Statistics and Its Interface

Volume 14 (2021)

Number 1

A robust nonlinear mixed-effects model for COVID-19 death data

Pages: 49 – 57



Fernanda L. Schumacher (Department of Statistics, Universidade Estadual de Campinas, Brazil)

Clécio S. Ferreira (Department of Statistics, Universidade Federal de Juiz de Fora, Brazil)

Marcos O. Prates (Department of Statistics, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil)

Alberto Lachos (National Institute of Neoplastic Diseases, Lima, Peru)

Victor H. Lachos (Department of Statistics, University of Connecticut, Storrs, Ct., U.S.A.)


The analysis of complex longitudinal data such as COVID-19 deaths is challenging due to several inherent features: (i) similarly-shaped profiles with different decay patterns; (ii) unexplained variation among repeated measurements within each country, possibly interpreted as clustered data since they are obtained from the same country at roughly the same time; and (iii) skewness, outliers or skewed heavy-tailed noises possibly embodied within response variables. This article formulates a robust nonlinear mixed effects model based on the class of scale mixtures of skew-normal distributions to model COVID-19 deaths, which allows analysts to model such data in the presence of the above described features simultaneously. An efficient EM-type algorithm is proposed to carry out maximum likelihood estimation of model parameters. The bootstrap method is used to determine inherent characteristics of the individual nonlinear profiles, such as confidence intervals of the predicted deaths and fitted curves. The specific target is to model COVID-19 death curves from some Latin American countries since this region is the new epicenter of the disease. Moreover, since a mixed-effect framework borrows information from the population-average effects, in our analysis we include some countries from Europe and North America that are in a more advanced stage of the COVID-19 death curve.


coronavirus disease, EM algorithm, scale mixtures of skew-normal distributions

This paper was written while Marcos O. Prates was a visiting professor in the Department of Statistics at the University of Connecticut (UConn). In addition to the support of UConn, he also thanks Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for partial financial support.

Fernanda L. Schumacher acknowledges the partial support of Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brazil (CAPES) – Finance Code 001, and by Conselho Nacional de Desenvolvimento Científico e Tecnológico – Brazil (CNPq).

Received 2 July 2020

Accepted 11 September 2020

Published 18 December 2020