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.

中文翻译：

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用于 COVID-19 死亡数据的稳健非线性混合效应模型

由于几个固有特征，对复杂的纵向数据（例如 COVID-19 死亡）的分析具有挑战性：（i）具有不同衰减模式的相似形状的轮廓；(ii) 每个国家内重复测量之间存在无法解释的差异，这些重复测量可被视为聚集数据，因为它们是在同一国家大致同时进行的；(iii) 偏度、异常值或偏重尾噪声可能包含在响应变量中。本文基于偏态正态分布的尺度混合类别制定了一个稳健的非线性混合效应模型，用于对 COVID-19 死亡进行建模，这允许分析人员在存在上述特征的情况下同时对此类数据进行建模。提出了一种有效的EM型算法来进行模型参数的最大似然估计。Bootstrap 方法用于确定非线性个体轮廓的固有特征，例如预测死亡和拟合曲线的置信区间。目标是模拟一些拉丁美洲国家的 COVID-19 死亡曲线，因为该地区是该疾病的新震中。此外，由于混合效应框架借鉴了人口平均效应的信息，因此在我们的分析中，我们包括了欧洲和北美的一些国家，这些国家处于 COVID-19 死亡曲线的更高级阶段。