Bayesian Joint Modelling of Longitudinal Data on Abstinence, Frequency and Intensity of Drinking in Alcoholism Trials

Abstract

Summary. In alcoholism research, several complementary outcomes are of interest:abstinence from drinking during a specific time frame, and, when the individual is drinking, frequency of drinking (the proportion of days on which drinking occurs) and intensity of drinking (the average number of drinks per drinking day). The outcomes are often measured repeatedly over time on the same subject and, although they are closely related, they are rarely modelled together. We propose a joint model that allows us to fit these longitudinal outcomes simultaneously, using correlated random effects to model the association between the outcomes and between repeated measurements on the same subject. The model has three parts: a logistic part for sustained abstinence over the period of interest, a truncated binomial part for frequency of drinking and a log-normal model for drinking intensity when drinking occurs. Because of the computational impracticality of fitting models with many random effects by using standard frequentist approaches, we use a Bayesian approach to fit the joint model. We also conduct a simulation study to investigate the gains in parameter estimate bias and mean-squared error associated with joint versus separate modelling. We illustrate the approach on data from an alcoholism clinical trial.

Joint modeling the frequency and duration of accelerometer‐measured physical activity from a lifestyle intervention trial

“…The constant 7.9 is added to the quantities in (10) and (11) to put total duration back on its original scale. In Section C of the supplementary materials, we provide details on integrating out the random effects in (11) in order to calculate marginal daily duration by treatment group and time.…”

“…The constant 7.9 is added to the quantities in (10) and (11) to put total duration back on its original scale. In Section C of the supplementary materials, we provide details on integrating out the random effects in (11) in order to calculate marginal daily duration by treatment group and time. If the goal is to calculate daily minutes of PA on exercise days, ( 9) is replaced with the mean of a truncated Poisson distribution E(n ij | n ij > 0, 𝜆 ij ).…”

“…Most relevant to our work are joint models that model both the frequency (often zero‐inflated) and intensity of a longitudinal process. Buta et al 11 developed a joint model of longitudinal data of drinking behavior in an alcoholism trial. Their joint model included two sub‐models: a hurdle‐binomial model for number of drinking days per week; and a log‐normal model for the average number of drinks per drinking day in a given week.…”

Bayesian joint modeling of patient-reported longitudinal data on frequency and duration of migraine

“…In the migraine study, migraine specialists were mainly interested in the co-evolution of migraine frequency and duration over time, as these two outcomes are biologically associated [25]. This medical research question led us to consider joint modeling of these two longitudinal outcomes, as it is known that joint models provide better insights in the analysis of longitudinal multivariate data with increased efficiency due to information exchange between outcomes and allow estimation of the association between outcomes [3,[10][11][12][13]. In this sense, following the novel papers of [8] and [16], a joint model can be constructed as follows: First, separate generalized linear mixed models (GLMMs) can be used to model each longitudinal outcome under an appropriate distribution from the exponential family, and then a bivariate GLMM can be constructed by imposing a bivariate normal distribution on random effects to jointly analyze the longitudinal migraine data with two count outcomes.…”

Analyzing discontinuities in longitudinal count data: A multilevel generalized linear mixed model.

“…Although continuous variables remain the most common response variable measurement scale for longitudinal psychological research, many variables of interest occur naturally as frequency counts (e.g., the number of cigarettes smoked during and following a smoking cessation treatment trial, Liu & Powers, 2007). Longitudinal count data research can be found in fields such as substance abuse (Ashenhurst, Harden, Corbin, & Fromme, 2015; Bowen et al, 2014; Burrow-Sánchez, Minami, & Hops, 2015; Buta, O’Malley, & Gueorguieva, 2018; Kaysen et al, 2014; Lindgren et al, 2016; Simons, Wills, Emery, & Marks, 2015; Witkiewitz et al, 2014), psychiatry and medicine (Bedics, Atkins, Harned, & Linehan, 2015; Jacob, Duran, Stinson, Lewis, & Zeltzer, 2013; Jobes et al, 2017; Kröger et al, 2015; Martin-Storey & Fromme, 2016; Neelon, O’Malley, & Normand, 2010; O’Neil, et al, 2016; Pennington et al, 2018; Russell et al, 2017; Vannier, Rosen, MacKinnon, & Bergeron, 2017; Yoon, Brown, Bowers, Sharkey, & Horn, 2015), education (Ickovics et al, 2019; Turner, Reynolds, Lee, Subasic, & Bromhead, 2014), and biodiversity (Ma, Mueller, & Rangel, 2016; Paukner, Pedersen, & Simpson, 2017; Robert, Garant, Vander Wal, & Pelletier, 2013; Taylor, Boutin, Humphries, & McAdam, 2014) to name only a few.…”