## False positives

06/02/2012 by jgluvna

It is known that the test used to identify a very rare disease or the presence of a performance enhancing drug results gives a positive result 98% of the time when the disease or drug is actually present and a false positive 0.5% of the time. What is the probability of a positive test result when a random individual is tested? Negative result?

### Theory

- Approximation and local linearity (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 146)
- Error propagation (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 149)
- Law of total probability (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 658)

### References

- Welsh, M. et al. 1997. Sexually transmitted disease risk assessment used among low-risk populations in East/Central Africa: A review. East African Medical Journal. 74(12): 764-771.
- Jorgensen, L. G. M. et al. 2004. Should we maintain the 95 percent reference intervals in the era of wellness testing? A concept paper. Clinical Chemistry and Laboratory Medicine. 42(7): 747-751.
- Lloyd, C. J. and D. Frommer 2004. Estimating the false negative fraction for a multiple screening test for bowel cancer when negatives are not verified. Australian & New Zealand Journal of Statistics. 46(4): 531-542.