Rizopoulos 2016 - Implementation MCMC and Baseline Hazard

Summary

jointModelBayes() takes a separately fitted lme() or glmmPQL() mixed model plus a coxph() object, and samples by random-walk Metropolis (slice sampling for the error precision, Wishart draw for the random-effects precision) with adaptive proposals taken from the separate fits. Defaults: 3,000 adaptive and 3,000 burn-in iterations, 20,000 kept iterations thinned to 2,000, one long chain, hierarchical centring when the random-effects variance exceeds ${\sigma }^2/n$.

Main Content

Design and defaults (Sec. 3.1-3.2)

Required arguments: mixed-model object, Cox object (x=TRUE), timeVar. Default association: current value $\alpha {\eta }_i(t)$. Baseline hazard: penalised B-splines (default 15 knots, 17 coefficients, equally spaced percentiles of event times; lng.in.kn, knots, baseHaz). Survival integral: GQsurv = "GaussKronrod" (default; 7 or 15 points) or "GaussLegendre", GQsurv.k points. Sampler: n.adapt 3000 (acceptance rate checked every n.batch 100), n.burnin 3000, n.iter 20000, n.thin retains 2000. Student-$t$ random effects if df.RE set (MH update of $D^{-1}$). Proposal covariances for $\beta$ and ${\mathbf{b}}_i$ come from the mixed model; survival coefficients and spline coefficients use a two-stage time-dependent Cox fit.

Convergence. One long chain (“one long chain school”); multiple chains by re-running with different init and processing the mcmc component in coda. Diagnostic plots (trace, ACF, density, CPO) in Appendix B via plot().

Hierarchical centring. Used when the largest random-effects variance exceeds ${\sigma }^2/n$, to improve mixing (compare E25’s centred vs non-centred vs hierarchically centred parametrisations).

Speed. For simple models JMbayes is slower than ML-based JM; for complex models comparable. Writing the MCMC in R is still many times faster than JAGS/WinBUGS/OpenBUGS, which need the “zeros trick” for the non-standard survival likelihood and in-program numerical integration. Fit times in the paper: 2.5-5.5 min typical, 59.3 min for the estimated weight-function model. The main advantage over ML is that extensions (categorical or censored longitudinal outcomes) are simple.

Appendix A: knot sensitivity (described in text)

The basic PBC model is refitted with 10 and 20 knots; results are little sensitive to the number and position of knots because spline coefficients are penalised (tauBs about 520). Left-truncated survival and exogenous time-varying covariates are handled by passing a counting-process coxph fit (Appendix C).

Connections

Efficient MCMC, MCMC Basics, Rizopoulos 2016 - Joint Model Specification and Posterior.

See Also

Rizopoulos 2016 - JMbayes Joint Models Overview