Logarithmic confidence estimation of a ratio of binomial proportions for dependent populations

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.