From GLMMs to Feedback: a staged roadmap for longitudinal hospital data

Abstract

Clinical decisions often respond to yesterday’s outcomes, creating feedback and time-dependent confounding that standard repeated-measures models don’t resolve. This presentation offers a practical, stepwise roadmap for binary longitudinal outcomes, illustrated by an inpatient glycemic stewardship case study: daily control status (Y), treatment intensification (A, binary), mean glucose (G, continuous, time-varying), and baseline HbA1c (Z). We progress from independent GLM (Stage 1) and marginal GEE (Stage 2A) to a subject-specific GLMM with random intercept and time slope (Stage 2B). We then add short-term memory via lagged outcomes and optional AR(1) residual correlation (Stage 3). To address treatment feedback, we model the assignment mechanism and fit a weighted marginal structural model with stabilized IPW through GEE (Stage 4). We extend clustering to multiple-membership providers and crossed clinic effects (Stage 5), and conclude with a joint model that links the binary outcome and continuous biomarker through shared random effects (Stage 6). Implementation is demonstrated in SAS (PROC GLIMMIX/GENMOD/MIXED/MCMC).

Keywords: GLMM; GEE; marginal structural model; inverse-probability weighting; time-dependent confounding; multiple membership; crossed effects; joint modeling; inpatient glycemic control.