  Objectives: Estimation of areas under receiver operating characteristic
curves (AUCs) and their differences is a key task in diagnostic studies. We
aimed to derive, evaluate, and implement simple sample size formulas for such
studies with a focus on estimation rather than hypothesis testing.
  Materials and Methods: Sample size formulas were developed by explicitly
incorporating pre-specified precision and assurance, with precision denoted by
the lower limit of confidence interval and assurance denoted by the probability
of achieving that lower limit. A new variance function was proposed for valid
estimation allowing for unequal variances of observations in the disease and
non-disease groups. Performance of the proposed formulas was evaluated through
simulation.
  Results: Closed-form sample size formulas were obtained. Simulation results
demonstrated that the proposed formulas produced empirical assurance
probability close to the pre-specified assurance probability and empirical
coverage probability close to the nominal 95%. Real-world worked examples were
presented for illustration.
  Conclusions: Sample size formulas based on estimation of AUCs and their
differences were developed. Simulation results suggested good performance in
terms of achieving pre-specified precision and assurance probability. An online
calculator for implementing the proposed formulas is openly available at
https://dishu.page/calculator/.
