Bounding Sample Size Projections for the Area Under a ROC Curve.

Area of Science:

• Biostatistics
• Medical Diagnostics
• Clinical Trial Design

Background:

• Area under the receiver operating characteristic curve (AUC) is a key metric for diagnostic test accuracy.
• Sample size calculations for AUC are highly sensitive to unknown correlation parameters, complicating study design.
• Existing methods struggle with reliable pre-study estimation of these crucial parameters.

Purpose of the Study:

• To derive achievable, parameter-free bounds for sample size projections in diagnostic accuracy studies.
• To provide robust minimum and maximum sample size estimates for single and multi-arm studies.
• To extend these bounds to multi-reader diagnostic scenarios, considering average and pooled AUC.

Main Methods:

• Derivation of theoretical bounds for sample size based on desired precision.
• Development of parameter-free formulas for lower and upper sample size bounds.
• Adaptation of bounds for multi-reader studies, addressing average and pooled AUC.

Main Results:

• Achievable lower and upper sample size bounds are derived, independent of specific correlation parameters.
• These bounds represent the absolute minimum and maximum sample sizes required for desired precision.
• New bounds are established for multi-reader studies, offering practical guidance for complex designs.

Conclusions:

• The derived sample size bounds offer a more reliable approach to designing diagnostic accuracy studies.
• These bounds mitigate the sensitivity to correlation parameters, improving planning and resource allocation.
• The methodology provides essential reference points for sample size determination in both single and multi-reader settings.