Many methods exist to jointly model either recurrent and related terminal survival events or longitudinal outcome measures and related terminal survival event. However, few methods exist which can account for the dependency between all three outcomes of interest, and none allow for the modeling of all three outcomes without strong correlation assumptions. We propose a joint model which uses subject-specific random effects to connect the survival model (terminal and recurrent events) with a longitudinal outcome model. In the proposed method, proportional hazards models with shared frailties are used to model dependence between the recurrent and terminal events, while a separate (but correlated) set of random effects are utilized in a generalized linear mixed model to model dependence with longitudinal outcome measures. All random effects are related based on an assumed multivariate normal distribution. The proposed joint modeling approach allows for flexible models, particularly for unique longitudinal trajectories, that can be utilized in a wide range of health applications. We evaluate the model through simulation studies as well as through an application to data from the Atherosclerosis Risk in Communities (ARIC) study.

In the context of right-censored data, we study the problem of predicting the restricted time to event based on a set of covariates. Under a quadratic loss, this problem is equivalent to estimating the conditional restricted mean survival time (RMST). To that aim, we propose a flexible and easy-to-use ensemble algorithm that combines pseudo-observations and super learner. The classical theoretical results of the super learner are extended to right-censored data, using a new definition of pseudo-observations, the so-called split pseudo-observations. Simulation studies indicate that the split pseudo-observations and the standard pseudo-observations are similar even for small sample sizes. The method is applied to maintenance and colon cancer datasets, showing the interest of the method in practice, as compared to other prediction methods. We complement the predictions obtained from our method with our RMST-adapted risk measure, prediction intervals and variable importance measures developed in a previous work.

Joint modeling of longitudinal responses and survival time has gained great attention in statistics literature over the last few decades. Most existing works focus on joint analysis of longitudinal data and right-censored data. In this article, we propose a new frailty model for joint analysis of a longitudinal response and interval-censored survival time. Such data commonly arise in real-life studies where participants are examined at periodical or irregular follow-up times. The proposed joint model contains a nonlinear mixed effects submodel for the longitudinal response and a semiparametric probit submodel for the survival time given a shared normal frailty. The proposed joint model allows the regression coefficients to be interpreted as the marginal effects up to a multiplicative constant on both the longitudinal and survival responses. Adopting splines allows us to approximate the unknown baseline functions in both submodels with only a finite number of unknown coefficients while providing great modeling flexibility. An efficient Gibbs sampler is developed for posterior computation, in which all parameters and latent variables can be sampled easily from their full conditional distributions. The proposed method shows a good estimation performance in simulation studies and is further illustrated by a real-life application to the patient data from the Aerobics Center Longitudinal Study. The R code for the proposed methodology is made available for public use.

In many clinical trials, one is interested in evaluating the treatment effect based on different types of outcomes, including recurrent and terminal events. The most popular approach is the time-to-first-event analysis (TTFE), based on the composite outcome of the time to the first event among all events of interest. The motivation for the composite outcome approach is to increase the number of events and potentially increase power. Other composite outcome or composite analysis methods are also studied in the literature, but are less adopted in practice. In this article, we first review the mainstream composite analysis methods and classify them into three categories: (A) Composite-outcome Methods, which combine multiple events into a composite outcome before analysis, e.g., combining events into a time-to-event outcome in TTFE and into a single recurrent event process in the combined-recurrent-event analysis (CRE); (B) Joint-analysis Methods, which test for the recurrent event process and the terminal event jointly, e.g., Joint Frailty Model (JFM), Ghosh-Lin Method (GL), and Nelsen-Aalen Method (NA); (C) Win-ratio type Methods that account for the ordering of two types of events, e.g., Win-fraction Regression (WR). We conduct comprehensive simulation studies to evaluate the performance of various types of methods in terms of type I error control and power under a wide range of scenarios. We found that the non-parametric joint testing approach (GL/NA) and CRE have overall the best performance. However, TTFE and WR exhibit relatively low power. Also, adding events that have no or weak association with treatment usually decreases power.

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.

Data analysis methods have been well developed for analyzing data to make inferences about adaptive treatment strategies in sequential multiple assignment randomized trials (SMART), when data are continuous or right-censored. However, in some clinical studies, time-to-event outcomes are interval censored, meaning that, for example, the time of interest is only observed between two random visit times to the clinic, which is common in some areas such as psychology studies. In this case, the appropriate analysis methods in SMART studies have not been considered in the literature. This article tries to fill this gap by developing methods for this purpose. Based on a proportional hazards model, we propose to use a weighted spline-based sieve maximum likelihood method to make inference about the group differences using a Wald test. Asymptotic properties of the estimator for the hazard ratio are derived, and variance estimation is considered. We conduct a simulation to assess its finite sample performance, and then analyze data from the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) trial.

Analyses of multi-source data, such as data from multi-center randomized trials, individual participant data meta-analyses, or pooled analyses of observational studies, combine information to estimate an overall average treatment effect. However, if average treatment effects vary across data sources, commonly used approaches for multi-source analyses may not have a clear causal interpretation with respect to a target population of interest. In this paper, we provide identification and estimation of average treatment effects in a target population underlying one of the data sources in a point treatment setting for failure time outcomes potentially subject to right-censoring. We do not assume the absence of effect heterogeneity and hence our results are valid, under certain assumptions, when average treatment effects vary across data sources. We derive the efficient influence functions for source-specific average treatment effects using multi-source data under two different sets of assumptions, and propose a novel doubly robust estimator for our estimand. We evaluate the finite-sample performance of our estimator in simulation studies, and apply our methods to data from the HALT-C multi-center trials.

A probability method to estimate cancer risk for asymptomatic individuals for the rest of life was developed based on one's current age and screening history using the disease progressive model. The risk is a function of the transition probability density from the disease-free to the preclinical state, the sojourn time in the preclinical state and the screening sensitivity if one had a screening history with negative results. The method can be applied to any chronic disease. As an example, the method was applied to estimate women's breast cancer risk using parameters estimated from the Health Insurance Plan of Greater New York under two scenarios: with and without a screening history, and obtain some meaningful results.

In this study, we investigate estimation and variable selection for semiparametric transformation models with length-biased survival data-a special case of left truncation commonly encountered in the social sciences and cancer prevention trials. To correct for sampling bias, conventional methods such as conditional likelihood, martingale estimating equations, and composite likelihood have been proposed. However, these methods may be less efficient due to their reliance on only partial information from the full likelihood. In contrast, we adopt a full-likelihood approach under the semiparametric transformation model and propose a unified and more efficient nonparametric maximum likelihood estimator (NPMLE). To perform variable selection, we incorporate an adaptive least absolute shrinkage and selection operator (ALASSO) penalty into the full likelihood. We show that when the NPMLE is used as the initial value, the resulting one-step ALASSO estimator-offering a simplified version of the Newton-Raphson method-achieves oracle properties. Theoretical properties of the proposed methods are established using empirical process techniques. The performance of the methods is evaluated through simulation studies and illustrated with a real data application.

We propose a joint model for multiple time-to-event outcomes where the outcomes have a cure structure. When a subset of a population is not susceptible to an event of interest, traditional survival models cannot accommodate this type of phenomenon. For example, for patients with melanoma, certain modern treatment options can reduce the mortality and relapse rates. Traditional survival models assume the entire population is at risk for the event of interest, i.e., has a non-zero hazard at all times. However, cure rate models allow a portion of the population to be risk-free of the event of interest. Our proposed model uses a novel truncated Gaussian copula to jointly model bivariate time-to-event outcomes of this type. In oncology studies, multiple time-to-event outcomes (e.g., overall survival and relapse-free or progression-free survival) are typically of interest. Therefore, multivariate methods to analyze time-to-event outcomes with a cure structure are potentially of great utility. We formulate a joint model directly on the time-to-event outcomes (i.e., unconditional on whether an individual is cured or not). Dependency between the time-to-event outcomes is modeled via the correlation matrix of the truncated Gaussian copula. A Markov Chain Monte Carlo procedure is proposed for model fitting. Simulation studies and a real data analysis using a melanoma clinical trial data are presented to illustrate the performance of the method and the proposed model is compared to independent models.