1035COVID-19: Boom or bust?

Background In the final weeks of 2019, a SARS-CoV-2 virus slipped furtively from animal to human in China. As of March 13, there have been 1,34,918 confirmed cases, out of which 4,990 is the death count. We are predicting extinction or explosion of the virus from the current realization of a Galton Watson process. Methods Based on the region wise reported number of cases, total was calculated. The observed offspring distribution was found by calculating the difference between the total number of cases in consecutive days. Hence the distribution modelled using Sequential Probability Ratio Tests (SPRT) to predict whether extinction or explosion will occur for the current realization of the process. Kolmogorov-Smirnov test was performed on the data to check the distribution of fit. Results We assume conservative approach of SPRT. The geometric distribution fits to the data taken from January 2020 to March 12, 2020. The SPRT on the offspring distribution predicts extinction of the disease if the number of cases reported on a new day are less than 58 then the disease will extinct, and will explode if more than 9,990 cases. Conclusions Our results show that if COVID-19 transmission is established, understanding the effectiveness of control measures in different settings will be crucial for understanding the likelihood that transmission can eventually be effectively mitigated. Key messages Our analysis highlights the value of recording individual cases and analyzing geographically heterogeneous data of COVID-19. Our results also have implications for estimation of transmission dynamics using the number of exported cases from a specific area.

Sequential probability ratio tests: conservative and robust

Because computers (except for parallel computers) generate simulation outputs sequentially, we recommend sequential probability ratio tests (SPRTs) for the statistical analysis of these outputs. However, until now simulation analysts have ignored SPRTs. To change this situation, we review SPRTs for the simplest case; namely, the case of choosing between two hypothesized values for the mean simulation output. For this case, the classic SPRT of Wald (Wald A. Sequential tests of statistical hypotheses. Ann Math Stat 1945; 16: 117–186) allows general types of distribution, including normal distributions with known variances. A modification permits unknown variances that are estimated. Hall (Hall WJ. Some sequential analogs of Stein’s two-stage test. Biometrika 1962; 49: 367–378) developed a SPRT that assumes normal distributions with unknown variances estimated from a pilot sample. A modification uses a fully sequential variance estimator. In this paper, we quantify the performance of the various SPRTs, using several Monte Carlo experiments. In experiment #1, simulation outputs are normal. Whereas Wald’s SPRT with estimated variance gives too high error rates, Hall’s original and modified SPRTs are “conservative”; that is, the actual error rates are smaller than those prespecified (nominal). Furthermore, our experiment shows that the most efficient SPRT is Hall’s modified SPRT. In experiment #2, we estimate the robustness of these SPRTs for non-normal output. For these two experiments, we provide details on their design and analysis; these details may also be useful for simulation experiments in general.

On Robustifying of the Sequential Probability Ratio Test for a Discrete Model under “Contaminations”

The problem of robustifying of the sequential probability ratio test is considered for a discrete hypothetical model. Exact values for error probabilities and for conditional expected sample sizes are obtained. Asymptotic robustness analysis for these characteristics is performed under “contaminations”. A two-parametric family of modified sequential probability ratio tests is proposed and analyzed to get the robust test by the minimax risk criterion. Numerical experiments illustrate the theoretical results.