ROC Curve and AUC for A Left-Truncated Sample from Rayleigh Distribution

SYNOPTIC ABSTRACT

Evaluation of biomarker performance in screening and diagnosis of a particular disease are topics of major interest in clinical diagnosis. The performance of diagnosis can be evaluated through the receiver operating characteristics (ROC) curve. In some situations, the variable/biomarker value for some of the subjects cannot be measured because of technical problems and we need to truncate the sample at some specific point. Discarding such observations will result in loss of valuable information. When the number of missing values in a sample is large, it will lead to biased estimates. Applying the traditional complete sample ROC procedures to the incomplete data to evaluate the accuracy may under- or overestimate the accuracy of classification. This article concerns modeling a parametric ROC curve for the left-truncated sample from Rayleigh distribution. The ROC model, area under the ROC curve (AUC) asymptotic variance and confidence interval for an estimated AUC have been discussed and analyzed through simulation studies as well as a real-life example.

Key Words and Phrases::

• ROC
• AUC
• left-truncated Rayleigh distribution
• approximate maximum likelihood estimation
• asymptotic confidence interval

Notes

The data is available in Zhou et al. (2002) and http://www.fhcrc.org/labs/pepe/dabs