodes within biological networks play a pivotal role in determining phenotypes and disease outcomes. In the multiple network setting, we are interested in understanding network similarities and differences across different experimental conditions or subtypes of disease. The majority of proposed approaches for joint modeling of multiple networks focus on the sharing of edges across graphs. Rather than assuming the network similarities are driven by individual edges, we instead focus on the presence of common hub nodes, which are more likely to be preserved across settings. Specifically, we formulate a Bayesian approach to the problem of multiple network inference which allows direct inference on shared and differential hub nodes. The proposed method not only allows a more intuitive interpretation of the resulting networks and clearer guidance on potential targets for treatment, but also improves power for identifying the edges of highly connected nodes. Through simulations, we demonstrate the utility of our method and compare its performance to current popular methods that do not borrow information regarding hub nodes across networks. We illustrate the applicability of our method to inference of co-expression networks from The Cancer Genome Atlas ovarian carcinoma dataset.

There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health outcome. A main focus in these studies is inference on dose levels associated with a given increase in risk relative to a baseline. In addressing this goal, popular methods either dichotomize the continuous response or focus on modeling changes with the dose in the expectation of the outcome. Such choices may lead to information loss and provide inaccurate inference on dose–response relationships. We instead propose a Bayesian convex mixture regression model that allows the entire distribution of the health outcome to be unknown and changing with the dose. To balance flexibility and parsimony, we rely on a mixture model for the density at the extreme doses, and express the conditional density at each intermediate dose via a convex combination of these extremal densities. This representation generalizes classical dose–response models for quantitative outcomes, and provides a more parsimonious, but still powerful, formulation compared to nonparametric methods, thereby improving interpretability and efficiency in inference on risk functions. A Markov chain Monte Carlo algorithm for posterior inference is developed, and the benefits of our methods are outlined in simulations, along with a study on the impact of dde exposure on gestational age.

Complex interplay between genetic and environmental factors characterizes the etiology of many diseases. Modeling gene-environment (GxE) interactions is often challenged by the unknown functional form of the environment term in the true data-generating mechanism. We study the impact of misspecification of the environmental exposure effect on inference for the GxE interaction term in linear and logistic regression models. We first examine the asymptotic bias of the GxE interaction regression coefficient, allowing for confounders as well as arbitrary misspecification of the exposure and confounder effects. For linear regression, we show that under gene-environment independence and some confounder-dependent conditions, when the environment effect is misspecified, the regression coefficient of the GxE interaction can be unbiased. However, inference on the GxE interaction is still often incorrect. In logistic regression, we show that the regression coefficient is generally biased if the genetic factor is associated with the outcome directly or indirectly. Further, we show that the standard robust sandwich variance estimator for the GxE interaction does not perform well in practical GxE studies, and we provide an alternative testing procedure that has better finite sample properties.

Assessment of the regularity of a sequence of events over time is important for clinical decision-making as well as informing public health policy. Our motivating example involves determining the effect of an intervention on the regularity of HIV self-testing behavior among high-risk individuals when exact self-testing times are not recorded. Assuming that these unobserved testing times follow a renewal process, the goals of this work are to develop suitable methods for estimating its distributional parameters when only the presence or absence of at least one event per subject in each of several observation windows is recorded. We propose two approaches to estimation and inference: a likelihood-based discrete survival model using only time to first event; and a potentially more efficient quasi-likelihood approach based on the forward recurrence time distribution using all available data. Regularity is quantified and estimated by the coefficient of variation (CV) of the interevent time distribution. Focusing on the gamma renewal process, where the shape parameter of the corresponding interevent time distribution has a monotone relationship with its CV, we conduct simulation studies to evaluate the performance of the proposed methods. We then apply them to our motivating example, concluding that the use of text message reminders significantly improves the regularity of self-testing, but not its frequency. A discussion on interesting directions for further research is provided.

We introduce a marginal version of the nested Dirichlet process to cluster distributions or histograms. We apply the model to cluster genes by patterns of gene–gene interaction. The proposed approach is based on the nested partition that is implied in the original construction of the nested Dirichlet process. It allows simulation exact inference, as opposed to a truncated Dirichlet process approximation. More importantly, the construction highlights the nature of the nested Dirichlet process as a nested partition of experimental units. We apply the proposed model to inference on clustering genes related to DNA mismatch repair (DMR) by the distribution of gene–gene interactions with other genes. Gene–gene interactions are recorded as coefficients in an auto‐logistic model for the co‐expression of two genes, adjusting for copy number variation, methylation and protein activation. These coefficients are extracted from an online database, called Zodiac, computed based on The Cancer Genome Atlas (TCGA) data. We compare results with a variation of k‐means clustering that is set up to cluster distributions, truncated NDP and a hierarchical clustering method. The proposed inference shows favorable performance, under simulated conditions and also in the real data sets.

In clinical practice, an informative and practically useful treatment rule should be simple and transparent. However, because simple rules are likely to be far from optimal, effective methods to construct such rules must guarantee performance, in terms of yielding the best clinical outcome (highest reward) among the class of simple rules under consideration. Furthermore, it is important to evaluate the benefit of the derived rules on the whole sample and in pre-specified subgroups (e.g., vulnerable patients). To achieve both goals, we propose a robust machine learning method to estimate a linear treatment rule that is guaranteed to achieve optimal reward among the class of all linear rules. We then develop a diagnostic measure and inference procedure to evaluate the benefit of the obtained rule and compare it with the rules estimated by other methods. We provide theoretical justification for the proposed method and its inference procedure, and we demonstrate via simulations its superior performance when compared to existing methods. Lastly, we apply the method to the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) trial on major depressive disorder and show that the estimated optimal linear rule provides a large benefit for mildly depressed and severely depressed patients but manifests a lack-of-fit for moderately depressed patients.

We propose a C-index (index of concordance) applicable to recurrent event data. The present work addresses the dearth of measures for quantifying a regression model's ability to discriminate with respect to recurrent event risk. The data which motivated the methods arise from the Dialysis Outcomes and Practice Patterns Study (DOPPS), a long-running prospective international study of end-stage renal disease patients on hemodialysis. We derive the theoretical properties of the measure under the proportional rates model (Lin et al., 2000), and propose computationally convenient inference procedures based on perturbed influence functions. The methods are shown through simulations to perform well in moderate samples. Analysis of hospitalizations among a cohort of DOPPS patients reveals substantial improvement in discrimination upon adding country indicators to a model already containing basic clinical and demographic covariates, and further improvement upon adding a relatively large set of comorbidity indicators.

Structural nested failure time models (SNFTMs) are models for the effect of a time-dependent exposure on a survival outcome. They have been introduced along with so-called G-estimation methods to provide valid adjustment for time-dependent confounding induced by time-varying variables. Adjustment for informative censoring in SNFTMs is possible via inverse probability of censoring weighting (IPCW). In the presence of considerable dropout, this can imply substantial information loss and consequently imprecise effect estimates. In this article, we aim to increase the efficiency of IPCW G-estimators under a SNFTM by deriving an augmented estimator that uses both censored and uncensored observations, and offers robustness against misspecification of the model for the censoring process, provided that a model for a specific functional of the survival time and time-dependent covariates is correctly specified. The empirical properties of the proposed estimators are studied in a simulation experiment, and the estimators are used in the analysis of surveillance data from the field of hospital epidemiology.

Phosphorylated proteins provide insight into tumor etiology and are used as diagnostic, prognostic, and therapeutic markers of complex diseases. However, pre-analytic variations, such as freezing delay after biopsy acquisition, often occur in real hospital settings and potentially lead to inaccurate results. The objective of this work is to develop statistical methodology to assess the stability of phosphorylated proteins under short-time cold ischemia. We consider a hierarchical model to determine if phosphorylation abundance of a protein at a particular phosphorylation site remains constant or not during cold ischemia. When phosphorylation levels vary across time, we estimate the direction of the changes in each protein based on the maximum overall posterior probability and on the pairwise posterior probabilities, respectively. We analyze a dataset of ovarian tumor tissues that suffered cold-ischemia shock before the proteomic profiling. Gajadhar et al. (2015) applied independent clusterings for each patient because of the high heterogeneity across patients, while our proposed model shares information allowing conclusions for the entire sample population. Using the proposed model, 15 out of 32 proteins show significant changes during 1-hour cold ischemia. Through simulation studies, we conclude that our proposed methodology has a higher accuracy for detecting changes compared to an order restricted inference method. Our approach provides inference on the stability of these phosphorylated proteins, which is valuable when using these proteins as biomarkers for a disease.

N-mixture models describe count data replicated in time and across sites in terms of abundance N and detectability p. They are popular because they allow inference about N while controlling for factors that influence p without the need for marking animals. Using a capture-recapture perspective, we show that the loss of information that results from not marking animals is critical, making reliable statistical modeling of N and p problematic using just count data. One cannot reliably fit a model in which the detection probabilities are distinct among repeat visits as this model is overspecified. This makes uncontrolled variation in p problematic. By counter example, we show that even if p is constant after adjusting for covariate effects (the "constant p" assumption) scientifically plausible alternative models in which N (or its expectation) is non-identifiable or does not even exist as a parameter, lead to data that are practically indistinguishable from data generated under an N-mixture model. This is particularly the case for sparse data as is commonly seen in applications. We conclude that under the constant p assumption reliable inference is only possible for relative abundance in the absence of questionable and/or untestable assumptions or with better quality data than seen in typical applications. Relative abundance models for counts can be readily fitted using Poisson regression in standard software such as R and are sufficiently flexible to allow controlling for p through the use covariates while simultaneously modeling variation in relative abundance. If users require estimates of absolute abundance, they should collect auxiliary data that help with estimation of p.

In practice, both testable and untestable assumptions are generally required to draw inference about the mean outcome measured at the final scheduled visit in a repeated measures study with drop-out. Scharfstein et al. (2014) proposed a sensitivity analysis methodology to determine the robustness of conclusions within a class of untestable assumptions. In their approach, the untestable and testable assumptions were guaranteed to be compatible; their testable assumptions were based on a fully parametric model for the distribution of the observable data. While convenient, these parametric assumptions have proven especially restrictive in empirical research. Here, we relax their distributional assumptions and provide a more flexible, semi-parametric approach. We illustrate our proposal in the context of a randomized trial for evaluating a treatment of schizoaffective disorder.

Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the article are available for Coordinate-Based Meta-Analysis (CBMA). Neuroimaging meta-analysis is used to (i) identify areas of consistent activation; and (ii) build a predictive model of task type or cognitive process for new studies (reverse inference). To simultaneously address these aims, we propose a Bayesian point process hierarchical model for CBMA. We model the foci from each study as a doubly stochastic Poisson process, where the study-specific log intensity function is characterized as a linear combination of a high-dimensional basis set. A sparse representation of the intensities is guaranteed through latent factor modeling of the basis coefficients. Within our framework, it is also possible to account for the effect of study-level covariates (meta-regression), significantly expanding the capabilities of the current neuroimaging meta-analysis methods available. We apply our methodology to synthetic data and neuroimaging meta-analysis datasets.

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely ignored due to a lack of methods that can assess the changing nature of the relationship through time. This article introduces a method for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates, which we refer to as conditional adaptive Bayesian spectrum analysis (CABS). The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. CABS is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The proposed methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse.