USMLE statistics practice question

Question

Note not typical USMLE question but demonstrates understanding of relationship between medical statistics essential for learning and USMLE (on all but heavily on step three)

The prevalence of the disease in a population is 5%.

Hypothetically the test of choice for this disease is a coin toss. (as standard heads are positive and tails or negative). Coin lands on heads. What is the positive predictive value of this test?

Answer 1

Answer is PPV 5%. Important theme in statistics/biostatistics/for USMLE. Recall Bayes theorem states (in layman‘s terms applicable to this situation), the accuracy of any test depends upon the prevalence of disease in the population being tested.

therefore in a population in which almost everyone has the disease a negative test is more likely to be a false negative. Conversely, in a population where a disease is very rare, a positive test is more likely to be a false positive. Prevalence is similar to pretest probability. Prevalence thus impacts the positive and negative predictive value of any test. Sensitivity and specificity are intrinsic to the test and do not change. Mathematically the formula for positive predictive value has in the denominator (1-prevalence). As prevalence increases towards 100%, (1-prevalence) in the denominator goes towards zero. That’s positive predictive value increases towards 100% and extremely high prevalence, and goes towards 0% an extremely low prevalence. At either extremes the positive predictive value will equal the prevalence in the situation described.

Helps to look at chart with prevalence plotted vs PPV, with sensitivity and specificity say 95% and 85%