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This article focuses on the estimation of the cross-product ratio ρ = p 1 (1 − p 2) p 2 (1 − p 1) under so-called special case of the direct-inverse sampling scheme, where the number of successes in the direct sampling scheme is used in the second sampling scheme of the inverse binomial scheme. Asymptotic confidence intervals are constructed. Our goal is to investigate the cases when the normal approximations for estimators of the cross-product ratio are reliable for the construction of confidence intervals. We use the closeness of the confidence coefficient to the nominal confidence level as our main evaluation criterion, and use the Monte-Carlo method to investigate the key probability characteristics of intervals. We present estimations of the coverage probability and interval width in tables. In the last section, Cytochrome Psychotropic Genotyping Under Investigation for Decision Support case study is discussed where the standard and genetically guided therapy is compared and estimates for the cross-product ratio are presented and interpreted when the participants are enrolled according to the special case of the direct-inverse sampling scheme. [ABSTRACT FROM AUTHOR]

The correlations between economic modeling input parameters directly impact the variance and may impact the expected values of model outputs. However, correlation coefficients are not often reported in the literature. We aim to understand the correlations between model inputs for probabilistic analysis from summary statistics. We provide proof that for correlated random variables X and Y (e.g. inpatient visits and outpatient visits), the Pearson correlation coefficients of sample means and samples are equal to each other ( c o r r X , Y = c o r r X ˉ , Y ˉ ). Therefore, when studies report summary statistics of correlated parameters, we can quantify the correlation coefficient between parameters. We use examples to illustrate how to estimate the correlation coefficient between the incidence rates of non-severe and severe hypoglycemia events, and the common coefficient of five cost components for patients with diabetic foot ulcers. We further introduce three types of correlations for utilities and provide two examples to estimate the correlations for utilities based on published data. We also evaluate how correlations between cost parameters and utility parameters impact the cost-effectiveness results using a Markov model for major depression. Incorporation of the correlations can improve the precision of cost-effectiveness results and increase confidence in evidence-based decision-making. Further empirical evidence is warranted. [ABSTRACT FROM AUTHOR]

Parameter estimation strategies have long been a focal point in research due to their significant implications for understanding data behavior, including the dynamics of big data. This study offers an advancement in these strategies by proposing an adaptive parameter estimation approach for the Generalized Extreme Value distribution (GEVD) using an artificial neural network (ANN). Through the proposed adaptive parameter estimation approach, based on ANNs, this study addresses the parameter estimation challenges associated with the GEVD. By harnessing the power of ANNs, the proposed methodology provides an innovative and effective solution for estimating the parameters of the GEVD, enhancing our understanding of extreme value analysis. To predict the flood risk areas in the Chi river watershed in Thailand, we first determine the variables that are significant in estimation of the three GEVD parameters μ , σ , and ξ by considering the respective correlation coefficient and then estimating these parameters. The data were compiled from satellite and meteorological data in the Chi watershed gathered from the Meteorological Department and 92 meteorological stations from 2010 to 2021, and consist of such variables as the Normalized Difference Vegetation Index (NDVI), climate, rainfall, runoff, and so on. The parameter estimation focuses on the GEVD. Taking into consideration that the processes could be stationary (parameters are constant over time, S) or non-stationary (parameters change over time, NS), maximum likelihood estimation and ANN approaches are applied, respectively. Both cases are modeled with the GEVD for the monthly maximum rainfall. The Nash-Sutcliffe coefficient (NSE), is used to compare the performance and accuracy of the models. The results illustrate that the non-stationary model was suitable for 82 stations, while the stationary model was suitable for only 10 stations. The NSE values in each model range from 0.6 to 0.9. This indicated that all 92 models were highly accurate. Furthermore, it is found that meteorological variables, geographical coordinates, and NDVI, that are correlated with the shape parameter in the ANN model, are more significant than others. Finally, two-dimensional maps of the return levels in the 2, 5, 10, 20, 50, and 100-year return periods are presented for further application. Overall, this study contributes to the advancement of parameter estimation strategies in the context of extreme value analysis and offers practical implications for water resource management and flood risk mitigation. [ABSTRACT FROM AUTHOR]

This article investigates the logarithmic interval estimation of a ratio of two binomial proportions in dependent samples. Previous studies suggest that the confidence intervals of the difference between two correlated proportions and their ratio typically do not possess closed-form solutions. Moreover, the computation process is complex and often based on a maximum likelihood estimator, which is a biased estimator of the ratio. We look at the data from two dependent samples and explore the general problem of estimating the ratio of two proportions. Each sample is obtained in the framework of direct binomial sampling. Our goal is to demonstrate that the normal approximation for the estimation of the ratio is reliable for the construction of a confidence interval. The main characteristics of confidence estimators will be investigated by a Monte Carlo simulation. We also provide recommendations for applying the asymptotic logarithmic interval. The estimations of the coverage probability, average width, standard deviation of interval width, and index H are presented as the criteria of our judgment. The simulation studies indicate that the proposed interval performs well based on the aforementioned criteria. Finally, the confidence intervals are illustrated with three real data examples. [ABSTRACT FROM AUTHOR]

We consider the problem of logarithmic interval estimation for a cross-product ratio ρ = p 1 (1 − p 2) p 2 (1 − p 1) with data from two independent Bernoulli samples. Each sample may be obtained in the framework of direct or inverse Binomial sampling schemes. Asymptotic logarithmic confidence intervals are constructed under different types of sampling schemes, with parameter estimators demonstrating exponentially decreasing bias. Our goal is to investigate the cases when the relatively simple normal approximations for estimators of the cross-product ratio are reliable for constructing logarithmic confidence intervals. We use the closeness of the confidence coefficient to the nominal confidence level as our main evaluation criterion, and use the Monte-Carlo method to investigate the key probability characteristics of intervals corresponding to all possible combinations of sampling schemes. We present estimations of the coverage probability, expectation and standard deviation of interval widths in tables. Also, we provide some recommendations for applying each logarithmic interval obtained. [ABSTRACT FROM AUTHOR]