Disjoint and Functional Principal Component Analysis for Infected Cases and Deaths Due to COVID-19 in South American Countries with Sensor-Related Data

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Governments have been challenged to provide timely medical care to face the COVID-19 pandemic. Under this pandemic, the demand for pharmaceutical products has changed significantly. Some of these products are in high demand, while, for others, their demand falls sharply. These changes in the random demand patterns are connected with changes in the skewness (asymmetry) and kurtosis of their data distribution. Such changes are critical to determining optimal lots and inventory costs. The lot-size model helps to make decisions based on probabilistic demand when calculating the optimal costs of supply using two-stage stochastic programming. The objective of this study is to evaluate how the skewness and kurtosis of the distribution of demand data, collected through sensors, affect the modeling of inventories of hospital pharmacy products helpful to treat COVID-19. The use of stochastic programming allows us to obtain results under demand uncertainty that are closer to reality. We carry out a simulation study to evaluate the performance of our methodology under different demand scenarios with diverse degrees of skewness and kurtosis. A case study in the field of hospital pharmacy with sensor-related COVID-19 data is also provided. An algorithm that permits us to use sensors when submitting requests for supplying pharmaceutical products in the hospital treatment of COVID-19 is designed. We show that the coefficients of skewness and kurtosis impact the total costs of inventory that involve order, purchase, holding, and shortage. We conclude that the asymmetry and kurtosis of the demand statistical distribution do not seem to affect the first-stage lot-size decisions. However, demand patterns with high positive skewness are related to significant increases in expected inventories on hand and shortage, increasing the costs of second-stage decisions. Thus, demand distributions that are highly asymmetrical to the right and leptokurtic favor high total costs in probabilistic lot-size systems.

Section: Symbology Introduction Bibliographical Review and Objectivesmentioning

confidence: 99%

Lot-Size Models with Uncertain Demand Considering Its Skewness/Kurtosis and Stochastic Programming Applied to Hospital Pharmacy with Sensor-Related COVID-19 Data

Rojas

Leiva

Huerta

et al. 2021

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“…x ω ik and ∑ ω ∑ i λ ω ij y j vanish in the objective function defined in (14). As before, we are assuming that customer i ranks for each scenario her/his favorite facility j ∈ J i with a number p ω ij ∈ {1, .…”

Section: Lagrangian Relaxationmentioning

confidence: 99%

“…The motivation for our study comes from a problem related to healthcare services, where service centers must be sited in strategic locations to meet the immediate needs of patients. The current situation due to the COVID-19 pandemic makes this problem particularly relevant [ 14 ]. Let us assume that each center corresponds to an assigned place for vaccination and that each center uses one or more vaccine brands from different laboratories.…”

Section: Introductionmentioning

confidence: 99%

A Two-Stage Location Problem with Order Solved Using a Lagrangian Algorithm and Stochastic Programming for a Potential Use in COVID-19 Vaccination Based on Sensor-Related Data

Cabezas

García

Martín-Barreiro

et al. 2021

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Healthcare service centers must be sited in strategic locations that meet the immediate needs of patients. The current situation due to the COVID-19 pandemic makes this problem particularly relevant. Assume that each center corresponds to an assigned place for vaccination and that each center uses one or more vaccine brands/laboratories. Then, each patient could choose a center instead of another, because she/he may prefer the vaccine from a more reliable laboratory. This defines an order of preference that might depend on each patient who may not want to be vaccinated in a center where there are only her/his non-preferred vaccine brands. In countries where the vaccination process is considered successful, the order assigned by each patient to the vaccination centers is defined by incentives that local governments give to their population. These same incentives for foreign citizens are seen as a strategic decision to generate income from tourism. The simple plant/center location problem (SPLP) is a combinatorial approach that has been extensively studied. However, a less-known natural extension of it with order (SPLPO) has not been explored in the same depth. In this case, the size of the instances that can be solved is limited. The SPLPO considers an order of preference that patients have over a set of facilities to meet their demands. This order adds a new set of constraints in its formulation that increases the complexity of the problem to obtain an optimal solution. In this paper, we propose a new two-stage stochastic formulation for the SPLPO (2S-SPLPO) that mimics the mentioned pandemic situation, where the order of preference is treated as a random vector. We carry out computational experiments on simulated 2S-SPLPO instances to evaluate the performance of the new proposal. We apply an algorithm based on Lagrangian relaxation that has been shown to be efficient for large instances of the SPLPO. A potential application of this new algorithm to COVID-19 vaccination is discussed and explored based on sensor-related data. Two further algorithms are proposed to store the patient’s records in a data warehouse and generate 2S-SPLPO instances using sensors.

“…A multivariate version of the RBSARMAX model might also be of interest [ 12 , 50 ], and local influence diagnostics could be derived, allowing the detection of potentially influential cases [ 16 ]. Other aspects for future study using this new model are associated with quantile, spatial, partial least squares, principal components, and sampling structures [ 51 , 52 , 53 , 54 , 55 , 56 ].…”

Section: Conclusion Limitations and Future Researchmentioning

confidence: 99%

Modeling Mortality Based on Pollution and Temperature Using a New Birnbaum–Saunders Autoregressive Moving Average Structure with Regressors and Related-Sensors Data

Saulo

Souza

Vila

et al. 2021

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Environmental agencies are interested in relating mortality to pollutants and possible environmental contributors such as temperature. The Gaussianity assumption is often violated when modeling this relationship due to asymmetry and then other regression models should be considered. The class of Birnbaum–Saunders models, especially their regression formulations, has received considerable attention in the statistical literature. These models have been applied successfully in different areas with an emphasis on engineering, environment, and medicine. A common simplification of these models is that statistical dependence is often not considered. In this paper, we propose and derive a time-dependent model based on a reparameterized Birnbaum–Saunders (RBS) asymmetric distribution that allows us to analyze data in terms of a time-varying conditional mean. In particular, it is a dynamic class of autoregressive moving average (ARMA) models with regressors and a conditional RBS distribution (RBSARMAX). By means of a Monte Carlo simulation study, the statistical performance of the new methodology is assessed, showing good results. The asymmetric RBSARMAX structure is applied to the modeling of mortality as a function of pollution and temperature over time with sensor-related data. This modeling provides strong evidence that the new ARMA formulation is a good alternative for dealing with temporal data, particularly related to mortality with regressors of environmental temperature and pollution.