The predictive value of a covariate is often of interest in studies with a survival endpoint. A common situation is that there are some well established predictors and a potential valuable new marker. The challenge is how to judge the potentially added predictive value of this new marker. We propose to use the positive predictive value (PPV) curve based on a nonparametric scoring rule. The estimand of interest is viewed as a single transformation of the underlying data generating probability measure, which allows us to develop a robust nonparametric estimator of the PPV by first calculating the corresponding efficient influence function. We provide asymptotic results and illustrate the approach with numerical studies and with 2 cancer data studies.

Exposure to environmental pollutants during the gestational period can significantly impact infant health outcomes, such as birth weight and neurological development. Identifying critical windows of susceptibility, which are specific periods during pregnancy when exposure has the most profound effects, is essential for developing targeted interventions. Distributed lag models (DLMs) are widely used in environmental epidemiology to analyze the temporal patterns of exposure and their impact on health outcomes. However, traditional DLMs focus on modeling the conditional mean, which may fail to capture heterogeneity in the relationship between predictors and the outcome. Moreover, when modeling the distribution of health outcomes like gestational birth weight, it is the extreme quantiles that are of most clinical relevance. We introduce 2 new quantile distributed lag model (QDLM) estimators designed to address the limitations of existing methods by leveraging smoothness and shape constraints, such as unimodality and concavity, to enhance interpretability and efficiency. We apply our QDLM estimators to the Colorado birth cohort data, demonstrating their effectiveness in identifying critical windows of susceptibility and informing public health interventions.

In cancer treatment, the development of combination therapies requires demonstrating the contribution of each individual drug and optimizing the dose during early-phase trials. This necessitates a large sample size, presenting formidable obstacles for drug developers. To address this issue, we propose a 2-stage randomized phase II design that seamlessly integrates combination dose optimization with component contribution assessment. In stage 1, the optimal combination dose is determined by maximizing the risk-benefit tradeoff across multiple candidate combination doses. In stage 2, a multi-arm randomized phase is initiated to evaluate the contribution of each component within the combination therapy. To increase trial efficiency and reduce the sample size, efficacy data from both stages are adaptively combined using a Bayesian logistic regression model with a spike-and-slab prior. The sample size and decision cutoffs of the proposed design are systematically determined based on a novel calibration procedure to achieve desired operating characteristics. Extensive simulation studies show that the proposed design achieves the dual goals of dose optimization and contribution assessment, while yielding substantial sample size savings compared to competing designs.

In the studies of time-to-event outcomes, it often happens that a fraction of subjects will never experience the event of interest, and these subjects are said to be cured. The studies with a cure fraction often yield a low event rate. To reduce cost and enhance study power, 2-phase sampling designs are often adopted, especially when the covariates of interest are expensive to measure or obtain. In this paper, we consider the generalized case-cohort design for studies with a cure fraction. Under this design, the expensive covariates are measured for a subset of the study cohort, called subcohort, and for all or a subset of the remaining subjects outside the subcohort who have experienced the event during the study, called cases. We propose a 2-step estimation procedure under a class of semiparametric transformation mixture cure models. We first develop a sieve maximum weighted likelihood method based only on the complete data and also devise an Expectation-Maximization (EM) algorithm for implementation. We then update the resulting estimator via a working model between the outcome and cheap covariates or auxiliary variables using the full data. We show that the proposed update estimator is consistent and asymptotically at least as efficient as the complete-data estimator, regardless of whether the working model is correctly specified or not. We also propose a weighted bootstrap procedure for variance estimation. Extensive simulation studies demonstrate the superior performance of the proposed method in finite-sample. An application to the National Wilms' Tumor Study is provided for illustration.

Zero-inflated data commonly arise in various fields, including economics, healthcare, and environmental sciences, where measurements frequently include an excess of zeros due to structural or sampling mechanisms. Traditional approaches, such as Zero-Inflated Poisson and Zero-Inflated Negative Binomial models, have been widely used to handle excess zeros in count data, but they rely on strong parametric assumptions that may not hold in complex real-world applications. In this paper, we propose a zero-inflated quantile single-index rank-score-based test (ZIQ-SIR) to detect associations between zero-inflated outcomes and covariates, particularly when nonlinear relationships are present. ZIQ-SIR offers a flexible, semi-parametric approach that accounts for the zero-inflated nature of the data and avoids the restrictive assumptions of traditional parametric models. Through simulations, we show that ZIQ-SIR outperforms existing methods by achieving higher power and better Type I error control, owing to its flexibility in modeling zero-inflated and overdispersed data. We apply our method to the real-world dataset: microbiome abundance from the Columbian Gut study. In this application, ZIQ-SIR identifies more significant associations than alternative approaches, while maintaining accurate type I error control.

The distribution-free method of conformal prediction has gained considerable attention in computer science, machine learning, and statistics. Candès etal. extended this method to right-censored survival data, addressing right-censoring complexity by creating a covariate shift setting, extracting a subcohort of subjects with censoring times exceeding a fixed threshold. Their approach only estimates the lower prediction bound for type I censoring, where all subjects have available censoring times regardless of their failure status. In medical applications, we often encounter more general right-censored data, observing only the minimum of failure time and censoring time. Subjects with observed failure times have unavailable censoring times. To address this, we propose a bootstrap method to construct 1- as well as 2-sided conformal predictive intervals for general right-censored survival data under different working regression models. Through simulations, our method demonstrates excellent average coverage for the lower bound and good coverage for the 2-sided predictive interval, regardless of working model is correctly specified or not, particularly under moderate censoring. We further extend the proposed method to several directions in medical applications. We apply this method to predict breast cancer patients' future survival times based on tumor characteristics and treatment.

The joint analysis of multimodal neuroimaging data is vital in brain research, revealing complex interactions between brain structures and functions. Our study is motivated by the analysis of a vast dataset of brain functional connectivity (FC) and multimodal structural imaging (SI) features from the UK Biobank. Specifically, we aim to investigate the effects of SI features, such as white matter microstructure integrity (WMMI) and cortical thickness, on the whole-brain functional connectome network. This analysis is inherently challenging due to the extensive structural-functional associations and the intricate network patterns present in multimodal high-dimensional neuroimaging data. To bridge methodological gaps, we developed a novel multi-level sub-graph extraction method (dense bipartite with nested unipartite graph) within a matrix(network)-on-vector regression model. This method identifies subsets of spatially specific SI features that intensely and systematically influence FC sub-networks, while effectively suppressing false positives in large-scale datasets. Applying our method to a multimodal neuroimaging dataset of 4242 participants ffrom the UK Biobank, we evaluated the effects of whole-brain WMMI and cortical thickness on resting-state FC. Our findings indicate that the WMMI in corticospinal tracts and inferior cerebellar peduncle significantly affect functional connections of sensorimotor, salience, and executive sub-networks, with an average correlation of 0.81 ($p < 0.001$).

This paper discusses the assessment of causal treatment effects on a time-to-event outcome, a crucial part of many scientific investigations. Although some methods have been developed for the problem, they are not applicable to situations where there exist both interval censoring and competing risks. We fill in this critical gap under a class of transformation models for cumulative incidence functions by developing an instrumented variable (IV) estimation approach. The IV is a valuable tool commonly used to mitigate the impact of endogenous treatment selection and to determine causal treatment effects in an unbiased manner. The proposed method is flexible as the model includes many commonly used models such as the sub-distributional proportional odds and hazards models (ie, the Fine-Gray model) as special cases. The resulting estimator for the regression parameter is shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate finite sample performance of the proposed approach and suggests that it works well in practice. It is applied to a breast cancer screening study.