Inference in longitudinal data analysis with terminating events
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Session: IPS 950 - Novel Statistical Approaches in Biomarker Discovery, Analysis & Disease Screening
Tuesday 7 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)
Abstract
In several studies, participants are followed up to monitor their functional abilities. For instance, in our motivating case study, patients diagnosed with Duchenne Muscular Dystrophy are monitored regularly on their motor ability using the North Star Ambulatory Assessment. This score takes values from 0 to 34, with higher scores indicating better motor performance. In practice, monitoring the participant’s motor performance is terminated when the participant loses his ambulation.
Current approaches to model the progression of the functional score over time do not consider this complication. In particular, mixed effects models extrapolate the progression beyond the age at which the function was lost. This is characterized in the literature as the unconditional inference (Kurland and Heagerty, 2005) and describes the mean progression as if the terminating event had not occurred. In such settings, estimating the mean function for the dynamic cohort of ambulant patients is more relevant. This is characterized in the literature as partly conditional inference and explicitly considers the time when the function is lost, which might depend on the functional score. Rouanet et al, 2019 have proposed partly conditional inference for normally distributed outcome data and derived both marginal and conditional on the random effects mean progressions. However, their approximate method cannot be applied to bounded responses. Besides, deriving parameters with a valid marginal interpretation for the current ambulant patient is not possible.
In this work, we propose partly conditional inference for bounded longitudinal data. In particular, we derive the mean progression given that the patient is still ambulant based on joint models of Beta mixed models and event time models. Besides, we derive both marginal and conditional on the random effects parameter estimates.