Rizopoulos 2016 - JMbayes Joint Models Overview
Summary
Rizopoulos (2016) presents the R package JMbayes, which fits Bayesian joint models: a generalised linear mixed model for a longitudinal biomarker linked, through the subject’s random effects (via current value, slope, cumulative area, weighted history, or the random effects themselves), to a relative-risk hazard for an event time with a penalised B-spline baseline. It also gives dynamic predictions, Bayesian model averaging over association structures, and time-dependent AUC and prediction-error validation, illustrated on the Mayo Clinic PBC data.
Overview
Why joint models. (1) Endogenous time-varying covariates (biomarkers) are measured with error and their future path depends on survival; the time-dependent Cox model is not optimal. (2) Informative dropout: if missingness depends on unobserved longitudinal values, the longitudinal and dropout processes must be modelled jointly (selection, pattern-mixture, shared-parameter frameworks; here dropout is a continuous-time event).
Key result (PBC). A doubling of serum bilirubin multiplies the hazard of death or transplantation by about 2.7 (95% CI 2.3-3.0) in the basic model, with time-dependent AUC around 0.85 at , .
Motivating PyMC examples
E25 “Joint longitudinal-survival models” (Mayo Clinic PBC: mixed model plus Weibull hazard sharing LKJ random effects, Gauss-Legendre cumulative hazard, baseline/LOCF/two-stage biases, informative dropout, centred vs non-centred parametrisations) - example gallery. Closely related: E36 MRP (for hierarchical/multilevel structure) and E117 (selection model; see Concept Note - Forecasting Replication from Published Effects).
Source Map
Connections
Survival Analysis, Hierarchical Models, Missing Data Models (dropout), Efficient MCMC (hierarchical centering), Model Comparison, HDDM (hazard-like first-passage modelling).
Relevance to marketing measurement
A latent customer trajectory (engagement, spend) linked to a churn or conversion hazard is the same structure; ignoring measurement error and dropout biases the apparent effect of engagement on churn. The paper’s evidence is clinical; the mapping is analogy.