Bayesian Regression Methodology for Estimating a Receiver Operating Characteristic Curve with Two Radiologic Applications: Prostate Biopsy and Spiral CT of Ureteral Stones

Rationale And Objectives: The authors evaluated two Bayesian regression models for receiver operating characteristic (ROC) curve analysis of continuous diagnostic outcome data with covariates.

Materials And Methods: Full and partial Bayesian regression models were applied to data from two studies (n = 180 and 100, respectively): (a) The diagnostic value of prostate-specific antigen (PSA) levels (outcome variable) for predicting disease after radical prostatectomy (gold standard) was evaluated for three risk groups (covariates) based on Gleason scores. (b) Spiral computed tomography was performed on patients with proved obstructing ureteral stones. The predictive value of stone size (outcome) was evaluated along with two treatment options (gold standard), as well as stone location (in or not in the ureterovesical junction [UVJ]) and patient age (covariates). Summary ROC measures were reported, and various prior distributions of the 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 decreased dramatically with age but otherwise were close to that under the partial model (ie, 0.774). The prior distribution had greater influence in the second example.

Conclusion: The diagnostic tests were accurate in both examples. PSA levels were most accurate for staging prostate cancer among intermediate-risk patients. Stone size was predictive of treatment option for all patients other than those 40 years or older and with a stone in the UVJ.