Background: Many studies have modeled and predicted the spread of COVID-19 (coronavirus disease 2019) in the U.S. using data that begins with the first reported cases. However, the shortage of testing services to detect infected persons makes this approach subject to error due to its underdetection of early cases in the U.S. Our new approach overcomes this limitation and provides data supporting the public policy decisions intended to combat the spread of COVID-19 epidemic. Methods: We used Centers for Disease Control and Prevention data documenting the daily new and cumulative cases of confirmed COVID-19 in the U.S. from January 22 to April 6, 2020, and reconstructed the epidemic using a 5-parameter logistic growth model. We fitted our model to data from a 2-week window (i.e., from March 21 to April 4, approximately one incubation period) during which large-scale testing was being conducted. With parameters obtained from this modeling, we reconstructed and predicted the growth of the epidemic and evaluated the extent and potential effects of underdetection. Results: The data fit the model satisfactorily. The estimated daily growth rate was 16.8% overall with 95% CI: [15.95, 17.76%], suggesting a doubling period of 4 days. Based on the modeling result, the tipping point at which new cases will begin to decline will be on April 7th, 2020, with a peak of 32,860 new cases on that day. By the end of the epidemic, at least 792,548 (95% CI: [789,162, 795,934]) will be infected in the U.S. Based on our model, a total of 12,029 cases were not detected between January 22 (when the first case was detected in the U.S.) and April 4. Conclusions: Our findings demonstrate the utility of a 5-parameter logistic growth model with reliable data that comes from a specified period during which governmental interventions were appropriately implemented. Beyond informing public health decision-making, our model adds a tool for more faithfully capturing the spread of the COVID-19 epidemic.

In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum likelihood, moment method and probability plot are derived, and their performance are compared based on simulation results in terms of the mean squared error and bias. A case application of plasma cell myeloma data is used for illustrating the proposed estimation methods

Background Survival analysis is the most appropriate method of analysis for time-to-event data. The classical accelerated failure-time model is a more powerful and interpretable model than the Cox proportional hazards model, provided that model imposed distribution and homoscedasticity assumptions satisfied. However, most of the real data are heteroscedastic which violates the fundamental assumption and consequently, the statistical inference could be erroneous in accelerated failure-time modeling. The weighted least-squares estimation for the accelerated failure-time model is an efficient semi-parametric approach for time-to-event data without the homoscedasticity assumption, which is developed recently and not often utilized for real data analysis. Thus, this study was conducted to ascertain the better performance of the weighted least-squares estimation method over the classical methods. Methods We analyzed a REAL dataset on Antiretroviral Therapy patients we recently collected. We compared the results from classical methods of estimation for the accelerated failure-time model with the results revealed from the weighted least-squares estimation. Results We found that the data are heteroscedastic and indicated that the weighted least-square method should be used to analyze this data. The weighted least-squares estimation revealed more accurate, and efficient estimates of covariates effect since its confidence intervals were shorter and it identified more significant covariates. Accordingly, the survival of HIV positives was found to be significantly linked with age, weight, functional status, CD4 (Cluster of Differentiation agent 4 glycoproteins), and clinical stages. Conclusions The weighted least-squares estimation performed the best in providing more significant effects and precise estimates than the classical accelerated failure-time methods of estimation if data are heteroscedastic. Thus, we recommend future researchers should utilize weighted least-squares estimation rather than the classical methods when the homoscedasticity assumption is violated.

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