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In this paper we examine several definitions of vaccine efficacy (VE) that we found in the literature, for diseases that express themselves in outbreaks, that is, when the force of infection grows in time, reaches a maximum and then vanishes. The fact that the disease occurs in outbreaks results in several problems that we analyse. We propose a mathematical model that allows the calculation of VE for several scenarios. Vaccine trials usually needs a large number of volunteers that must be enrolled. Ideally, all volunteers should be enrolled in approximately the same time, but this is generally impossible for logistic reasons and they are enrolled in a fashion that can be replaced by a continuous density function (for example, a Gaussian function). The outbreak can also be replaced by a continuous density function, and the use of these density functions simplifies the calculations. Assuming, for example Gaussian functions, one of the problems one can immediately notice is that the peak of the two curves do not occur at the same time. The model allows us to conclude: First, the calculated vaccine efficacy decreases when the force of infection increases; Second, the calculated vaccine efficacy decreases when the gap between the peak in the force of infection and the peak in the enrollment rate increases; Third, different trial protocols can be simulated with this model; different vaccine efficacy definitions can be calculated and in our simulations, all result are approximately the same. The final, and perhaps most important conclusion of our model, is that vaccine efficacy calculated during outbreaks must be carefully examined and the best way we can suggest to overcome this problem is to stratify the enrolled volunteer's in a cohort-by-cohort basis and do the survival analysis for each cohort, or apply the Cox proportional hazards model for each cohort., Competing Interests: The authors declare they have no conflict of interest., (© 2024 The Authors.)

Objectives: Percutaneous mitral balloon commissurotomy (PMBC) remains the preferred treatment for patients with severe symptomatic rheumatic mitral stenosis (MS) and suitable anatomy. The objective of this study was to propose a new score for the prediction of immediate and late success., Methods: This is a single-center, retrospective analysis of all 1582 patients with severe mitral stenosis who underwent PMBC from August 1987 to July 2010. The composite outcome was cardiovascular death, new PMBC, or mitral valve repair surgery up to 24 years of follow-up., Results: Mean patient age was 36.8 ± 12.9 years, most (86.4%) were female, and Wilkins score was between 9-11 in 49.1% of patients. In the multivariate analysis, the predictors of immediate success were age (odds ratio [OR], 0.98; 95% confidence interval [CI], 0.96-0.99; P=.01), left atrium size (OR, 0.96; 95% CI, 0.93-0.99; P=.01), mean preprocedure mitral gradient (OR, 0.93; 95% CI, 0.89-0.96; P<.001), intermediate Wilkins score 9-11 (OR, 0.62; 95% CI, 0.40-0.94; P=.02), and high Wilkins score ≥12 (OR, 0.35; 95% CI, 0.16-0.76; P<.01). For prediction of late events, age (hazard ratio [HR], 0.98; 95% CI, 0.97-0.98; P<.001), New York Heart Association class III-IV (HR, 1.50; 95% CI, 1.18-1.92; P<.001), left atrium size (HR, 1.02; 95% CI, 1.02-0.04; P<.01), and high Wilkins score ≥12 (HR, 2.02; 95% CI, 1.30-3.15; P<.01) were significant. Two nomograms were developed using significant predictors from the model., Conclusions: In this large population, not only the Wilkins score, but also clinical and hemodynamic features, seem to be relevant in predicting immediate and late success for patients with rheumatic MS who underwent PMBC.