A hypothesis testing procedure for random changepoint mixed models

Functional Principal Component Analysis as an Alternative to Mixed-Effect Models for Describing Sparse Repeated Measures in Presence of Missing Data

Analyzing longitudinal data in health studies is challenging due to sparse and error-prone measurements, strong within-individual correlation, missing data and various trajectory shapes. While mixed-effect models (MM) effectively address these challenges, they remain parametric models and may incur computational costs. In contrast, functional principal component analysis (FPCA) is a non-parametric approach developed for regular and dense functional data that flexibly describes temporal trajectories at a potentially lower computational cost. This article presents an empirical simulation study evaluating the behavior of FPCA with sparse and error-prone repeated measures and its robustness under different missing data schemes in comparison with MM. The results show that FPCA is well-suited in the presence of missing at random data caused by dropout, except in scenarios involving most frequent and systematic dropout. Like MM, FPCA fails under missing not at random mechanism. The FPCA was applied to describe the trajectories of four cognitive functions before clinical dementia and contrast them with those of matched controls in a case-control study nested in a population-based aging cohort. The average cognitive declines of future dementia cases showed a sudden divergence from those of their matched controls with a sharp acceleration 5 to 2.5 years prior to diagnosis.

Regression analysis of longitudinal data with random change point

A great deal of literature has been established for regression analysis of longitudinal data and in particular, many methods have been proposed for the situation where there exist some change points. However, most of these methods only apply to continuous response and focus on the situations where the change point only occurs on the response or the trend of the individual trajectory. In this article, we propose a new joint modeling approach that allows not only the change point to vary for different subjects or be subject-specific but also the effect heterogeneity of the covariates before and after the change point. The method combines a generalized linear mixed effect model with a random change point for the longitudinal response and a log-linear regression model for the random change point. For inference, a maximum likelihood estimation procedure is developed and the asymptotic properties of the resulting estimators, which differ from the standard asymptotic results, are established. A simulation study is conducted and suggests that the proposed method works well for practical situations. An application to a set of real data on COVID-19 is provided.

nlive: an R package to facilitate the application of the sigmoidal and random changepoint mixed models

BACKGROUND

The use of mixed effect models with a specific functional form such as the Sigmoidal Mixed Model and the Piecewise Mixed Model (or Changepoint Mixed Model) with abrupt or smooth random change allows the interpretation of the defined parameters to understand longitudinal trajectories. Currently, there are no interface R packages that can easily fit the Sigmoidal Mixed Model allowing the inclusion of covariates or incorporating recent developments to fit the Piecewise Mixed Model with random change.

RESULTS

To facilitate the modeling of the Sigmoidal Mixed Model, and Piecewise Mixed Model with abrupt or smooth random change, we have created an R package called nlive. All needed pieces such as functions, covariance matrices, and initials generation were programmed. The package was implemented with recent developments such as the polynomial smooth transition of the piecewise mixed model with improved properties over Bacon-Watts, and the stochastic approximation expectation-maximization (SAEM) for efficient estimation. It was designed to help interpretation of the output by providing features such as annotated output, warnings, and graphs. Functionality, including time and convergence, was tested using simulations. We provided a data example to illustrate the package use and output features and interpretation. The package implemented in the R software is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=nlive .

CONCLUSIONS

The nlive package for R fits the Sigmoidal Mixed Model and the Piecewise Mixed: abrupt and smooth. The nlive allows fitting these models with only five mandatory arguments that are intuitive enough to the less sophisticated users.

Power analysis of longitudinal studies with piecewise linear growth and attrition

In longitudinal research, the development of some outcome variable(s) over time (or age) is studied. Such relations are not necessarily smooth, and piecewise growth models may be used to account for differential growth rates before and after a turning point in time. Such models have been well developed, but the literature on power analysis for these models is scarce. This study investigates the power needed to detect differential growth for linear-linear piecewise growth models in further detail while taking into account the possibility of attrition. Attrition is modeled using the Weibull survival function, which allows for increasing, decreasing or constant attrition across time. Furthermore, this work takes into account the realistic situation where subjects do not necessarily have the same turning point. A multilevel mixed model is used to model the relation between time and outcome, and to derive the relation between sample size and power. The required sample size to achieve a desired power is smallest when the turning points are located halfway through the study and when all subjects have the same turning point. Attrition has a diminishing effect on power, especially when the probability of attrition is largest at the beginning of the study. An example on alcohol use during middle and high school shows how to perform a power analysis. The methodology has been implemented in a Shiny app to facilitate power calculations for future studies.

Random changepoint segmented regression with smooth transition

We consider random changepoint segmented regression models to analyse data from a study conducted to verify whether treatment with stem cells may delay the onset of a symptom of amyotrophic lateral sclerosis in genetically modified mice. The proposed models capture the biological aspects of the data, accommodating a smooth transition between the periods with and without symptoms. An additional changepoint is considered to avoid negative predicted responses. Given the nonlinear nature of the model, we propose an algorithm to estimate the fixed parameters and to predict the random effects by fitting linear mixed models iteratively via standard software. We compare the variances obtained in the final step with bootstrapped and robust ones.