Sequence length for repeated screening tests.

The cost of detecting asymptomatic colonic cancer with a sequence of occult blood tests by the guaiac method is investigated to determine theelfect of sequence length. The results are sensitive to the definition of a screen positive and a variety of definitions of a positive screen are investigated. It is found that additional tests, when practical, can be used elfectively to reduce the average cost ofdetection per case and to decrease markedly the probability of a false positive screen without sacrificing high sensitivity even when the prevalence of disease is low. The results hold for a variety of combinations of test and prevalence parameters. This strengthens the conclusion and makes the results more generally applicable. THE COST of detecting asymptomatic colonic cancer with a six-sequential-stool-guaiac protocol was studied by Neuhauser and Lewicki [ 11. They found that the marginal cost of the sixth test may be 20,000 times the average cost. In their calculations they estimated the sensitivity and specificity of an individual guaiac test and the prevalence rate for colonic cancer from a fairly small study by Greegor [2], but their findings would have been the same for any parameter specifications of the same order of magnitude. However, their conclusions are sensitive to the definition of a screen positive. They defined a person as screen positive if at least one of a sequence of guaiac tests were positive. Since the prevalence rate was assumed to be low (0.0072) and the sensitivity of the guaiac test to colonic cancer was assumed to be high, a sequence of, say, six guaiac tests with a single positive result was more apt to happen because of a test error than because of the presence of colonic cancer. Thus the probability that a positive screen was false was high, as was the average cost of detection of cancer cases. In this study a variety of definitions of a positive screen are investigated for a sequence of tests. Protocols for both fixed length and variable length sequences are considered. It is found that additional tests can be used effectively to reduce the average cost of detection per case and to markedly decrease the probability of a false positive screen even when the prevalence of disease is low. Sequences qfji.ued length ANALYSIS Consider a sequence of independent guaiac tests with results X ,, X,, . . . , X, where X, = I if the ith test is positive and Xi = 0 if the ith test is negative, i = 1,. . , n. Let 0