# Probability of False Prostate Cancer Diagnosis Using a Logistic Function Given Age and f/t PSA Ratio

Prostate specific antigen (PSA) is a protein of free and complex forms found in the bloodstream of patients suffering from prostatic diseases. The free/total PSA ratio is often used in the detection of prostate cancer. We define a logistic function that assigns the probability of having cancer given a specific value of the f/t PSA ratio and the age of the patient. Since the levels of PSA in a serum sample are affected by storage conditions over time, we construct a model to show the effect of improper storage of serum samples on the f/t PSA readings. We then use the logistic function and the model of sample decay over time to determine the probability of a false positive given the storage conditions. In addition we provide an analysis of cut-off values, and a function that predicts the time necessary for the diagnosis of a patient to change from negative to positive given his age, f/t PSA Ratio, and a cut-off value.

*Poster session award recipient at the 1999 National SACNAS Convention in Portland, OR**Poster session award recipient at the 2000 AMS/MAA Joint Mathematics Meeting in Washington DC*

Article Number:

BU-1523-M

Year:

1999

Authors:

Aldo Crossa, Wittenberg University

Johnny Guzmán, California State University, Long Beach

Andie Hodge, University of the Virgin Islands

Brisa N. Sánchez, University of Texas, El Paso