Development of predictive models for COVID-19 prognosis based on patients’ demographic and clinical data

This work was supported by Instituto Politécnico de Lisboa, grant IDI&CA/IPL/2020/NephoMD/ISEL, and the FCT grant DSAIPA/DS/0117/2020 - PREMO - Predictive Models of COVID-19 Outcomes for Higher Risk Patients Towards a Precision Medicine. This work was conducted in the Engineering & Health Laboratory, established through a collaboration between Universidade Católica Portuguesa and Instituto Politécnico de Lisboa.Mestrado em Engenharia BiomédicaABSTRACT - Background – Cases of infection by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) were first reported in late December 2019. Due to the large spectrum of clinical presentations and outcomes, the disease was named Coronavirus Disease 2019 (COVID-19) and characterized as a pandemic due to the elevated number of cases worldwide, the high transmission rate, and the lack of action measures. Since then, a lot of progress has been made, but the study of demographic and clinical information and the determination of possible laboratory biomarkers for COVID-19 prognosis is crucial. Purpose – Determine predictive biomarkers for COVID-19’s outcome (death or survival), in critically ill patients, using clinical, demographic, and laboratory data from the intensive care unit (ICU). Methods – Demographic, clinical, and laboratory data from 337 COVID-19 patients admitted to the ICU of Centro Hospitalar Universitário Lisboa Central, Portugal, between March 2020 and March 2021, was extracted from the hospital’s electronic medical record system, pre-processed, and analyzed. Comparisons were made regarding death, the need for invasive mechanical ventilation (IMV), the first three COVID-19 waves, and age groups. Longitudinal data was gathered throughout the patient's stay in the ICU. To infer the evolution of the patient's condition in the first week of ICU admission, a comparative analysis was carried out between the data from the 2nd (335 patients) and 7th days (216 patients). Comparisons of laboratory parameters between discharged and deceased patients, at these time points were performed. The associations between the several biomarkers and death were tested by means of Univariate Generalized Estimating Equations (GEEs) models. Additionally, to analyze the impact of some biomarkers on mortality, crude odds ratios were estimated and interpreted, with the corresponding 95% confidence intervals (CIs). Death event-free survival rates were obtained by the Kaplan-Meier estimator. All P values were considered statistically significant at P<0.05. Results – Deceased patients were considerably older, had more comorbidities, required more IMV, and spent less time in the hospital than discharged patients. Death rates did not differ significantly between COVID-19 waves. Patients from the 1st wave were significantly older and relied more on IMV and extracorporeal membrane oxygenation (ECMO). Most of the detected differences regarding laboratory biomarkers were found between discharged and deceased patients from the 2nd and 3rd waves, being that the deceased ones had almost always worse results. In general, worse results were obtained in the 1st wave and the 7th day of ICU admission. On 2nd day of ICU admission, 2nd wave, higher mortality rates were observed for patients with lymphocyte (LYM) levels under normality ranges. In the 3rd wave, mortality rates were higher for patients with high sensitivity troponin I (hs-cTn I) levels above normality ranges on the 2nd day of ICU admission, with LYM levels under normality ranges on the 7th day of ICU admission, and with platelet (PLT) levels below normality ranges, either in the 2nd or 7th days of ICU admission. Through the univariate logistic regression’s results on 2nd day of ICU admission, 2nd wave, hs-cTn I, red blood cell (RBC) counts, platelet-lymphocyte ratio (PLR) and neutrophil-lymphocyte ratio (NLR) showed significant association with the risk of death. On the 7th day of ICU admission, C-reactive protein (CRP), RBC counts, hematocrit (HCT), hemoglobin (HGB), white blood cell (WBC), and neutrophil (NEU) counts, eosinophil (EO) counts and NLR, revealed significant association with the risk of death. On the 2nd day of ICU admission, the 3rd wave, hs-cTn I, PLT counts, lactate dehydrogenase (LDH), and CRP showed significant association with the risk of death. For the 7th day, PCT, CRP, WBC, and NEU counts, LYM counts, NLR, and PLT count results were also associated with higher risks of death. Univariate GEEs model results demonstrated that, in the 1st wave, hs-cTn I, myoglobin, and EO counts, results were associated with higher risks of death. In the 2nd wave, the risk of death was significantly associated with hs-cTn I, myoglobin levels, EO counts, WBC and NEU counts, LYM counts, and INR. Finally, in the 3rd wave, hs-cTn I, CK, EO counts, WBC and NEU counts, LYM counts, NLR, and PLT counts, were also associated with the risk of death. Conclusion - This study provides useful information for prognostic evaluation that can be used to guide treatment and monitoring. Most importantly, it consists of valuable data that can be employed as the foundation of a variety of future research. Aside from the positive results, more research is needed to develop reliable and robust biomarkers for COVID-19’s outcomes.RESUMO - Introdução – Casos de infeção pelo vírus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) foram relatados pela primeira vez no final de dezembro de 2019. Devido ao grande espetro de apresentações e outcomes clínicos, a doença foi denominada Coronavirus Disease 2019 (COVID-19) e considerada uma pandemia devido ao elevado número de casos em todo o mundo, à alta taxa de transmissão e à falta de medidas de ação. Apesar desta patologia estar a ser aprofundadamente investigada, o estudo de informação demográfica e clínica e a determinação de possíveis biomarcadores laboratoriais para o prognóstico da COVID-19 continua a ser crucial. Objetivos – Determinar biomarcadores preditivos para o outcome da COVID-19 (morte ou vida), em pacientes críticos, usando dados clínicos, demográficos e laboratoriais da unidade de cuidados intensivos (UCI). Métodos – Dados demográficos, clínicos e laboratoriais de 337 pacientes com COVID-19 internados na UCI do Centro Hospitalar Universitário Lisboa Central, em Portugal, entre março de 2020 e março de 2021, foram extraídos das bases de dados eletrónicas do hospital, pré-processados e analisados. Foram feitas comparações em relação ao óbito na UCI, necessidade de ventilação mecânica invasiva (VMI), três vagas de COVID-19 e faixas etárias. Dados longitudinais foram obtidos ao longo da permanência dos pacientes na UCI. Para inferir sobre a evolução do quadro dos pacientes na primeira semana de internamento na UCI, foi realizada uma análise comparativa entre os dados do 2º (335 pacientes) e 7º dias (216 pacientes). Foram realizadas comparações de parâmetros laboratoriais entre pacientes que receberam alta e pacientes falecidos, nestes momentos. As associações entre os diversos biomarcadores e a morte foram testadas por meio de modelos, do inglês, Generalized Estimating Equation (GEEs) univariados. Adicionalmente, para analisar o impacto de alguns biomarcadores na mortalidade, foram estimados e interpretados os odds ratios, com os correspondentes intervalos de confiança de 95%. As taxas de sobrevivência, em relação a cada biomarcador, foram obtidas pelo estimador Kaplan-Meier. Todos os valores de P foram considerados estatisticamente significantes para P<0,05. Resultados – Os pacientes que faleceram eram consideravelmente mais velhos, tinham mais comorbidades, necessitavam mais de VMI e passavam menos tempo no hospital do que os pacientes que receberam alta. As taxas de mortalidade não diferiram significativamente entre as vagas de COVID-19. Os pacientes da 1ª vaga eram significativamente mais velhos e dependiam mais da VMI e da ECMO. A maioria das diferenças detetadas quanto aos biomarcadores laboratoriais foi entre pacientes que receberam alta e os que faleceram na 2ª e 3ª ondas, sendo que os falecidos demonstraram quase sempre piores resultados. A nível de biomarcadores, os piores resultados foram obtidos na 1ª vaga e no 7º dia de internamento UCI. Na 2ª vaga, as maiores taxas de mortalidade foram observadas para pacientes com níveis de linfócitos abaixo da normalidade no 2º dia de internamento na UCI. Na 3ª vaga, as taxas de mortalidade foram maiores para pacientes com níveis de troponina de alta sensibilidade acima da normalidade no 2º dia de internamento na UCI, com níveis de linfócitos abaixo da normalidade no 7º dia de internamento na UCI e com níveis de plaquetas abaixo da normalidade, no 2º e 7º dias de internamento na UCI. Por meio de regressão logística univariada, determinou-se que, para a 2ª vaga, os resultados das troponinas de alta sensibilidade, eritrócitos, rácios entre plaquetas e linfócitos e dos rácios entre neutrófilos e linfócitos poderiam prever o risco de morte no 2º dia de internamento na UCI. O mesmo foi observado para a proteína C-reativa, hemácias, hematócrito, hemoglobina, leucócitos, neutrófilos, eosinófilos e rácio entre neutrófilos e linfócitos, no 7º dia de internamento. Na 3ª vaga, os resultados das troponinas de alta sensibilidade, plaquetas, lactato desidrogenase e proteína C-reativa também demonstraram capacidade para prever o risco de morte no 2º dia de internamento na UCI. Para o 7º dia, os resultados da procalcitonina, proteína C-reativa, leucócitos, linfócitos, neutrófilos e dos rácios entre neutrófilos e linfócitos e plaquetas e linfócitos também demonstraram capacidade preditiva para riscos de morte superiores. Através dos modelos Generalized Estimating Equation (GEEs) univariados, na 1ª vaga os resultados das troponinas de elevada sensibilidade, mioglobina e eosinófilos foram associados a maiores riscos de morte. Na 2ª vaga, o mesmo foi novamente verificado para as troponinas de elevada sensibilidade, a mioglobina e os eosinófilos, e também para os leucócitos, neutrófilos, linfócitos e INR. Por fim, na 3ª vaga, as troponinas de elevada sensibilidade, a creatinina cinase, eosinófilos, leucócitos, neutrófilos, linfócitos, rácio entre neutrófilos e linfócitos e as plaquetas também foram associados ao risco de morte. Conclusão - Este estudo fornece informações úteis para uma avaliação prognóstica e que podem ser usadas para orientar o tratamento e a monitorização de pacientes com COVID-19. É ainda composto por dados que podem vir a ser empregados numa grande variedade de estudos futuros. Além dos resultados positivos, é necessária mais investigação nesta área de maneira a desenvolver biomarcadores confiáveis e robustos para os outcomes da COVID-19.N/

A BAYESIAN ANALYSIS OF THE AGES OF FOUR OPEN CLUSTERS

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Radius Stabilization by Two-Loop Casimir Energy

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BAYESIAN ANALYSIS OF TWO STELLAR POPULATIONS IN GALACTIC GLOBULAR CLUSTERS I: STATISTICAL AND COMPUTATIONAL METHODS

We develop a Bayesian model for globular clusters composed of multiple stellar populations, extending earlier statistical models for open clusters composed of simple (single) stellar populations (e.g., van Dyk et al. 2009; Stein et al. 2013). Specifically, we model globular clusters with two populations that differ in helium abundance. Our model assumes a hierarchical structuring of the parameters in which physical properties—age, metallicity, helium abundance, distance, absorption, and initial mass—are common to (i) the cluster as a whole or to (ii) individual populations within a cluster, or are unique to (iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm is devised for model fitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Our model and computational tools are incorporated into an open-source software suite known as BASE-9. We use numerical studies to demonstrate that our method can recover parameters of two-population clusters, and also show model misspecification can potentially be identified. As a proof of concept, we analyze the two stellar populations of globular cluster NGC 5272 using our model and methods. (BASE-9 is available from GitHub: https://github.com/argiopetech/base/releases)