Joint modeling of geometric features of longitudinal process and discrete survival time measured on nested timescales: an application to fecundity studies

TL;DR

This paper introduces a joint modeling approach for cyclical longitudinal data and discrete survival times, focusing on geometric features like peaks and curvature, with applications in fecundity studies such as time-to-pregnancy.

Contribution

It develops a shared parameter joint model that captures cycle-specific geometric features and their association with time-to-event, extending existing models to nested timescales.

Findings

Geometric features of hormonal cycles are linked to time-to-pregnancy.

The model accurately predicts survival probabilities based on longitudinal measurements.

Simulation and real data demonstrate the model's effectiveness.

Abstract

In biomedical studies, longitudinal processes are collected till time-to-event, sometimes on nested timescales (example, days within months). Most of the literature in joint modeling of longitudinal and time-to-event data has focused on modeling the mean or dispersion of the longitudinal process with the hazard for time-to-event. However, based on the motivating studies, it may be of interest to investigate how the cycle-level {\it geometric features} (such as the curvature, location and height of a peak), of a cyclical longitudinal process is associated with the time-to-event being studied. We propose a shared parameter joint model for a cyclical longitudinal process and a discrete survival time, measured on nested timescales, where the cycle-varying geometric feature is modeled through a linear mixed effects model and a proportional hazards model for the discrete survival time. The proposed approach allows for prediction of survival probabilities for future subjects based on their available longitudinal measurements. Our proposed model and approach is illustrated through simulation and analysis of Stress and Time-to-Pregnancy, a component of Oxford Conception Study. A joint modeling approach was used to assess whether the cycle-specific geometric features of the lutenizing hormone measurements, such as its peak or its curvature, are associated with time-to-pregnancy (TTP).