On repeated diagnostic testing in screening for a medical condition: How often should the diagnostic test be repeated?

In screening large populations a diagnostic test is frequently used repeatedly. An example is screening for bowel cancer using the fecal occult blood test (FOBT) on several occasions such as at 3 or 6 days. The question that is addressed here is how often should we repeat a diagnostic test when screening for a specific medical condition. Sensitivity is often used as a performance measure of a diagnostic test and is considered here for the individual application of the diagnostic test as well as for the overall screening procedure. The latter can involve an increasingly large number of repeated applications, but how many are sufficient? We demonstrate the issues involved in answering this question using real data on bowel cancer at St Vincents Hospital in Sydney. As data are only available for those testing positive at least once, an appropriate modeling technique is developed on the basis of the zero-truncated binomial distribution which allows for population heterogeneity. The latter is modeled using discrete nonparametric maximum likelihood. If we wish to achieve an overall sensitivity of 90%, the FOBT should be repeated for 2 weeks instead of the 1 week that was used at the time of the survey. A simulation study also shows consistency in the sense that bias and standard deviation for the estimated sensitivity decrease with an increasing number of repeated occasions as well as with increasing sample size.