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Overview
Section* *

A diagnostic test is any approach used to gather clinical information for the purpose of making a clinical decision (i.e., diagnosis). Some examples of diagnostic tests include X-rays, biopsies, pregnancy tests, medical histories, and results from physical examinations.

From a statistical point of view there are two points to keep in mind:

- the clinical decision-making process is based on probability;
- the goal of a diagnostic test is to move the estimated probability of disease toward either end of the probability scale (i.e., 0 rules out disease, 1 confirms the disease).

Here is an example taken from Greenberg et al (2000, *Medical Epidemiology, Third Edition *). A 54-year-old woman visits her family physician for an annual check-up. The physician observes that:

- she had no illnesses during the preceding year and there is no family history of breast cancer,
- her physical exam is unremarkable, (nothing unusual is apparent),
- her breast exam is normal (no signs of a palpable mass), and
- her pelvic and rectal exams are unremarkable.

Based on the woman's age and medical history, the initial (prior) probability estimate of breast cancer is 0.003. The physician recommends that the woman have a mammogram, due to her age. Unfortunately, the results of the mammogram are abnormal. This yields a modification of the women's prior probability of breast cancer from 0.003 to 0.13 (notice the Bayesian flavor of this approach - prior probability modified via existing data). Next, the woman is referred to a surgeon who agrees that the physical breast exam is normal. The surgeon consults with a radiologist and they decide that the woman should undergo fine needle aspiration (FNA) of the abnormal breast detected by the mammogram. (diagnostic test #2) The FNA specimen reveals abnormal cells, which again revises the probability of breast cancer, from 0.13 to 0.64. Finally, the woman is scheduled for a breast biopsy the following week to get a definitive diagnosis.

Ideally, diagnostic tests always would be correct, non-invasive, and inflict no side effects. If this were the case, a positive test result would unequivocally indicate the presence of disease and a negative result would indicate the absence of disease. Realistically, however, every diagnostic test is fallible.

## Objectives

- calculate and provide confidence intervals for the sensitivity and specificity of a diagnostic test,
- calculate accuracy and predictive values of a diagnostic test,
- state the relationship of prevalence of disease to the sensitivity, specificity and predictive values of a diagnostic test,
- test whether sensitivity or specificity of 2 tests are significantly different, whether the results come from a study in two groups of patients or one group of patients tested with both tests, and
- select an appropriate cut-off for a positive test result, given an ROC curve, for different cost ratios of false positive/false negative results.