Curve registration for non -linear mixed effect ordinary differential equation models
Year: 2025
Type: preprint
Abstract: Curve registration refers to the alignment of temporal trajectories when individuals experience similar dynamics at different speeds. We study this problem in the context of nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs), which are commonly used to describe biological mechanisms in longitudinal data. We extend NLME-ODEs by introducing subject and state specific time-warping functionsthat represent local accelerations or decelerations of the dynamics. The goal is to propose mechanistic longitudinal population data analysiswhich incorporates and locates model error presence to mitigate its effect on model parameter estimation and acknowledge the action of mechanisms ignored by the ODE structure. We then focus on the treatment effect inference problem where these warping functions help to locate as accurately and exhaustively as possible the effects of a given therapy from a followed treated population. From the original model, we quantify treatment effects on well-identified mechanisms specified as ODE parameter covariates, now robustly estimated in model error presence. From the time-warping functions, we infer its action on mechanisms not included in the assumed ODE but appearing as distorted dynamics for treated subjects compared to the untreated ones. We formulate the joint estimation of ODE parameters and warping functions in amixed-effects likelihood framework and implement it in standard softwares such as Monolix implementing SAEM algorithm. Simulation studies show that including time warping improves estimation accuracy. Application to simian immunodeficiency virus (SIV) pre-clinical trial data demonstrates that the method can detect treatment effects on both modeled mechanisms and unmodeled processes. This framework combines mechanistic interpretability with descriptive flexibility, enhancing robustness in the analysis of longitudinal trial data.
Source: HAL
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417280585