Bayesian methods for estimating ROC curves

Receiver operating characteristic (ROC) analysis is a fundamental method for assessing imaging systems. However, clinical trials to estimate ROC curves can be costly as cancer prevalence is often low for medical screening tasks and new technologies may offer only marginal improvements over previous modalities, requiring many cases to demonstrate a difference. The hypothesis of this dissertation is that Bayesian methods can be used as an alternative to maximum-likelihood methods for ROC analysis. This dissertation validates a Bayesian implementation of the "proper" binormal ROC model using two different low-information prior distributions, and also evaluates a stratified random sampling (SRS) and Bayesian multiple imputation study design as a method for estimating the ROC curve for a single reader performing screening mammography. Based on simulation study results, we show that for the prior distribution that is flat on ROC-curve and cut-point parameters that the maximum-likelihood estimate (MLE) and Bayesian point estimates are similar. We show that for the prior that is marginally flat on area under the ROC curve (AUC) value the MLE and Bayesian point estimates are similar for data sources that we call well-behaved, but that the Bayesian estimates are much better than MLE for data sources that are likely to produce degenerate datasets. For the SRS scheme we defined strata based on cancer status and BI-RADS assessment categories. We validated the SRS and multiple imputation method, showing that a low-information prior exists that leads to multiple imputation that removes all the bias created from SRS. However, the lowinformation priors are not shown to reduce root-mean-squared error (RMSE). We showed that SRS with proportional allocation alone reduced the RMSE of AUC and sensitivity estimates by approximately 10-14% when the cancer prevalence was 25%. Multiple imputation with informative priors can reduce the RMSE below that of SRS with proportional allocation, but for screening mammography the improvement requires a high proportion of cancer cases in the observer study, making our particular scheme impractical. The conclusion is that Bayesian methods for estimating ROC curves can be a reliable alternative to maximum-likelihood methods.