PAI 789 Advanced Policy Analysis

Tests for Low Prevalence Diseases (p10)

Suppose that 5% of a given population has a disease that is difficult to detect. Call the state where the person has the disease D and the state where they don't have it N. A test for the disease is available that reports rD or rN for whether or not the person has the disease. However, it's imperfect: if the person has the disease (D), there is a 10% chance it will report they don't have it, rN. In addition, there's also a 10% chance that it will report that a person who doesn't have the disease (N) has it, rD.

  1. What percent of reports of the disease, rD, are false positives? That is, what is the probability of N given rD or Pr(N|rD)?
  2. What percent of the reports that the person doesn't have the disease, rN, are false negatives? That is, what is the probability of D given rN or Pr(D|rN)?
  3. How many people in a population of 100,000 will be undertreated? Overtreated?
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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 03/14/2022