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A Beta-Binomial Model for Estimating Zero- or One-inflated Pain Trajectories
Preprint   Open access

A Beta-Binomial Model for Estimating Zero- or One-inflated Pain Trajectories

Yanxi Liu, Richard E. Harris, Daniel Clauw, Emine Bayman, Andrew Leroux and Martin A. Lindquist
bioRxiv
Cold Spring Harbor Laboratory Preprints
05/11/2026
DOI: 10.64898/2026.05.07.721507
PMCID: PMC13192909
PMID: 42182272
url
https://doi.org/10.64898/2026.05.07.721507View
Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Chronic pain is a widespread public health issue that imposes substantial health, emotional, and economic burdens on individuals and communities. Because pain is subjective and lacks objective biomarkers, it is typically measured using patient-reported scores, often on a numerical scale from zero to ten. Increasingly, pain studies use ecological momentary assessment, with multiple daily assessments over days and across study phases (e.g., a series of baseline and post-intervention assessments). These data frequently show many ratings at the extremes (i.e., at minimum or maximum pain scores), commonly referred to as zero- and one-inflation in the statistical literature, along with considerable within-person variability both within and across days. These phenomena present challenges for statistical analyses, as they violate assumptions of most commonly used statistical techniques (e.g., the normality assumption of linear mixed models). We propose a Bayesian beta-binomial mixed-effects model for modeling potential zero- or one-inflated pain scores while accounting for variability using random effects on the mean and variance parameters across subjects. A simulation study demonstrates that the method accurately estimates model parameters across realistic sample sizes, time points, and zero- and one-inflation levels. An application to data from two longitudinal pain studies demonstrates that the model fits the data better and, when correctly specified, yields accurate uncertainty intervals for longitudinal changes in pain compared to existing models, especially for zero- and one-inflated outcomes. Additionally, the model directly estimates the probability of clinically meaningful pain events. The proposed method provides a powerful statistical framework for studying the patient-reported pain trajectories.

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