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Objectives: Estimation of areas under receiver operating characteristiccurves (AUCs) and their differences is a key task in diagnostic studies. Weaimed to derive, evaluate, and implement simple sample size formulas for suchstudies with a focus on estimation rather than hypothesis testing.  Materials and Methods: Sample size formulas were developed by explicitlyincorporating pre-specified precision and assurance, with precision denoted bythe lower limit of confidence interval and assurance denoted by the probabilityof achieving that lower limit. A new variance function was proposed for validestimation allowing for unequal variances of observations in the disease andnon-disease groups. Performance of the proposed formulas was evaluated throughsimulation.  Results: Closed-form sample size formulas were obtained. Simulation resultsdemonstrated that the proposed formulas produced empirical assuranceprobability close to the pre-specified assurance probability and empiricalcoverage probability close to the nominal 95%. Real-world worked examples werepresented for illustration.  Conclusions: Sample size formulas based on estimation of AUCs and theirdifferences were developed. Simulation results suggested good performance interms of achieving pre-specified precision and assurance probability. An onlinecalculator for implementing the proposed formulas is openly available athttps://dishu.page/calculator/.

Revisiting sample size planning for receiver operating characteristic studies: a confidence interval approach with precision and assurance