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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

probability_of_false_prostate_cancer_diagnosis_using_a_logistic_function_given_age_and_ft_psa_ratio_.pdf