Goodness-of-fit statistics for age-specific reference intervals

Area of Science:

• Biostatistics
• Medical Statistics
• Clinical Reference Standards

Background:

• Age-specific reference intervals are essential for medical screening.
• Accurate estimation of extreme quantile curves (e.g., 5th and 95th centiles) requires models with excellent data fit.
• Existing goodness-of-fit assessment procedures are limited and underevaluated.

Purpose of the Study:

• To evaluate goodness-of-fit procedures for age-specific reference interval estimation.
• To compare the performance of Z-score based methods and Pearson chi-squared statistics.

Main Methods:

• Analysis of Z-score distributions (standardized residuals).
• Application of Pearson chi-squared statistics on grouped observed and expected counts.
• Evaluation of inferential (Q-tests, grid tests) and graphical (permutation bands, B-tests) procedures.
• Approximation of null distributions and examination of test statistics' size and power.

Main Results:

• Q-tests demonstrate generality, ease of calculation, and high power for Z-score analysis.
• Permutation bands and B-tests offer graphical assessment capabilities.
• Grid tests were consistently outperformed by Q- and B-tests in the evaluated scenarios.

Conclusions:

• Q-tests are the preferred method for assessing goodness-of-fit when Z-scores are available.
• The study provides a systematic evaluation of statistical methods for validating reference interval models.
• Recommendations are made for selecting appropriate statistical procedures based on data availability and analytical goals.