High-dimensional data with left-censored responses are increasingly common in modern applications, yet existing methods for analyzing them are limited. Classical Tobit models fail to handle nonlinear relationships or perform high-dimensional variable selection, whereas deep learning approaches often prioritize prediction performance but lack selection and interpretation capabilities. To address this gap, we propose an integrated deep learning framework, the Deep Tobit model, which employs the negative Tobit log-likelihood as its loss function to properly account for data censoring. A two-stage feature selection algorithm is further developed, with theoretical guarantees on convergence rate and selection consistency. Extensive simulation studies and real-data applications on left-censored aero-engine casing vibration data and HIV viral load data demonstrate that the proposed framework outperforms several state-of-the-art baselines in both variable selection and prediction accuracy.

Joint modeling of longitudinal outcomes and time-to-event data has been extensively used in medical studies because it can simultaneously model the longitudinal trajectories and assess their effects on the event-time. However, in many applications we come across heterogeneous populations, and therefore the subjects need to be clustered for a powerful statistical inference. We consider multivariate binary longitudinal outcomes for which we use Bayesian data-augmentation and get the corresponding latent continuous outcomes. These latent outcomes are clustered using Bayesian consensus clustering, and then we perform a cluster-specific joint analysis. Longitudinal outcomes are modeled by generalized linear mixed models, and we use the proportional hazards model for modeling time-to-event data. Our work is motivated by a clinical trial conducted by Tata Translational Cancer Research Center, Kolkata, where 184 cancer patients were treated for the first twoyears, and then were followed for the next threeyears. Three biomarkers (lymphocyte count, neutrophil count and platelet count), categorized as normal/abnormal, were measured during the treatment, and the relapse time (if any) was recorded for each patient. Our analysis finds three latent clusters for which the effects of the covariates and the median non-relapse probabilities substantially differ. Through a simulation study we illustrate the effectiveness of the proposed simultaneous clustering and joint modeling.

We study shape-constrained nonparametric estimation of the underlying survival function in a cross-sectional study without follow-up. Assuming the rate of initiation event is stationary over time, the observed current duration becomes a length-biased and multiplicatively censored counterpart of the underlying failure time of interest. We focus on two shape constraints for the underlying survival function, namely, log-concavity and convexity. The log-concavity constraint is versatile as it allows for log-concave densities, bi-log-concave distributions, increasing densities, and multi-modal densities. We establish the consistency and pointwise asymptotic distribution of the shape-constrained estimators. Specifically, the proposed estimator under log-concavity is consistent and tuning-parameter-free, thus circumventing the well-known inconsistency issue of the Grenander estimator at 0, where correction methods typically involve tuning parameters.

To investigate pairwise interactions arising from recurrent event processes in a longitudinal network, the framework of the stochastic block model is followed, where every node belongs to a latent group and interactions between node pairs from two specified groups follow a conditional nonhomogeneous Poisson process. Our focus lies on discrete observation times, which are commonly encountered in reality for cost-saving purposes. The variational EM algorithm and variational maximum likelihood estimation are applied for statistical inference. A specific method based on the defined distribution function F and self-consistency algorithm for recurrent events is used when estimating the intensity functions of edges. Numerical simulations illustrate the performance of our proposed estimation procedure in uncovering the underlying structure in the longitudinal networks with recurrent event processes. The dataset of interactions between French schoolchildren for influenza monitoring is analyzed.

Nested case–control design (NCC) is a cost-effective outcome-dependent design in epidemiology that collects all cases and a fixed number of controls at the time of case diagnosis from a large cohort. Due to inefficiency relative to full cohort studies, previous research developed various estimation methodologies but changing designs in the formulation of risk sets was considered only in view of potential bias in the partial likelihood estimation. In this paper, we study a modified design that excludes previously selected controls from risk sets in view of efficiency improvement as well as bias. To this end, we extend the inverse probability weighting method of Samuelsen which was shown to outperform the partial likelihood estimator in the standard setting. We develop its asymptotic theory and a variance estimation of both regression coefficients and the cumulative baseline hazard function that takes account of the complex feature of the modified sampling design. In addition to good finite sample performance of variance estimation, simulation studies show that the modified design with the proposed estimator is more efficient than the standard design. Examples are provided using data from NIH-AARP Diet and Health Cohort Study.

This paper discusses regression analysis of current status data with dependent censoring, a problem that often occurs in many areas such as cross-sectional studies, epidemiological investigations and tumorigenicity experiments. Copula model-based methods are commonly employed to tackle this issue. However, these methods often face challenges in terms of model and parameter identification. The primary aim of this paper is to propose a copula-based analysis for dependent current status data, where the association parameter is left unspecified. Our method is based on a general class of semiparametric linear transformation models and parametric copulas. We demonstrate that the proposed semiparametric model is identifiable under certain regularity conditions from the distribution of the observed data. For inference, we develop a sieve maximum likelihood estimation method, using Bernstein polynomials to approximate the nonparametric functions involved. The asymptotic consistency and normality of the proposed estimators are established. Finally, to demonstrate the effectiveness and practical applicability of our method, we conduct an extensive simulation study and apply the proposed method to a real data example.

Data analysis methods for the study of treatments or exposures in relation to a clinical outcome in the presence of competing risks have a long history, often with inference targets that are hypothetical, thereby requiring strong assumptions for identifiability with available data. Here data analysis methods are considered that are based on single and higher dimensional marginal hazard rates, quantities that are identifiable under standard independent censoring assumptions. These lead naturally to joint survival function estimators for outcomes of interest, including competing risk outcomes, and provide the basis for addressing a variety of data analysis questions. These methods will be illustrated using simulations and Women's Health Initiative cohort and clinical trial data sets, and additional research needs will be described.

The case-cohort design obtains complete covariate data only on cases and on a random sample (the subcohort) of the entire cohort. Subsequent publications described the use of stratification and weight calibration to increase efficiency of estimates of Cox model log-relative hazards, and there has been some work estimating pure risk. Yet there are few examples of these options in the medical literature, and we could not find programs currently online to analyze these various options. We therefore present a unified approach and R software to facilitate such analyses. We used influence functions adapted to the various design and analysis options together with variance calculations that take the two-phase sampling into account. This work clarifies when the widely used “robust” variance estimate of Barlow (Biometrics 50:1064–1072, 1994) is appropriate. The corresponding R software, CaseCohortCoxSurvival, facilitates analysis with and without stratification and/or weight calibration, for subcohort sampling with or without replacement. We also allow for phase-two data to be missing at random for stratified designs. We provide inference not only for log-relative hazards in the Cox model, but also for cumulative baseline hazards and covariate-specific pure risks. We hope these calculations and software will promote wider use of more efficient and principled design and analysis options for case-cohort studies.

This paper studies a novel model averaging estimation issue for linear regression models when the responses are right censored and the covariates are measured with error. A novel weighted Mallows-type criterion is proposed for the considered issue by introducing multiple candidate models. The weight vector for model averaging is selected by minimizing the proposed criterion. Under some regularity conditions, the asymptotic optimality of the selected weight vector is established in terms of its ability to achieve the lowest squared loss asymptotically. Simulation results show that the proposed method is superior to the other existing related methods. A real data example is provided to supplement the actual performance.