My research in robust mixed models has developed methodologies that can be applied to a wide range of longitudinal data since it relaxes the usual Gaussian assumptions by considering a skewed and heavy-tailed class of distributions called Scale Mixture of Skew-Normal.
Additionally, longitudinal data might present serial dependence, which was accounted for using some useful dependence structures. As a result of this project, two methodological papers discussing linear and nonlinear mixed models under this flexibilization and an application to the first wave of COVID-19 data were published.
A user-friendly R package called skewlmm was developed as part of this project, facilitating the use and evaluation of the proposed models in applications.
Selected publications:
Schumacher, F. L., Lachos, V. H., Matos, L. A. (2021). Scale mixture of skew‐normal linear mixed models with within‐subject serial dependence. Statistics in Medicine, 40(7), 1790-1810. doi.org/10.1002/sim.8870
Castro, K. T., Matos, L. A., Schumacher, F. L. (2025). Diagnostic analysis in scale mixture of skew-normal linear mixed models. Statistica Neerlandica, 79(1), e70002. doi.org/10.1111/stan.70002
Schumacher, F. L., Ferreira, C. S., Prates, M. O., Lachos, A., Lachos, V. H. (2021). A robust nonlinear mixed-effects model for COVID-19 death data. Statistics and Its Interface, 14, 49-57. doi.org/10.4310/20-SII637
Data collected over time may contain censored or missing observations, making the use of standard statistical procedures inadequate. Missing observations are common in long time series and can occur due to a temporary lack of funding or failure of measuring instruments, for example. Censored observations usually result from detection limits of the measuring instruments, below and above which observations are not quantifiable.
Disregarding these restrictions may result in biased estimates and invalid statistical inferences; therefore, a proper approach based on the truncated normal distribution was developed for this project. Recently, an extension to account for heavy tails considering the Student-t distribution was developed.
Aiming to facilitate the use of the methodology in different applications, the methods were implemented in the R package ARCensReg.
Selected publications:
Zhong, K., Schumacher, F. L., Castro, L. M., Lachos, V. H. (2025). Bayesian analysis of censored linear mixed-effects models for heavy-tailed irregularly observed repeated measures. Statistics in Medicine, 44: e10295. doi.org/10.1002/sim.10295
Loor Valeriano, K. A., Schumacher, F. L., Galarza, C. E., Matos, L. A. (2024). Censored autoregressive regression models with Student-t innovations. Canadian Journal of Statistics, 52: 804-828. doi.org/10.1002/cjs.11804
Schumacher, F. L., Lachos, V. H., Dey, D. K. (2017). Censored regression models with autoregressive errors: A likelihood-based perspective. Canadian Journal of Statistics, 45, 375-392. doi.org/10.1002/cjs.11338
Multiple Sclerosis (MS) is a multifaceted and debilitating neurological disorder that affects millions of individuals worldwide. Chronological age is the strongest risk factor for MS progression. However, biological age, which takes into account the cumulative damage experienced by cells and tissues over time, may more accurately predict future functional capacity, given that the rate of biological aging across individuals of the same chronological age can vary substantially.
Several biomarkers of different aging mechanisms have been studied in humans. The study of epigenetic modifications has been linked to aging through several factors, including alterations in DNA methylation (DNAm). Specifically, patterns of cytosine-phosphateguanine (CpG) site methylation are used as a reliable biomarker to predict chronological age, and epigenetic “clock” algorithms have been developed using statistical and machine learning methods to predict chronological age, biological age, and health outcomes in the general population and in specific disease conditions.
Ongoing research evaluates the measurement of epigenetic aging in MS and its relation to MS outcomes. Identifying and exploring characteristics of accelerated biological aging in MS patients could provide important insights for the development of therapeutic strategies to target aging processes to slow disability progression and delay or prevent the onset of progressive MS.