A Bayesian mixture of semiparametric mixed‐effects joint models for skewed‐longitudinal and time‐to‐event data

Abstract

In longitudinal studies, it is of interest to investigate how repeatedly measured markers in time are associated with a time to an event of interest, and in the mean time, the repeated measurements are often observed with the features of a heterogeneous population, non-normality, and covariate measured with error because of longitudinal nature. Statistical analysis may complicate dramatically when one analyzes longitudinal-survival data with these features together. Recently, a mixture of skewed distributions has received increasing attention in the treatment of heterogeneous data involving asymmetric behaviors across subclasses, but there are relatively few studies accommodating heterogeneity, non-normality, and measurement error in covariate simultaneously arose in longitudinal-survival data setting. Under the umbrella of Bayesian inference, this article explores a finite mixture of semiparametric mixed-effects joint models with skewed distributions for longitudinal measures with an attempt to mediate homogeneous characteristics, adjust departures from normality, and tailor accuracy from measurement error in covariate as well as overcome shortages of confidence in specifying a time-to-event model. The Bayesian mixture of joint modeling offers an appropriate avenue to estimate not only all parameters of mixture joint models but also probabilities of class membership. Simulation studies are conducted to assess the performance of the proposed method, and a real example is analyzed to demonstrate the methodology. The results are reported by comparing potential models with various scenarios.

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

“…We have found the joint modelling methods developed under the four categories: single outcome for both of the longitudinal and event-time data (39/75, 52%); single longitudinal outcome and multiple event-time outcomes (13/ 75, 17.3%); multiple longitudinal outcomes and single event-time outcome (15/75, 20%); both outcomes are multiple (8/75, 10.7%). The majority of the articles were based on shared random effect joint models , whereas several articles explored joint models in terms of latent classes [42,54,58,[67][68][69][70], additive model [71,72] and functional model [73,74]. We reviewed the methodology for each sub-model and association structure.…”

“…When individuals experienced the event of interest within a known time period (e.g., between follow up appointments), they are interval-censored. Seven articles were based on interval-censored event-times [44,51,59,60,69,70,92]. For example, if an individual experienced a heart attack between the last two follow up appointments, it is known that the event of interest has happened, but it is not known exactly when it is happened.…”

“…Garre et al [67] modelled the longitudinal outcome using an intercept-only random-effects model and a segmented random change-point model. To model a non-linear pattern in longitudinal outcome, Chen and Huang [70] considered a mixture of semiparametric mixed-effects models under multivariate ST distribution. Entink et al [58] proposed a mixture multilevel item response model.…”

“…Using the available information to provide risk assessment of a disease or predict a future longitudinal measurement is valuable in clinical studies. Dynamic prediction is based on updating the prediction from the [13,17,20,24,26,30,31,33,38,39,43,46,49,50,53,57,58,60,62,67,68,72,75,76,82,[84][85][86] Gibbs sampler and Metropolis Hastings (MH) 24(33.3%) [14,15,22,23,25,27,29,35,37,41,42,44,48,51,54,56,59,61,69,70,[77][78]…”

A Bayesian Joint Dispersion Model with Flexible Links

“…In our study, we resorted to this strategy with promising results (section 4.4). Others authors, namely Jiang et al (2015) assumed a latent class model for that variability and Chen and Huang (2015) and Huang et al (2014) modelled the error process with a skew-t distribution.…”