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

TL;DR

This paper introduces a robust nonlinear mixed-effects model using skew-normal distributions to analyze COVID-19 death data, effectively handling skewness, outliers, and clustered longitudinal measurements across multiple countries.

Contribution

It presents a novel modeling approach combining robustness and flexibility for complex COVID-19 death data, with an efficient estimation algorithm and bootstrap-based confidence intervals.

Findings

Model captures diverse decay patterns in COVID-19 deaths.

Method provides reliable estimates despite skewness and outliers.

Application to Latin American, European, and North American data demonstrates effectiveness.

Abstract

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, these repeated measurements may be viewed as clustered data since they are taken on the same country at roughly the same time; (iii) Skewness, outliers or skew-heavy-tailed noises are possibly embodied within response variables. This article formulates a robust nonlinear mixed-effects model based in the class of scale mixtures of skew-normal distributions for modeling COVID-19 deaths, which allows the 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 nonlinear individual profiles such as confidence interval of the predicted deaths and fitted curves. The target is to model COVID-19 deaths 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 their COVID-19 deaths curve.