Beyond the Mean: A Two-Stage GAMLSS Framework for Physical Activity Bout Patterns and Survival in COPD

Irantzu Barrio; Cristóbal Esteban; Thomas Kneib

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arXiv · 2610.27862

Beyond the Mean: A Two-Stage GAMLSS Framework for Physical Activity Bout Patterns and Survival in COPD

Irantzu Barrio·Cristóbal Esteban·Thomas Kneib

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Abstract

Physical activity patterns in chronic obstructive pulmonary disease (COPD) are typically summarised using simple metrics such as total daily activity or mean time spent in moderate-to-vigorous physical activity. In many studies, this activity is further characterized through physical activity bouts, defined as periods of at least 10 consecutive minutes above 3 metabolic equivalent tasks (METs). However, such summaries overlook the highly skewed, heterogeneous and patient-specific nature of bout-related variables, which may contain clinically relevant information. We propose a distributional modelling approach for accelerometer-derived bout-related physical activity outcomes based on Generalised Additive Models for Location, Scale and Shape (GAMLSS). The framework models multiple parameters of the outcome distributions, including location, scale, and the probability of observing no bouts, allowing the analysis to extend beyond average levels of activity. In a second stage, the estimated distributional parameters are incorporated into a survival analysis to investigate whether information beyond the mean is associated with patient prognosis. The proposed framework is illustrated using accelerometer data from a cohort of 512 COPD patients and considering bout-related outcomes such as minutes accumulated in bouts per day, total number of bouts, and area under MET in bouts per day. The resulting distributional parameters were significantly associated with mortality and provided information beyond average activity levels, particularly through differences in variability across patients. These findings suggest that information contained in distributional parameters beyond the mean may be relevant for understanding the relationship between physical activity patterns and survival.

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Irantzu Barrio, Cristóbal Esteban, Thomas Kneib. 2026-10-20. Beyond the Mean: A Two-Stage GAMLSS Framework for Physical Activity Bout Patterns and Survival in COPD. https://arxiv.org/abs/2610.27862

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