Joint two-part Tobit models for longitudinal and time-to-event data

Two-part joint model for a longitudinal semicontinuous marker and a terminal event with application to metastatic colorectal cancer data

Joint models for a longitudinal biomarker and a terminal event have gained interests for evaluating cancer clinical trials because the tumor evolution reflects directly the state of the disease. A biomarker characterizing the tumor size evolution over time can be highly informative for assessing treatment options and could be taken into account in addition to the survival time. The biomarker often has a semicontinuous distribution, i.e., it is zero inflated and right skewed. An appropriate model is needed for the longitudinal biomarker as well as an association structure with the survival outcome. In this article, we propose a joint model for a longitudinal semicontinuous biomarker and a survival time. The semicontinuous nature of the longitudinal biomarker is specified by a two-part model, which splits its distribution into a binary outcome (first part) represented by the positive versus zero values and a continuous outcome (second part) with the positive values only. Survival times are modeled with a proportional hazards model for which we propose three association structures with the biomarker. Our simulation studies show some bias can arise in the parameter estimates when the semicontinuous nature of the biomarker is ignored, assuming the true model is a two-part model. An application to advanced metastatic colorectal cancer data from the GERCOR study is performed where our two-part model is compared to one-part joint models. Our results show that treatment arm B (FOLFOX6/FOLFIRI) is associated to higher SLD values over time and its positive association with the terminal event leads to an increased risk of death compared to treatment arm A (FOLFIRI/FOLFOX6).

Hospital-free Days: A Pragmatic and Patient-centered Outcome for Trials Among Critically and Seriously Ill Patients

Hospital-free days (HFDs), alternatively known as "days alive and outside the hospital," is increasingly used as a primary or secondary outcome in randomized trials among critically and seriously ill patients. This novel outcome measure addresses an existing gap in the availability of patient-centered, reliably obtained outcome measures among patients with acute respiratory failure, advanced lung diseases, lung transplantation, and other serious and critical illnesses. Traditional outcomes such as mortality, organ-failure-free days, and longitudinal patient-reported measures have distinct drawbacks that limit their suitability as endpoints in trials of patients with serious illness, particularly those trials with pragmatic designs. By contrast, HFDs provides a summary measure of important health events and is easily calculated from administrative or electronic health record data, thereby balancing the goals of patient-centeredness and pragmatic measurement. However, before HFDs can be widely adopted as an endpoint in trials of patients with respiratory and critical illnesses, several questions must be addressed regarding the optimal definition, measurement, and analysis of HFDs. In this perspective, we outline important considerations relevant to the use of HFDs as a trial endpoint and suggest directions for further development of the measure.

Bayesian joint modelling of longitudinal and time to event data: a methodological review

BACKGROUND

In clinical research, there is an increasing interest in joint modelling of longitudinal and time-to-event data, since it reduces bias in parameter estimation and increases the efficiency of statistical inference. Inference and prediction from frequentist approaches of joint models have been extensively reviewed, and due to the recent popularity of data-driven Bayesian approaches, a review on current Bayesian estimation of joint model is useful to draw recommendations for future researches.

METHODS

We have undertaken a comprehensive review on Bayesian univariate and multivariate joint models. We focused on type of outcomes, model assumptions, association structure, estimation algorithm, dynamic prediction and software implementation.

RESULTS

A total of 89 articles have been identified, consisting of 75 methodological and 14 applied articles. The most common approach to model the longitudinal and time-to-event outcomes jointly included linear mixed effect models with proportional hazards. A random effect association structure was generally used for linking the two sub-models. Markov Chain Monte Carlo (MCMC) algorithms were commonly used (93% articles) to estimate the model parameters. Only six articles were primarily focused on dynamic predictions for longitudinal or event-time outcomes.

CONCLUSION

Methodologies for a wide variety of data types have been proposed; however the research is limited if the association between the two outcomes changes over time, and there is also lack of methods to determine the association structure in the absence of clinical background knowledge. Joint modelling has been proved to be beneficial in producing more accurate dynamic prediction; however, there is a lack of sufficient tools to validate the prediction.

Heterogeneous growth bent-cable models for time-to-event and longitudinal data: application to AIDS studies

The major limitations of growth curve mixture models for HIV/AIDS data are the usual assumptions of normality and monophasic curves within latent classes. This article addresses these limitations by using non-normal skewed distributions and multiphasic patterns for outcomes of prospective studies. For such outcomes, new skew-t (ST) distributions are proposed for modeling heterogeneous growth trajectories, which exhibit not abrupt but gradual multiphasic changes from a declining trend to an increasing trend over time. We assess these clinically important features of longitudinal HIV/AIDS data using the bent-cable framework within a context of a joint modeling of time-to-event process and response process. A real dataset from an AIDS clinical study is used to illustrate the proposed methods.