Recent statistical methodology for precision medicine has focused on either identification of subgroups with enhanced treatment effects or estimating optimal treatment decision rules so that treatment is allocated in a way that maximizes, on average, predefined patient outcomes. Less attention has been given to subgroup testing, which involves evaluation of whether at least a subgroup of the population benefits from an investigative treatment, compared to some control or standard of care. In this work, we propose a general framework for testing for the existence of a subgroup with enhanced treatment effects based on the difference of the estimated value functions under an estimated optimal treatment regime and a fixed regime that assigns everyone to the same treatment. Our proposed test does not require specification of the parametric form of the subgroup and allows heterogeneous treatment effects within the subgroup. The test applies to cases when the outcome of interest is either a time-to-event or a (uncensored) scalar, and is valid at the exceptional law. To demonstrate the empirical performance of the proposed test, we study the type I error and power of the test statistics in simulations and also apply our test to data from a Phase III trial in patients with hematological malignancies.

Exposure to air pollution is associated with increased morbidity and mortality. Recent technological advancements permit the collection of time-resolved personal exposure data. Such data are often incomplete with missing observations and exposures below the limit of detection, which limit their use in health effects studies. In this paper, we develop an infinite hidden Markov model for multiple asynchronous multivariate time series with missing data. Our model is designed to include covariates that can inform transitions among hidden states. We implement beam sampling, a combination of slice sampling and dynamic programming, to sample the hidden states, and a Bayesian multiple imputation algorithm to impute missing data. In simulation studies, our model excels in estimating hidden states and state-specific means and imputing observations that are missing at random or below the limit of detection. We validate our imputation approach on data from the Fort Collins Commuter Study. We show that the estimated hidden states improve imputations for data that are missing at random compared to existing approaches. In a case study of the Fort Collins Commuter Study, we describe the inferential gains obtained from our model including improved imputation of missing data and the ability to identify shared patterns in activity and exposure among repeated sampling days for individuals and among distinct individuals.

We present methods for causally interpretable meta-analyses that combine information from multiple randomized trials to draw causal inferences for a target population of substantive interest. We consider identifiability conditions, derive implications of the conditions for the law of the observed data, and obtain identification results for transporting causal inferences from a collection of independent randomized trials to a new target population in which experimental data may not be available. We propose an estimator for the potential outcome mean in the target population under each treatment studied in the trials. The estimator uses covariate, treatment, and outcome data from the collection of trials, but only covariate data from the target population sample. We show that it is doubly robust in the sense that it is consistent and asymptotically normal when at least one of the models it relies on is correctly specified. We study the finite sample properties of the estimator in simulation studies and demonstrate its implementation using data from a multicenter randomized trial.

The existing methods for subgroup analysis can be roughly divided into two categories: finite mixture models (FMM) and regularization methods with an ℓ1 -type penalty. In this paper, by introducing the group centers and ℓ2 -type penalty in the loss function, we propose a novel center-augmented regularization (CAR) method; this method can be regarded as a unification of the regularization method and FMM and hence exhibits higher efficiency and robustness and simpler computations than the existing methods. In particular, its computational complexity is reduced from the O(n2) of the conventional pairwise-penalty method to only O(nK) , where n is the sample size and K is the number of subgroups. The asymptotic normality of CAR is established, and the convergence of the algorithm is proven. CAR is applied to a dataset from a multicenter clinical trial, Buprenorphine in the Treatment of Opiate Dependence; a larger R2 is produced and three additional significant variables are identified compared to those of the existing methods.

A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal procedures become more complex. In this paper, we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the procedures. This leads us to an explicit optimization problem with objective and constraints that describe its specific desiderata. We present a complete solution for deriving optimal procedures for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal procedures that are identical to existing procedures, such as Hommel's procedure or the procedure of Bittman et al. (2009), while for other cases it yields completely novel and more powerful procedures than existing ones. We demonstrate the nature of our novel procedures and their improved power extensively in a simulation and on the APEX study (Cohen et al., 2016).

High throughput spatial transcriptomics (HST) is a rapidly emerging class of experimental technologies that allow for profiling gene expression in tissue samples at or near single-cell resolution while retaining the spatial location of each sequencing unit within the tissue sample. Through analyzing HST data, we seek to identify sub-populations of cells within a tissue sample that may inform biological phenomena. Existing computational methods either ignore the spatial heterogeneity in gene expression profiles, fail to account for important statistical features such as skewness, or are heuristic-based network clustering methods that lack the inferential benefits of statistical modeling. To address this gap, we develop SPRUCE: a Bayesian spatial multivariate finite mixture model based on multivariate skew-normal distributions, which is capable of identifying distinct cellular sub-populations in HST data. We further implement a novel combination of Pólya-Gamma data augmentation and spatial random effects to infer spatially correlated mixture component membership probabilities without relying on approximate inference techniques. Via a simulation study, we demonstrate the detrimental inferential effects of ignoring skewness or spatial correlation in HST data. Using publicly available human brain HST data, SPRUCE outperforms existing methods in recovering expertly annotated brain layers. Finally, our application of SPRUCE to human breast cancer HST data indicates that SPRUCE can distinguish distinct cell populations within the tumor microenvironment. An R package spruce for fitting the proposed models is available through The Comprehensive R Archive Network.

Recent Hi-C technology enables more comprehensive chromosomal conformation research, including the detection of structural variations, especially translocations. In this paper, we formulate the interchromosomal translocation detection as a problem of scan clustering in a spatial point process. We then develop TranScan, a new translocation detection method through scan statistics with the control of false discovery. The simulation shows that TranScan is more powerful than an existing sophisticated scan clustering method, especially under strong signal situations. Evaluation of TranScan against current translocation detection methods on realistic breakpoint simulations generated from real data suggests better discriminative power under the receiver-operating characteristic curve. Power analysis also highlights TranScan's consistent outperformance when sequencing depth and heterozygosity rate is varied. Comparatively, Type I error rate is lowest when evaluated using a karyotypically normal cell line. Both the simulation and real data analysis indicate that TranScan has great potentials in interchromosomal translocation detection using Hi-C data.

Over the past decade, there has been growing enthusiasm for using electronic medical records (EMRs) for biomedical research. Quantile regression estimates distributional associations, providing unique insights into the intricacies and heterogeneity of the EMR data. However, the widespread nonignorable missing observations in EMR often obscure the true associations and challenge its potential for robust biomedical discoveries. We propose a novel method to estimate the covariate effects in the presence of nonignorable missing responses under quantile regression. This method imposes no parametric specifications on response distributions, which subtly uses implicit distributions induced by the corresponding quantile regression models. We show that the proposed estimator is consistent and asymptotically normal. We also provide an efficient algorithm to obtain the proposed estimate and a randomly weighted bootstrap approach for statistical inferences. Numerical studies, including an empirical analysis of real-world EMR data, are used to assess the proposed method's finite-sample performance compared to existing literature.

Many bioinformatics pipelines include tests for equilibrium. Tests for diploids are well studied and widely available, but extending these approaches to autopolyploids is hampered by the presence of double reduction, the comigration of sister chromatid segments into the same gamete during meiosis. Though a hindrance for equilibrium tests, double reduction rates are quantities of interest in their own right, as they provide insights about the meiotic behavior of autopolyploid organisms. Here, we develop procedures to (i) test for equilibrium while accounting for double reduction, and (ii) estimate the double reduction rate given equilibrium. To do so, we take two approaches: a likelihood approach, and a novel U-statistic minimization approach that we show generalizes the classical equilibrium χ2 test in diploids. For small sample sizes and uncertain genotypes, we further develop a bootstrap procedure based on our U-statistic to test for equilibrium. We validate our methods on both simulated and real data.

We consider analyses of case-control studies assembled from electronic health records (EHRs) where the pool of cases is contaminated by patients who are ineligible for the study. These ineligible patients, referred to as "false cases," should be excluded from the analyses if known. However, the true outcome status of a patient in the case pool is unknown except in a subset whose size may be arbitrarily small compared to the entire pool. To effectively remove the influence of the false cases on estimating odds ratio parameters defined by a working association model of the logistic form, we propose a general strategy to adaptively impute the unknown case status without requiring a correct phenotyping model to help discern the true and false case statuses. Our method estimates the target parameters as the solution to a set of unbiased estimating equations constructed using all available data. It outperforms existing methods by achieving robustness to mismodeling the relationship between the outcome status and covariates of interest, as well as improved estimation efficiency. We further show that our estimator is root-n-consistent and asymptotically normal. Through extensive simulation studies and analysis of real EHR data, we demonstrate that our method has desirable robustness to possible misspecification of both the association and phenotyping models, along with statistical efficiency superior to the competitors.

Inverse-probability-weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an effect of interest by constructing a pseudopopulation in which selection biases are eliminated. Despite their ease of use, these estimators require the correct specification of a model for the weighting mechanism, are known to be inefficient, and suffer from the curse of dimensionality. We propose a class of nonparametric inverse-probability-weighted estimators in which the weighting mechanism is estimated via undersmoothing of the highly adaptive lasso, a nonparametric regression function proven to converge at nearly n-1/3 -rate to the true weighting mechanism. We demonstrate that our estimators are asymptotically linear with variance converging to the nonparametric efficiency bound. Unlike doubly robust estimators, our procedures require neither derivation of the efficient influence function nor specification of the conditional outcome model. Our theoretical developments have broad implications for the construction of efficient inverse-probability-weighted estimators in large statistical models and a variety of problem settings. We assess the practical performance of our estimators in simulation studies and demonstrate use of our proposed methodology with data from a large-scale epidemiologic study.

Valid surrogate endpoints S can be used as a substitute for a true outcome of interest T to measure treatment efficacy in a clinical trial. We propose a causal inference approach to validate a surrogate by incorporating longitudinal measurements of the true outcomes using a mixed modeling approach, and we define models and quantities for validation that may vary across the study period using principal surrogacy criteria. We consider a surrogate-dependent treatment efficacy curve that allows us to validate the surrogate at different time points. We extend these methods to accommodate a delayed-start treatment design where all patients eventually receive the treatment. Not all parameters are identified in the general setting. We apply a Bayesian approach for estimation and inference, utilizing more informative prior distributions for selected parameters. We consider the sensitivity of these prior assumptions as well as assumptions of independence among certain counterfactual quantities conditional on pretreatment covariates to improve identifiability. We examine the frequentist properties (bias of point and variance estimates, credible interval coverage) of a Bayesian imputation method. Our work is motivated by a clinical trial of a gene therapy where the functional outcomes are measured repeatedly throughout the trial.

Cancer (treatment) vaccines that are made of neoantigens, or peptides unique to tumor cells due to somatic mutations, have emerged as a promising method to reinvigorate the immune response against cancer. A key step to prioritizing neoantigens for cancer vaccines is computationally predicting which neoantigens are presented on the cell surface by a human leukocyte antigen (HLA). We propose to address this challenge by training a neural network using mass spectrometry (MS) data composed of peptides presented by at least one of several HLAs of a subject. We embed the neural network within a mixture model and train the neural network by maximizing the likelihood of the mixture model. After evaluating our method using data sets where the peptide presentation status was known, we applied it to analyze somatic mutations of 60 melanoma patients and identified a group of neoantigens more immunogenic in tumor cells than in normal cells. Moreover, neoantigen burden estimated by our method was significantly associated with a measurement of the immune system activity, suggesting these neoantigens could induce an immune response.

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among all the subjects, such an assumption may not be realistic when there is potential heterogeneity in regression coefficients among subjects. In this paper, we develop a flexible and interpretable approach, called grouped GEE analysis, to modeling longitudinal data with allowing heterogeneity in regression coefficients. The proposed method assumes that the subjects are divided into a finite number of groups and subjects within the same group share the same regression coefficient. We provide a simple algorithm for grouping subjects and estimating the regression coefficients simultaneously, and show the asymptotic properties of the proposed estimator. The number of groups can be determined by the cross validation with averaging method. We demonstrate the proposed method through simulation studies and an application to a real data set.

In the context of time-to-event analysis, a primary objective is to model the risk of experiencing a particular event in relation to a set of observed predictors. The Concordance Index (C-Index) is a statistic frequently used in practice to assess how well such models discriminate between various risk levels in a population. However, the properties of conventional C-Index estimators when applied to left-truncated time-to-event data have not been well studied, despite the fact that left-truncation is commonly encountered in observational studies. We show that the limiting values of the conventional C-Index estimators depend on the underlying distribution of truncation times, which is similar to the situation with right-censoring as discussed in Uno et al. (2011) [On the C-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data. Statistics in Medicine 30(10), 1105-1117]. We develop a new C-Index estimator based on inverse probability weighting (IPW) that corrects for this limitation, and we generalize this estimator to settings with left-truncated and right-censored data. The proposed IPW estimators are highly robust to the underlying truncation distribution and often outperform the conventional methods in terms of bias, mean squared error, and coverage probability. We apply these estimators to evaluate a predictive survival model for mortality among patients with end-stage renal disease.

Electronic health record (EHR) data are increasingly used for biomedical research, but these data have recognized data quality challenges. Data validation is necessary to use EHR data with confidence, but limited resources typically make complete data validation impossible. Using EHR data, we illustrate prospective, multiwave, two-phase validation sampling to estimate the association between maternal weight gain during pregnancy and the risks of her child developing obesity or asthma. The optimal validation sampling design depends on the unknown efficient influence functions of regression coefficients of interest. In the first wave of our multiwave validation design, we estimate the influence function using the unvalidated (phase 1) data to determine our validation sample; then in subsequent waves, we re-estimate the influence function using validated (phase 2) data and update our sampling. For efficiency, estimation combines obesity and asthma sampling frames while calibrating sampling weights using generalized raking. We validated 996 of 10,335 mother-child EHR dyads in six sampling waves. Estimated associations between childhood obesity/asthma and maternal weight gain, as well as other covariates, are compared to naïve estimates that only use unvalidated data. In some cases, estimates markedly differ, underscoring the importance of efficient validation sampling to obtain accurate estimates incorporating validated data.