In studies that require long-term and/or costly follow-up of participants to evaluate a treatment, there is often interest in identifying and using a surrogate marker to evaluate the treatment effect. While several statistical methods have been proposed to evaluate potential surrogate markers, available methods generally do not account for or address the potential for a surrogate to vary in utility or strength by patient characteristics. Previous work examining surrogate markers has indicated that there may be such heterogeneity, that is, that a surrogate marker may be useful (with respect to capturing the treatment effect on the primary outcome) for some subgroups, but not for others. This heterogeneity is important to understand, particularly if the surrogate is to be used in a future trial to replace the primary outcome. In this paper, we propose an approach and estimation procedures to measure the surrogate strength as a function of a baseline covariate W and thus examine potential heterogeneity in the utility of the surrogate marker with respect to W. Within a potential outcome framework, we quantify the surrogate strength/utility using the proportion of treatment effect on the primary outcome that is explained by the treatment effect on the surrogate. We propose testing procedures to test for evidence of heterogeneity, examine finite sample performance of these methods via simulation, and illustrate the methods using AIDS clinical trial data.

Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event (the time origin). In some studies including preventive HIV vaccine efficacy trials, some participants have biomarkers measured starting at the time origin, whereas others have biomarkers measured starting later with the time origin unknown. The semiparametric additive time-varying coefficient model is investigated where the effects of some covariates vary nonparametrically with time while the effects of others remain constant. Weighted profile least squares estimators coupled with kernel smoothing are developed. The method uses the expectation maximization approach to deal with the censored time origin. The Kaplan-Meier estimator and other failure time regression models such as the Cox model can be utilized to estimate the distribution and the conditional distribution of left censored event time related to the censored time origin. Asymptotic properties of the parametric and nonparametric estimators and consistent asymptotic variance estimators are derived. A two-stage estimation procedure for choosing weight is proposed to improve estimation efficiency. Numerical simulations are conducted to examine finite sample properties of the proposed estimators. The simulation results show that the theory and methods work well. The efficiency gain of the two-stage estimation procedure depends on the distribution of the longitudinal error processes. The method is applied to analyze data from the Merck 023/HVTN 502 Step HIV vaccine study.

Complementary features of randomized controlled trials (RCTs) and observational studies (OSs) can be used jointly to estimate the average treatment effect of a target population. We propose a calibration weighting estimator that enforces the covariate balance between the RCT and OS, therefore improving the trial-based estimator's generalizability. Exploiting semiparametric efficiency theory, we propose a doubly robust augmented calibration weighting estimator that achieves the efficiency bound derived under the identification assumptions. A nonparametric sieve method is provided as an alternative to the parametric approach, which enables the robust approximation of the nuisance functions and data-adaptive selection of outcome predictors for calibration. We establish asymptotic results and confirm the finite sample performances of the proposed estimators by simulation experiments and an application on the estimation of the treatment effect of adjuvant chemotherapy for early-stage non-small-cell lung patients after surgery.

Participant-level meta-analysis across multiple studies increases the sample size for pooled analyses, thereby improving precision in effect estimates and enabling subgroup analyses. For analyses involving biomarker measurements as an exposure of interest, investigators must first calibrate the data to address measurement variability arising from usage of different laboratories and/or assays. In practice, the calibration process involves reassaying a random subset of biospecimens from each study at a central laboratory and fitting models that relate the study-specific "local" and central laboratory measurements. Previous work in this area treats the calibration process from the perspective of measurement error techniques and imputes the estimated central laboratory value among individuals with only a local laboratory measurement. In this work, we propose a repeated measures method to calibrate biomarker measurements pooled from multiple studies with study-specific calibration subsets. We account for correlation between measurements made on the same person and between measurements made at the same laboratory. We demonstrate that the repeated measures approach provides valid inference, and compare it to existing calibration approaches grounded in measurement error techniques in an example describing the association between circulating vitamin D and stroke.

For how many days during the past 30 days was your mental health not good?" The responses to this question measure self-reported mental health and can be linked to important covariates in the National Health and Nutrition Examination Survey (NHANES). However, these count variables present major distributional challenges: The data are overdispersed, zero-inflated, bounded by 30, and heaped in 5- and 7-day increments. To address these challenges-which are especially common for health questionnaire data-we design a semiparametric estimation and inference framework for count data regression. The data-generating process is defined by simultaneously transforming and rounding (star) a latent Gaussian regression model. The transformation is estimated nonparametrically and the rounding operator ensures the correct support for the discrete and bounded data. Maximum likelihood estimators are computed using an expectation-maximization (EM) algorithm that is compatible with any continuous data model estimable by least squares. star regression includes asymptotic hypothesis testing and confidence intervals, variable selection via information criteria, and customized diagnostics. Simulation studies validate the utility of this framework. Using star regression, we identify key factors associated with self-reported mental health and demonstrate substantial improvements in goodness-of-fit compared to existing count data regression models.

Although most statistical methods for the analysis of longitudinal data have focused on retrospective models of association, new advances in mobile health data have presented opportunities for predicting future health status by leveraging an individual's behavioral history alongside data from similar patients. Methods that incorporate both individual-level and sample-level effects are critical to using these data to its full predictive capacity. Neural networks are powerful tools for prediction, but many assume input observations are independent even when they are clustered or correlated in some way, such as in longitudinal data. Generalized linear mixed models (GLMM) provide a flexible framework for modeling longitudinal data but have poor predictive power particularly when the data are highly nonlinear. We propose a generalized neural network mixed model that replaces the linear fixed effect in a GLMM with the output of a feed-forward neural network. The model simultaneously accounts for the correlation structure and complex nonlinear relationship between input variables and outcomes, and it utilizes the predictive power of neural networks. We apply this approach to predict depression and anxiety levels of schizophrenic patients using longitudinal data collected from passive smartphone sensor data.

The current approach to using machine learning (ML) algorithms in healthcare is to either require clinician oversight for every use case or use their predictions without any human oversight. We explore a middle ground that lets ML algorithms abstain from making a prediction to simultaneously improve their reliability and reduce the burden placed on human experts. To this end, we present a general penalized loss minimization framework for training selective prediction-set (SPS) models, which choose to either output a prediction set or abstain. The resulting models abstain when the outcome is difficult to predict accurately, such as on subjects who are too different from the training data, and achieve higher accuracy on those they do give predictions for. We then introduce a model-agnostic, statistical inference procedure for the coverage rate of an SPS model that ensembles individual models trained using K-fold cross-validation. We find that SPS ensembles attain prediction-set coverage rates closer to the nominal level and have narrower confidence intervals for its marginal coverage rate. We apply our method to train neural networks that abstain more for out-of-sample images on the MNIST digit prediction task and achieve higher predictive accuracy for ICU patients compared to existing approaches.

Screening mammography aims to identify breast cancer early and secondarily measures breast density to classify women at higher or lower than average risk for future breast cancer in the general population. Despite the strong association of individual mammography features to breast cancer risk, the statistical literature on mammogram imaging data is limited. While functional principal component analysis (FPCA) has been studied in the literature for extracting image-based features, it is conducted independently of the time-to-event response variable. With the consideration of building a prognostic model for precision prevention, we present a set of flexible methods, supervised FPCA (sFPCA) and functional partial least squares (FPLS), to extract image-based features associated with the failure time while accommodating the added complication from right censoring. Throughout the article, we hope to demonstrate that one method is favored over the other under different clinical setups. The proposed methods are applied to the motivating data set from the Joanne Knight Breast Health cohort at Siteman Cancer Center. Our approaches not only obtain the best prediction performance compared to the benchmark model, but also reveal different risk patterns within the mammograms.

Human tissue samples are often mixtures of heterogeneous cell types, which can confound the analyses of gene expression data derived from such tissues. The cell type composition of a tissue sample may itself be of interest and is needed for proper analysis of differential gene expression. A variety of computational methods have been developed to estimate cell type proportions using gene-level expression data. However, RNA isoforms can also be differentially expressed across cell types, and isoform-level expression could be equally or more informative for determining cell type origin than gene-level expression. We propose a new computational method, IsoDeconvMM, which estimates cell type fractions using isoform-level gene expression data. A novel and useful feature of IsoDeconvMM is that it can estimate cell type proportions using only a single gene, though in practice we recommend aggregating estimates of a few dozen genes to obtain more accurate results. We demonstrate the performance of IsoDeconvMM using a unique data set with cell type-specific RNA-seq data across more than 135 individuals. This data set allows us to evaluate different methods given the biological variation of cell type-specific gene expression data across individuals. We further complement this analysis with additional simulations.