Screening Test for Occult Cancer 100 patients with occult cancer: 95 have "x" in their blood 100 patients without occult cancer: 95 do not have "x" in their blood 5 out of every 1000 randomly selected individuals will have occult cancer SENSITIVITY SPECIFICITY PREVALENCE

2 X 2 Table Occult Cancer Present Occult Cancer Absent "x" present"x" absent 100,000 99, ,97594,525 5,45094,550 If a patient has “x” in his blood, chance of occult cancer is 475 / 5450 = 8.7%

Standard Terminology Disease Present Disease Absent Test positive Test negative Entire Population FP + TN TP + FN True Positives (TP’s) False Positives (FP’s) True Negatives (TN’s) False Negatives (FN’s) TP + FP FN + TN

Definitions

Positive Predictive Value Formula (Sens)(Prev) + (1-Spec)(1-Prev) PV + = (Sens)(Prev)

Detection of Prostatic Cancer by Solid-Phase Radioimmunoassay of Serum Prostatic Acid Phosphatase

Editorial “The clear implication of the accompanying report is that mass screening on the basis of a blood test alone can reverse this gloomy experience [of fatal delays in diagnosis of prostate cancer].” New England Journal of Medicine December 22, 1977

Medical Journal Advertisement to Physicians

Posed by a Professional Model

Medical Journal Advertisement to Physicians

Advertisement “(You should be aware of) a new blood test called the Male-P.A.P. test... a new, more sensitive method that your physician can use to detect chemical signals of a cancerous growth in the prostate.... And even though all lab tests must be ordered by a physician, we believe that you should know the facts.” New York Times, January 21, 1979

Sensitivity Patients with prostate % cancer Stage I24833% Stage II332679% Stage III312271% Stage IV252392% # of patients # of positive tests sensitivity

Specificity Patients without prostate % cancer Normal controls500 BPH362 After total prosta-281 tectomy Other cancers839 Misc. GI disorders201 # of patients # of positive tests specificity

Use As Screening Test Without rectal examination: –Sensitivity = 70% Specificity = 94% –Prevalence ­ 33/100,000 –PV+ = 0.41% (i.e., 1 in 244 subjects) With rectal examination: –Sensitivity = 33% Specificity = 94% –Prevalence ­ 33/100,000 –PV+ = 0.19% (i.e., 1 in 526 subjects)

When is the test useful for screening? Suppose patient has a nodule on rectal examination: –Sensitivity (Stage 2 of disease) = 79% –Specificity = 94% –Prevalence = 50% !! PV + = 93% (chance of cancer if acid phosphatase is positive) PV - = 82% (chance that there is no cancer if acid phosphatase is negative)

Predictive Values in Patients with a Nodule PAP+ PAP- 50% 93% 18%

Combining Tests For Screening: If a prostate biopsy is now performed, it needs to be considered as another test. Specificity = 100% Sensitivity depends on talent and statistics of surgeon doing the procedure Prevalence is 50% if acid phosphatase has not been measured, but is 93% if acid phosphatase is positive and 18% if acid phosphatase is negative.

Sequential Testing PAP+ PAP- 50% 93% 18% BX+ 100%

Chance of Cancer after Negative Biopsy Sensitivity of Biopsy Acid Phosphatase positive (93% chance before biopsy) Acid Phosphatase negative (18% chance before biopsy) 50% 87% 10% 70% 80% 6% 90% 56% 2%

Sequential Testing PAP+ PAP- 50% 93% 18% BX+ BX- 100% 56% < 2%

BAYES’ THEOREM OR

Typical Assumptions with the Use of Bayes' Theorem Completeness (for example, all men either have or do not have prostate cancer; there are no other possibilities) Mutual exclusivity (for example, if a man has prostate cancer, he cannot simultaneously NOT have prostate cancer) Conditional independence (for example, acid phosphatase and a biopsy result ARE conditionally independent tests; rectal exams and acid phosphatase may NOT be conditionally independent)

References Foti et al. “Detection of prostate cancer by solid- phase radioimmunoassay of serum prostatic acid phosphatase.” New England Journal of Medicine 297: (1977) Watson, R.A. and Tang, D.B. “The predictive value of prostatic acid phosphatase as a screening test for prostatic cancer.” New England Journal of Medicine 303: (1980) Berwick, D.M., Fineberg, H.V., and Weinstein, M.C. “When doctors meet numbers.” American Journal of Medicine 71:991 (1981)

What is a “Positive Test”? All the analysis has assumed that it is clear whether a test is positive or negative In reality, many tests involve continuous values so that one result may be “more positive” than another How should one define the cut-off at which a test is judged to be abnormal?

Continuously Valued Variables Normal Diseased Result “Normal” cutoff False Positives False Negatives True Negatives True Positives

Continuously Valued Variables Normal Diseased Result “Normal” cutoff Fewer false positives (more “conservative”) More false negatives Higher specificity Lower sensitivity

Continuously Valued Variables Normal Diseased Result “Normal” cutoff Fewer false negatives (more “aggressive”) More false positives Higher sensitivity Lower specificity

Receiver Operating Characteristic (ROC) Curves True Positive Rate = Sensitivity False Positive Rate = 1 - Specificity Test A Test B ROC curve shifts to left, indicating the new test (B) is “better” – or a better indicator to disease presence (more discriminatory).

The Importance of the Gold Standard Evaluating the value of a new test requires having some other method for determining “truth” Methods for determining truth are called gold standards Gold standards are often expensive, time consuming, uncomfortable, or risky –Biopsies –Major invasive procedures or surgery –Autopsies –Integrated opinions of “super experts” We often seek simple, inexpensive, rapid, and safe tests that can perform almost as well as the gold standard