Bayesian Analysis

The Emergency departments leading the transformation of Alzheimer’s and dementia care (ED-LEAD) study, which I have written about in the past, is approaching the end of its third year. This multifactorial design evaluates three independent, yet potentially synergistic, interventions aimed at improving care for persons living with dementia (PLWD) and their caregivers.

To estimate intervention effects, we are using what I’ve called the HEx-factor model, a Bayesian hierarchical exchangeable factorial model. The original plan was to conduct all analyses using Stan. However, we’ve run into a bit of a snafu. I’ve been working through the problem, and thought I’d share here.

In recent posts, I introduced a Bayesian approach to proportional hazards modeling and then extended it to incorporate a penalized spline. (There was also a third post on handling ties when multiple individuals share the same event time.) This post describes another extension: a random effect to account for clustering in a cluster randomized trial. With this in place, I’ll be ready to tackle the final step—building a model for analyzing a stepped-wedge cluster-randomized trial that incorporates both splines and site-specific random effects.

Over my past few posts, I’ve been progressively building towards a Bayesian model for a stepped-wedge cluster randomized trial with a time-to-event outcome, where time will be modeled using a spline function. I started with a simple Cox proportional hazards model for a traditional RCT, ignoring time as a factor. In the next post, I introduced a nonlinear time effect. For the third post—one I initially thought was ready to publish—I extended the model to a cluster randomized trial without explicitly incorporating time. I was then working on the grand finale, the full model, when I ran into an issue: I couldn’t recover the effect-size parameter used to generate the data.

In my previous post, I outlined a Bayesian approach to proportional hazards modeling. This post serves as an addendum, providing code to incorporate a spline to model a time-varying hazard ratio non linearly. In a second addendum to come I will present a separate model with a site-specific random effect, essential for a cluster-randomized trial. These components lay the groundwork for analyzing a stepped-wedge cluster-randomized trial, where both splines and site-specific random effects will be integrated into a single model. I plan on describing this comprehensive model in a final post.