Notes from "Elementary Uses of the Gibbs Sampler:
Applications to Medical Screening Tests"

by Eric A. Suess, Christopher M. Fraser, and Bruce E. Trumbo
STATS, #27, Winter 2000

These notes are brief auxiliary comments denoted by raised numerals in the article.

 

1. Theactual sensitivity and specificity of an ELISA test procedure for any particular virus would depend on whether tests are done once or several times on each unit of blood, and whether borderline results are declared as "positive" or "negative." When the immediate purpose is to protect the blood supply from contamination with the virus, such issues would be settled in favor of increasing the sensitivity. But the consequence would be to decrease the specificity, which we see in Section 2 can make our task of estimating prevalence more difficult.

   For a more complete discussion of sensitivity and specificity in screening tests, see Gastwirth, J.L., "The statistical precision of medical screening procedures: Applications to polygraph and AIDS antibody test data" (including discussion), Statistical Science, Vol. 2, No. 3 (1987), pages 213-238.

 

2. Procedures called "Western blot" tests, are regarded as a gold standard for some viruses. (They use a different technology than ELISA tests and are considerably more accurate, and expensive to use, than ELISA tests.) However, in practice, no such procedure is absolutely perfect. Both the Western blot test and the ELISA test actually detect antibodies to a specific virus, which in most circumstances would indicate the presence of the virus itself. (But perhaps not in people on whom experimental vaccines have been tested.)

   In clinical situations a gold-standard test may or may not be available. For a treatment, using the Gibbs Sampler, of a situation where there is no gold standard, see Joseph, L.; Gyorkos. T.; and Coupal, L.; "Bayesian estimation of disease prevalence and the parameters of diagnostic tests in the absence of a gold standard," American Journal of Epidemiology, Vol. 141, No. 3 (1995), pages 263-171.

 

3. The conditional distribution of T is Bernoulli. Conditional on D =1, the probability that T = 1 is h = P(T=1|D=1) = 0.99. To simulate T we could generate a pseudorandom number U, uniformly distributed on the interval (0, 1). If U < 0.99, then the simulated value of T is 1, otherwise 0. Subsequent values of D and T could be simulated in the same way.

   In S-plus the Bernoulli distribution is simulated with a command that uses pseudorandom numbers as above to select observations from a binomial distribution with one trial and the desired probability of success. (The full S-plus code for the simulation in Section 4 of the article is available on this site.)