Gene-environment (G-E) interactions have important implications for cancer outcomes and phenotypes beyond the main G and E effects. Compared to main-effect-only analysis, G-E interaction analysis more seriously suffers from a lack of information caused by higher dimensionality, weaker signals, and other factors. It is also uniquely challenged by the "main effects, interactions" variable selection hierarchy. Effort has been made to bring in additional information to assist cancer G-E interaction analysis. In this study, we take a strategy different from the existing literature and borrow information from pathological imaging data. Such data are a "byproduct" of biopsy, enjoys broad availability and low cost, and has been shown as informative for modeling prognosis and other cancer outcomes/phenotypes in recent studies. Building on penalization, we develop an assisted estimation and variable selection approach for G-E interaction analysis. The approach is intuitive, can be effectively realized, and has competitive performance in simulation. We further analyze The Cancer Genome Atlas (TCGA) data on lung adenocarcinoma (LUAD). The outcome of interest is overall survival, and for G variables, we analyze gene expressions. Assisted by pathological imaging data, our G-E interaction analysis leads to different findings with competitive prediction performance and stability.

Epidemiologists are often interested in estimating the effect of functions of time-varying exposure histories in relation to continuous outcomes, for example, cognitive function. However, the individual exposure measurements that constitute the history upon which an exposure history function is constructed are usually mismeasured. To obtain unbiased estimates of the effects for mismeasured functions in longitudinal studies, a method incorporating main and validation studies was developed. Simulation studies under several realistic assumptions were conducted to assess its performance compared to standard analysis, and we found that the proposed method has good performance in terms of finite sample bias reduction and nominal confidence interval coverage. We applied it to a study of long-term exposure to PM2.5 , in relation to cognitive decline in the Nurses' Health Study Previously, it was found that the 2-year decline in the standard measure of cognition was 0.018 (95% CI, -0.034 to -0.001) units worse per 10 μg/m3 increase in PM2.5 exposure. After correction, the estimated impact of PM2.5 on cognitive decline increased to 0.027 (95% CI, -0.059 to 0.005) units lower per 10 μg/m3 increase. To put this into perspective, effects of this magnitude are about 2/3 of those found in our data associated with each additional year of aging: 0.044 (95% CI, -0.047 to -0.040) units per 1 year older after applying our correction method.

Inverse probability weighting (IPW) methods are commonly used to analyze nonignorable missing data (NIMD) under the assumption of a logistic model for the missingness probability. However, solving IPW equations numerically may involve nonconvergence problems when the sample size is moderate and the missingness probability is high. Moreover, those equations often have multiple roots, and identifying the best root is challenging. Therefore, IPW methods may have low efficiency or even produce biased results. We identify the pitfall in these methods pathologically: they involve the estimation of a moment-generating function (MGF), and such functions are notoriously unstable in general. As a remedy, we model the outcome distribution given the covariates of the completely observed individuals semiparametrically. After forming an induced logistic regression (LR) model for the missingness status of the outcome and covariate, we develop a maximum conditional likelihood method to estimate the underlying parameters. The proposed method circumvents the estimation of an MGF and hence overcomes the instability of IPW methods. Our theoretical and simulation results show that the proposed method outperforms existing competitors greatly. Two real data examples are analyzed to illustrate the advantages of our method. We conclude that if only a parametric LR is assumed but the outcome regression model is left arbitrary, then one has to be cautious in using any of the existing statistical methods in problems involving NIMD.

Group variable selection is often required in many areas, and for this many methods have been developed under various situations. Unlike the individual variable selection, the group variable selection can select the variables in groups, and it is more efficient to identify both important and unimportant variables or factors by taking into account the existing group structure. In this paper, we consider the situation where one only observes interval-censored failure time data arising from the Cox model, for which there does not seem to exist an established method. More specifically, a penalized sieve maximum likelihood variable selection and estimation procedure is proposed and the oracle property of the proposed method is established. Also, an extensive simulation study is performed and suggests that the proposed approach works well in practical situations. An application of the method to a set of real data is provided.

Q-learning has been one of the most commonly used methods for optimizing dynamic treatment regimes (DTRs) in multistage decision-making. Right-censored survival outcome poses a significant challenge to Q-Learning due to its reliance on parametric models for counterfactual estimation which are subject to misspecification and sensitive to missing covariates. In this paper, we propose an imputation-based Q-learning (IQ-learning) where flexible nonparametric or semiparametric models are employed to estimate optimal treatment rules for each stage and then weighted hot-deck multiple imputation (MI) and direct-draw MI are used to predict optimal potential survival times. Missing data are handled using inverse probability weighting and MI, and the nonrandom treatment assignment among the observed is accounted for using a propensity-score approach. We investigate the performance of IQ-learning via extensive simulations and show that it is more robust to model misspecification than existing Q-Learning methods, imputes only plausible potential survival times contrary to parametric models and provides more flexibility in terms of baseline hazard shape. Using IQ-learning, we developed an optimal DTR for leukemia treatment based on a randomized trial with observational follow-up that motivated this study.

This work presents a new model and estimation procedure for the illness-death survival data where the hazard functions follow accelerated failure time (AFT) models. A shared frailty variate induces positive dependence among failure times of a subject for handling the unobserved dependency between the nonterminal and the terminal failure times given the observed covariates. The motivation behind the proposed modeling approach is to leverage the well-known interpretability advantage of AFT models with respect to the observed covariates, while also benefiting from the simple and intuitive interpretation of the hazard functions. A semiparametric maximum likelihood estimation procedure is developed via a kernel smoothed-aided expectation-maximization algorithm, and variances are estimated by weighted bootstrap. We consider existing frailty-based illness-death models and place particular emphasis on highlighting the contribution of our current research. The breast cancer data of the Rotterdam tumor bank are analyzed using the proposed as well as existing illness-death models. The results are contrasted and evaluated based on a new graphical goodness-of-fit procedure. Simulation results and data analysis nicely demonstrate the practical utility of the shared frailty variate with the AFT regression model under the illness-death framework.

Continuous glucose monitors (CGMs) are increasingly used to measure blood glucose levels and provide information about the treatment and management of diabetes. Our motivating study contains CGM data during sleep for 174 study participants with type II diabetes mellitus measured at a 5-min frequency for an average of 10 nights. We aim to quantify the effects of diabetes medications and sleep apnea severity on glucose levels. Statistically, this is an inference question about the association between scalar covariates and functional responses observed at multiple visits (sleep periods). However, many characteristics of the data make analyses difficult, including (1) nonstationary within-period patterns; (2) substantial between-period heterogeneity, non-Gaussianity, and outliers; and (3) large dimensionality due to the number of study participants, sleep periods, and time points. For our analyses, we evaluate and compare two methods: fast univariate inference (FUI) and functional additive mixed models (FAMMs). We extend FUI and introduce a new approach for testing the hypotheses of no effect and time invariance of the covariates. We also highlight areas for further methodological development for FAMM. Our study reveals that (1) biguanide medication and sleep apnea severity significantly affect glucose trajectories during sleep and (2) the estimated effects are time invariant.