In context-aware decision analysis, mean can be an important measure, even when the distribution is skewed. Previous comparative studies showed that it is a real challenge to construct a confidence interval that performs well for highly skewed data. In this study, we propose new confidence intervals for the population mean based on Edgeworth expansion that include both skewness and kurtosis corrections. We compared existing and newly proposed confidence intervals for a range of samples from symmetric and skewed distributions of varying levels of kurtosis. Using Monte Carlo simulations, we evaluated the performance of these intervals based on the coverage probability, mean length, and standard deviation of the length. The proposed bootstrap Edgeworth-based confidence interval outperformed other confidence intervals in terms of coverage probability for both symmetric and skewed distributions and can be recommended for general use in practice.

In economic statistical design of a control chart, the economic-loss function is minimized subject to a constrained minimum value of power, maximum value of probability of false alarms and average time to signal an expected shift. This paper is concerned with the optimum economic statistical design of the X bar chart when quality characteristic has non-normal symmetric distribution. We considered three types of distributions: Student distribution, standard Laplace distribution and logistic distribution. For each of these distributions, we calculated theoretical distribution of standardized sample mean (or its best approximation) and approximated it with normal, Pearson VII and Johnson SU distributions. For considered example, constrained minimization of expected loss function was done using genetic algorithm in statistical software R. We compared results of economic statistical design of X-bar chart for theoretical distribution of standardized sample mean with the results for normal, Pearson and Johnson distributions. We found that, for all chosen distributions of quality characteristic, Pearson VII distribution and Johnson SU distribution give results very close to results based on theoretical distribution of standardized sample mean, while normal distribution gives much worse fit.

The Republic of Srpska (RS), as a part of the Western Balkans (WB) region, has a higher diabetes prevalence than the EU. This study aims to assess the cost-effectiveness of early treatment of high-risk patients with pre-diabetes and undiagnosed diabetes in our setting. We designed a Markov chain Monte Carlo (MCMC) model which reflects the current International Diabetes Federation (IDF) three-step plan for the prevention of T2DM in those at increased risk. The model captures the evolution of the disease in FINDRISC high-risk patients from normal glucose tolerance (NGT) to impaired fasting glucose (IFG) or impaired glucose tolerance (IGT) and then to T2DM and its complications. We developed two MCMC models, in order to follow the progression of the disease in high-risk cases, ie, when early treatment is undertaken or when it is not undertaken. The health costs and quality adjusted life years (QALY) were discounted at an annual rate of 3%. The key model parameters were varied in one-way and probabilistic sensitivity analysis. Early treatment resulted in increased life expectancy, postponement of the onset of diabetes and increased QALY for all patients. The discounted incremental cost-effectiveness-ratios (ICER) in NGT, IFG, IGT, and T2DM patients were -289.9, 9724.03, -1478.59 and 4084.67 €. In high-risk IGT patients, ICER was the most favorable, being both a cost saving and QALY gaining, with the consistent results confirmed by the sensitivity analysis. The results recommend the acceptance of a new health policy of identifying IGT patients with the use of FINDRISC questionnaire and plasma glucose measurements; providing them with a lifestyle change program; and implementing intensive diabetes treatment, as their disease progresses. Our results are especially significant for the Western Balkan countries, since this was the first cost-effectiveness study of T2DM prevention in this region.