Bayesian regression methodology for estimating a receiver operating characteristic curve with two radiologic applications: Prostate biopsy and spiralCT of ureteral stones

Rationale and Objectives. The authors evaluated two Bayesian regression mod els for receiver operating characteristic (ROC) curve analysis of continuou s diagnostic outcome data with covariates. Materials and Methods. Full and partial Bayesian regression models were app lied to data from two studies (n = 180 and 100, respectively): (a) The diag nostic value of prostate-specific antigen (PSA) levels (outcome variable) f or predicting disease after radical prostatectomy (gold standard) was evalu ated for three risk groups (covariates) based on Gleason scores. (b) Spiral computed tomography was performed on patients with proved obstructing uret eral stones. The predictive value of stone size (outcome) was evaluated alo ng with two treatment options (gold standard), as well as stone location (i n or not in the ureterovesical junction [UVJ]) and patient age (covariates) . Summary ROC measures were reported, and various prior distributions of th e regression coefficients were investigated. Results. (a) In the PSA example, the ROC areas under the full model were 0. 667, 0.769, and 0.703, respectively, for the low-, intermediate-, and high- risk groups. Under the partial model, the area beneath the ROC curve was 0. 706. (b) The ROC areas for patients with ureteral stones in the UVJ decreas ed dramatically with age but otherwise were close to that under the partial model (ie, 0.774). The prior distribution had greater influence in the sec ond example. Conclusion. The diagnostic tests were accurate in both examples. PSA levels were most accurate for staging prostate cancer among intermediate-risk pat ients. Stone size was predictive of treatment option for all patients other than those 40 years or older and with a stone in the UVJ.