Confidence Intervals Based on the Modified Chi-Squared Distribution and Its Applications in Medicine
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Updated: Nov 5, 2026

An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
Mulan Wu1, Mengyu Xu2, Dong-Yun Kim3
1University of Chicago Laboratory High School, Chicago, IL, 60637 USA.
Abstract:
Small sample sizes in clinical studies arise 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.
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