Population-average trajectories and slopes in smooth random changepoint mixed models

Divan A. Burger; Sean van der Merwe; Emmanuel Lesaffre

Home/Archive/arXiv

arXiv · 2610.34165

Population-average trajectories and slopes in smooth random changepoint mixed models

Divan A. Burger·Sean van der Merwe·Emmanuel Lesaffre

View original source ↗Read source document ↗Export metadata ↓

Abstract

Two-slope mixed-effects models with subject-specific changepoints are widely used to describe biphasic longitudinal trajectories. Treatment-arm summaries are often reported using a single "typical subject" curve obtained by plugging mean parameter values into the subject-specific model. This can be misleading when changepoint timing varies across individuals, because averaging subject-specific curves is not the same as evaluating one curve at average parameter values. A related issue is that individual trajectories may bend gradually rather than change slope through a literal kink, with transition sharpness varying between subjects. We propose population-average estimands for two-slope mixed models with random changepoints and smooth subject-level transitions. These estimands target the treatment-arm mean trajectory and instantaneous slope by averaging over fitted heterogeneity in changepoint timing and transition sharpness. We use a baseline-anchored normal-convolution soft hinge, which preserves the broken stick interpretation, includes the abrupt changepoint model as a limiting case, and allows analytic evaluation of the changepoint-marginalized kernels under a truncated normal changepoint distribution for fixed transition sharpness. Averaging over the fitted transition sharpness distribution is then performed by deterministic one-dimensional quadrature. In an application to HIV-1 RNA data from ACTG Protocol 315, with censoring and heavy-tailed residuals, the marginal summaries reveal a more gradual population-level transition than conventional plug-in summaries. The marginal slope remains more negative for longer, and the marginal mean continues to decline after the plug-in curve has begun to flatten. These results illustrate the main reporting implication: in random changepoint models, representative subject curves should not be treated as population-average trajectories or slopes.

Explore related subjects

stat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Divan A. Burger, Sean van der Merwe, Emmanuel Lesaffre. 2026-10-25. Population-average trajectories and slopes in smooth random changepoint mixed models. https://arxiv.org/abs/2610.34165

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Denoising Data with Measurement Error Using a Reproducing Kernel-Based Diffusion Model

Recent advancements in measurement technologies have facilitated the acquisition of high-resolution data in fields such as engineering, biology, and medicine. However, these observations are frequently corrupted by measurement noise. To address this challenge, we propose a denoising framework that employs diffusion models to recover the underlying error-free data distribution, thereby enabling reliable downstream analysis. Central to our framework is a novel Reproducing Kernel Hilbert Space (RKHS)-based method that trains the diffusion model using only error-contaminated data. This method admits a closed-form solution and achieves a fast convergence rate in terms of estimation error. Theoretically, we validate our approach by deriving an upper bound on the total variation distance between the distributions of the generated denoised data and the true error-free data. Extensive simulations demonstrate the superior empirical performance of our method compared to state-of-the-art baselines. Finally, we illustrate the framework's practical utility in digital health and epidemiology by applying it to Continuous Glucose Monitor (CGM) data and the association analysis between blood lipids and coronary heart disease.

stat.ME↗

arXiv2026

Two-stage least squares with treatment-covariate interactions for treatment effect heterogeneity

Treatment effect heterogeneity with respect to covariates is common in instrumental variable (IV) analyses. An intuitive approach, which we call the interacted two-stage least squares (2sls), is to regress the outcome on the treatment, covariates, and treatment-covariate interactions, using the IV, covariates, and IV-covariate interactions as instruments. We clarify the causal interpretation of the interacted 2sls under the local average treatment effect (LATE) framework when the IV is valid conditional on the covariates. Our main findings are twofold. First, we show that the coefficients on the treatment-covariate interactions from the interacted 2sls identify treatment effect heterogeneity with respect to covariates among compliers for any outcome-generating process if and only if the product of the IV propensity score and the covariates is linear in the covariates, a requirement we call the linear IV-covariate interactions condition. Second, when the covariate vector has dimension K and includes a constant term, we show that the linear IV-covariate interactions condition requires the IV propensity score to take at most K distinct values. The condition holds when (a) the covariates take exactly K distinct values, or (b) the IV is randomly assigned independently of the covariates, but is restrictive beyond these cases. These results underscore the difficulty of interpreting regression coefficients from specifications with treatment-covariate interactions when the covariates are not saturated and the IV is not unconditionally randomized, absent correct specification of the outcome model. We then connect these results to the literature on LATE estimation, and show that under the linear IV-covariate interactions condition, the interacted 2sls with covariates demeaned by their complier means recovers the LATE as a single coefficient.

stat.ME↗

arXiv2026

Sliding-Window Signatures as Features for Time Series Forecasting

The evolution of a time series is often influenced not only by its past values but also by external covariates, giving rise to forecasting with exogenous variables. Nonlinear and delayed effects between covariates and the target series make this task particularly challenging. We propose a forecasting framework based on Ridge regression with sliding-window signature features, combining the computational efficiency of (semi-)parametric models with the flexibility of nonparametric approaches. These features capture complex dependencies between the target and the exogenous variables without relying on prior assumptions about the form of these relationships or the influence of past observations. We establish theoretical guarantees in the discrete-time setting, including universality of approximation and stationarity for the sliding-window transform. To ease implementation, we introduce a novel sequential algorithm that exploits window overlap for efficient signature updates. The method is evaluated on both synthetic and real electricity demand data. Results show that signature features effectively encode temporal and nonlinear dependencies, yielding accurate forecasts competitive with those based on expert knowledge and recent neural network approaches.

stat.ME↗