Fast inference for robust nonlinear mixed-effects models.

The interest for nonlinear mixed-effects models comes from application areas as pharmacokinetics, growth curves and HIV viral dynamics. However, the modeling procedure usually leads to many difficulties, as the inclusion of random effects, the estimation process and the model sensitivity to atypical or nonnormal data. The scale mixture of normal distributions include heavy-tailed models, as the Student-t, slash and contaminated normal distributions, and provide competitive alternatives to the usual models, enabling the obtention of robust estimates against outlying observations. Our proposal is to compare two estimation methods in nonlinear mixed-effects models where the random components follow a multivariate scale mixture of normal distributions. For this purpose, a Monte Carlo expectation-maximization algorithm (MCEM) and an efficient likelihood-based approximate method are developed. Results show that the approximate method is much faster and enables a fairly efficient likelihood maximization, although a slightly larger bias may be produced, especially for the fixed-effects parameters. A discussion on the robustness aspects of the proposed models are also provided. Two real nonlinear applications are discussed and a brief simulation study is presented.

Safety-Stock: Predicting the demand for supplies in Brazilian hospitals during the COVID-19 pandemic.

Many challenges lie ahead when dealing with COVID-19, not only related to the acceleration of the pandemic, but also to the prediction of personal protective equipment sets consumption to accommodate the explosive demand. Due to this situation of uncertainty, hospital administration encourages the excess stock of these materials, over-stocking products in some hospitals, and provoking shortages in others. The number of available personal protective equipment sets is one of the three main factors that limit the number of patients at a hospital, as well as the number of available beds and the number of professionals per shift. In this scenario, we developed an easy-to-use expert system to predict the demand for personal protective equipment sets in hospitals during the COVID-19 pandemic, which can be updated in real-time for short term planning. For this system, we propose a naive statistical modeling which combines historical data of the consumption of personal protective equipment sets by hospitals, current protocols for their uses and epidemiological data related to the disease, to build predictive models for the demand for personal protective equipment in Brazilian hospitals during the pandemic. We then embed this modeling in the free Safety-Stock system, which provides useful information for the hospital, especially the safety-stock level and the prediction of consumption/demand for each personal protective equipment set over time. Considering our predictions, a hospital may have its needs related to specific personal protective equipment sets estimated, taking into account its historical stock levels and possible scheduled purchases. The tool allows for adopting strategies to control and keep the stock at safety levels to the demand, mitigating the risk of stock-out. As a direct consequence, it also enables the interchange and cooperation between hospitals, aiming to maximize the availability of equipment during the pandemic.