Two-stage transformation systems for normalization of reference distributions evaluated

Area of Science:

• Statistics
• Biostatistics
• Data Normalization

Background:

• Two-stage transformation systems are used to normalize reference distributions by correcting asymmetry and kurtosis.
• Previous assessments of these systems may have been overly optimistic due to neglecting sample variation.

Purpose of the Study:

• To re-evaluate the effectiveness of two-stage transformation systems for normalizing reference distributions.
• To identify the impact of sample variation on the accuracy of transformation parameters and goodness-of-fit tests.

Main Methods:

• Simulation studies were conducted to assess the performance of two-stage transformation systems.
• Goodness-of-fit tests were applied to transformed data to evaluate Gaussianity.
• Confidence intervals for reference limits were calculated and adjusted.

Main Results:

• The accuracy of two-stage transformation systems was previously overestimated because sample variation of transformation parameters was ignored.
• A higher p-value threshold (0.15 instead of 0.05) is recommended for accepting Gaussianity.
• A 25% expansion of 90% confidence intervals for reference limits is suggested.
• Sample sizes of 50-450 for parametric and 125-700 for nonparametric estimation are needed for precise 95% reference intervals, with larger sizes for skewed distributions.

Conclusions:

• Stricter statistical criteria are necessary for validating normalized reference distributions.
• Accurate estimation of reference intervals requires substantial sample sizes, particularly for non-Gaussian distributions.
• The findings necessitate adjustments in the application and interpretation of two-stage transformation systems in statistical analysis.