Confidence Intervals Based on the Modified Chi-Squared Distribution and its Applications in Medicine

TL;DR

This paper introduces a new method for calculating more accurate confidence intervals in small sample medical studies using a modified chi-squared distribution, improving statistical reliability.

Contribution

It proposes a quadratic-form based statistic for better confidence intervals in small samples, with practical guidelines and real data applications.

Findings

Improved confidence interval accuracy for small samples.

Guidelines for sample sizes and proportions for the quadratic method.

Enhanced reliability of statistical inferences in clinical studies.

Abstract

Small sample sizes in clinical studies arises from factors such as reduced costs, limited subject availability, and the rarity of studied conditions. This creates challenges for accurately calculating confidence intervals (CIs) using the normal distribution approximation. In this paper, we employ a quadratic-form based statistic, from which we derive more accurate confidence intervals, particularly for data with small sample sizes or proportions. Based on the study, we suggest reasonable values of sample sizes and proportions for the application of the quadratic method. Consequently, this method enhances the reliability of statistical inferences. We illustrate this method with real medical data from clinical trials.