Clinical prediction models for mortality in patients with covid-19: external validation and individual participant data meta-analysis

OBJECTIVE: To externally validate various prognostic models and scoring rules for predicting short term mortality in patients admitted to hospital for covid-19. DESIGN: Two stage individual participant data meta-analysis. SETTING: Secondary and tertiary care. PARTICIPANTS: 46 914 patients across 18 countries, admitted to a hospital with polymerase chain reaction confirmed covid-19 from November 2019 to April 2021. DATA SOURCES: Multiple (clustered) cohorts in Brazil, Belgium, China, Czech Republic, Egypt, France, Iran, Israel, Italy, Mexico, Netherlands, Portugal, Russia, Saudi Arabia, Spain, Sweden, United Kingdom, and United States previously identified by a living systematic review of covid-19 prediction models published in The BMJ, and through PROSPERO, reference checking, and expert knowledge. MODEL SELECTION AND ELIGIBILITY CRITERIA: Prognostic models identified by the living systematic review and through contacting experts. A priori models were excluded that had a high risk of bias in the participant domain of PROBAST (prediction model study risk of bias assessment tool) or for which the applicability was deemed poor. METHODS: Eight prognostic models with diverse predictors were identified and validated. A two stage individual participant data meta-analysis was performed of the estimated model concordance (C) statistic, calibration slope, calibration-in-the-large, and observed to expected ratio (O:E) across the included clusters. MAIN OUTCOME MEASURES: 30 day mortality or in-hospital mortality. RESULTS: Datasets included 27 clusters from 18 different countries and contained data on 46 914patients. The pooled estimates ranged from 0.67 to 0.80 (C statistic), 0.22 to 1.22 (calibration slope), and 0.18 to 2.59 (O:E ratio) and were prone to substantial between study heterogeneity. The 4C Mortality Score by Knight et al (pooled C statistic 0.80, 95% confidence interval 0.75 to 0.84, 95% prediction interval 0.72 to 0.86) and clinical model by Wang et al (0.77, 0.73 to 0.80, 0.63 to 0.87) had the highest discriminative ability. On average, 29% fewer deaths were observed than predicted by the 4C Mortality Score (pooled O:E 0.71, 95% confidence interval 0.45 to 1.11, 95% prediction interval 0.21 to 2.39), 35% fewer than predicted by the Wang clinical model (0.65, 0.52 to 0.82, 0.23 to 1.89), and 4% fewer than predicted by Xie et al's model (0.96, 0.59 to 1.55, 0.21 to 4.28). CONCLUSION: The prognostic value of the included models varied greatly between the data sources. Although the Knight 4C Mortality Score and Wang clinical model appeared most promising, recalibration (intercept and slope updates) is needed before implementation in routine care

The simulation of flow shop production system in PTO environment through a matrix approach in system dynamics logic

This paper faces the problem of industrial production optimization through a simulation based approach and in a context of high rigidity production constraints. When an industrial plant is made by several work centers, operating in a typical flow shop configuration, its operation can be seen as a sequence of discrete events, whose optimization can be solved as a scheduling problem. The approach shown in this work is based on a System Dynamics simulation logic. In despite of an apparent greater complexity if compared to traditional discrete event simulation approaches, this logic allows to identify at each instant the position and the confluence of each single order and, moreover, to decide in a dynamic way operations planning at each work center. The simulation approach makes use of matrices to develop the model. In order to evaluate the efficacy of the proposed approach, we have applied it to a case study, considering a flow shop production system in a PTO environment