The person-time ratio distribution for the exact monitoring of adverse events: Historical vs surveillance Poisson data.

In the postmarket drug and vaccine safety surveillance, when the number of adverse events follows a Poisson distribution, the ratio between the exposed and the unexposed person-time information is the random variable that governs the decision rule about the safety of the drug or vaccine. The probability distribution function of such a ratio is derived in this paper. Exact point and interval estimators for the relative risk are discussed as well as statistical hypothesis testing. To the best of our knowledge, this is the first paper that provides an unbiased estimator for the relative risk based on the person-time ratio. The applicability of this new distribution is illustrated through a real data analysis aimed to detect increased risk of occurrence of Myocarditis/Pericarditis following mRNA COVID-19 vaccination in Manitoba, Canada.

Fixed-length interval estimation of population sizes: sequential adaptive Monte Carlo mark–recapture–mark sampling

Mark–recapture sampling schemes are conventional approaches for population size (N) estimation. In this paper, we mainly focus on providing fixed-length confidence interval estimation methodologies for N under a mark–recapture–mark sampling scheme, where, during the resampling phase, non-marked items are marked before they are released back in the population. Using a Monte Carlo method, the interval estimates for N are obtained through a purely sequential procedure with an adaptive stopping rule. Such an adaptive decision criterion enables the user to "learn” with the subsequent marked and newly tagged items. The method is then compared with a recently developed accelerated sequential procedure in terms of coverage probability and expected number of captured items during the resampling stage. To illustrate, we explain how the proposed procedure could be applied to estimate the number of infected COVID-19 individuals in a near-closed population. In addition, we present a numeric application inspired on the problem of estimating the population size of endangered monkeys of the Atlantic forest in Brazil.

Regression model for the reported infected during emerging pandemics under the stochastic SEIR

The COVID-19 pandemic revealed the necessity of measuring the statistical relationship between the transmission rate of epidemic diseases and the social/behavioral, logistical, and economic variables of the affected region. This paper introduces a regression model to estimate the impact of such covariates on the infectious rate of epidemiological agents. Hidden logistical predictor components, such as weekly seasonality of reported data, can also be accessed with the proposed methodology. For this, we assume that the dynamics of officially reported data of emerging pandemics, related to infected groups, follows a stochastic SEIR model. The main advantage of our method is that it is based on a new three-step algorithm that combines the classical likelihood principle, the minimization of the mean squared error, and a tri-section algorithm to estimate, simultaneously, the coefficients of the covariates and the parameters of the compartmental model. Simulation studies are provided to certify the accuracy of the proposed inference methodology. The model is further applied to analyze the official statistical reports of COVID-19 data in the state of São Paulo, Brazil. Supplementary Information The online version contains supplementary material available at 10.1007/s40314-023-02241-w.