Multilevel Bayesian Models for Survival Times and Longitudinal Patient-Reported Outcomes With Many Zeros

Abstract

Regulatory approval of new therapies often depends on demonstrating prolonged survival.Particularly when these survival benefits are modest, consideration of therapeutic benefits to patient-reported outcomes (PROs) may add value to the traditional biomedical clinical trial endpoints. We extend a popular class of joint models for longitudinal and survival data to accommodate the excessive zeros common in PROs, building hierarchical Bayesian models that combine information from longitudinal PRO measurements and survival outcomes. Model development is motivated by a clinical trial for malignant pleural mesothelioma, a rapidly fatal form of pulmonary cancer usually associated with asbestos exposure. By separately modeling the presence and severity of PROs, using our zero-augmented beta likelihood, we are able to model PROs on their original scale and learn about individual-level parameters from both presence and severity of symptoms. Correlations among an individual's PROs and survival are modeled using latent random variables, adjusting the fitted trajectories to better accommodate the observed data for each individual. This work contributes to understanding the impact of treatment on two aspects of mesothelioma: patients' subjective experience of the disease process and their progression-free survival times. We uncover important differences between outcome types that are associated with therapy (periodic, worse in both treatment groups after therapy initiation) and those that are responsive to treatment (aperiodic, gradually widening gap between treatment groups). Finally, our work raises questions for future investigation into multivariate modeling, choice of link functions, and the relative contributions of multiple data sources in joint modeling contexts.

Clinically relevant graphical predictions from Bayesian joint longitudinal-survival models

“…Symptom severity was measured using a visual analog scale on which 0 indicates no symptoms and 100 is the worst possible symptom severity. As reported in Hatfield et al (2012a), some symptoms increased immediately following treatment initiation in both arms; these were termed ''therapy-related''. Other symptoms were slowly worsening in both arms (due to the progressive nature of the disease), but the rate of deterioration differed by treatment arm.…”

“…In what follows, we demonstrate these approaches on simulated data designed to replicate key features of two oncology clinical trials previously analyzed by Hatfield et al (2011Hatfield et al ( , 2012a. In those trials, patients self-reported their symptoms at baseline and then were randomized to one of two treatment regimens.…”

A Spatio-Temporal Model for Mountain Pine Beetle Damage

“…More appropriate is the work by Ospina and Ferrari (2010); Wieczorek and Hawala (2011);Ospina and Ferrari (2012), and Wieczorek et al (2012) who develop zero, one and zero-and-oneaugmented beta regression models. Perhaps most pertinent to the data described here is the work by Hatfield et al (2012) who develop a zero-augmented beta regression model with individual-specific latent trajectories to explain the probability of a zero outcome and the mean of a non-zero outcome. None of these approaches for modeling random variables on [0, 1), however, account for the monotonicity constraints which need to be imposed on the y gt .…”

Tutorial in Joint Modeling and Prediction: A Statistical Software for Correlated Longitudinal Outcomes, Recurrent Events and a Terminal Event

“…This joint model estimates simultaneously the longitudinal and survival processes using the relationship via a latent structure of random effects (Wulfsohn and Tsiatis 1997). Extensions of these include, among others, models for multiple longitudinal outcomes (Hatfield, Boye, Hackshaw, and Carlin 2012), multiple failure times (Elashoff, Li, and Li 2008) and both (Chi and Ibrahim 2006). A review of the joint modeling of longitudinal and survival data was already given elsewhere (McCrink, Marshall, and Cairns 2013;Lawrence Gould et al 2015;Asar, Ritchie, Kalra, and Diggle 2015).…”