1. What is the justification for assuming 72 colon cancers per 10,000 people? (Show your calculation.)

2. What is the justification for assuming a single guaiac test can correctly detect 91.66% of colon cancer cases? (Show your calculation.)

3. What is the justification for assuming that a single guaiac test will yield a false-positive result 36.51% of the time? (Show your calculation.)

4. What percent will be given false positives after two tests? (Show your calculations.)

5. Calculate the total screening costs of 2 tests for an individual. (Show your calculations.)

6. Calculate the ICER of a two guaiac test protocol over one guaiac test protocol in terms of cases detected. (Show your calculations.)

7. For a moment assume the marginal benefit of detection of a case of colon cancer is $100,000. What is the optimal number of screening tests? Why?

8. What do Neuhauser and Lewicki say about the benefit of early detection of colon cancer?

9. What do Neuhauser and Lewicki conclude about the usefulness of the guaiac test?

WHAT DO WE GAIN FROM THE SIXTH STOOL GUAIAC? Duncan Neuhauser, Ph. D., and AnN M. Lewicki, M.D. Abstract The six sequential stool guaiac protocol creased with lower prevalence of colonic cancer. This has been advocated for screening of colonic cancer. result shows that even an inexpensive test can beAnalysis of the expenditures involved in such a pro- come quite costly in terms of cases detected. The margram shows that the cost of detecting cancer rises ex- ginal cost per case detected depends on the prevaponentially so that the marginal cost of the sixth test lence of the condition in the population screened and may be 20,000 times the average cost. The marginal the sensitivity of the test applied. ( N Engl J Med cost is decreased with lower test sensitivity and in- 293:226228,1975 ) From the Center for the Analysis of Health Practices, Harvard School of Public Health, and the Department of Radiology, Harvard Medical School and Peter Bent Brigham Hospital (address reprint requests to Dr. NeuhausPractices and in part by a grant (GM 1-8674) from the U. S. Public Health least once on six sequential tests. In the initial 278 people Service. Marginal cost refers to the extra effort required to produce one extra unit batic cancers were eventually found by barium-enema study. This rate is equivalent to finding 72 cases among Table 1 was constructed by calculation of the expected yield from six sequential guaiac tests. It expresses the ingly. Incremental cost also decreased. Thus, the increpercentage and the case rate when the six tests are applied mental cost for the sixth stool guaiac test over the fifth is to a population of 10,000 people of whom 72 are assumed $13,190 as compared to $17,917 for the fourth over the tohavecoloniccancer.Undersuchconditions,forexam-ple,ifoneguaiactestdetects91.67percentofthecasesofthirdexamination.Thisdeclineisdueinparttothehigh-ercostthatweassumedforthefirsttestandalsotoade- cancer, and a second examination will detect an additional clining rate of false-positive results (fewer people who 91.67 per cent of the remainder, the total proportion of need further screening by barium-enema examination). cases detected by the two tests would be equal to 99.31 per One should note, however, the staggering rise in the cent (10091.67=8.33;8.330.9167=7.6491.67+ marginal cost calculated from the above-mentioned valcent (10091.67=8.33;8.330.9167=7.64;91.67+ marginal cost calculated from the above-mentioned val- 7.64=99.31). 7.64=99.31).scuredintheaveragecostfigure(Table2,column7)cancerdetection(Table2,column6).Thisexpenseisob- Table 1. True-Positive and False-Positive Rates with Sequen- tial Guaiac Tests. The percentage and number of people without cancer who can be expected to test positively on sequential testing were calculated in a similar manner. Effect of Test Sensitivity and Cancer Prevalence on Marginal Cost In interpreting the results, we assumed that the six- guaiac screening protocol represents one laboratory pro- To evaluate what effect lower one-test sensitivity of a cedure with six possible distinct cutoff points. Thus, a screening test has on marginal cost, we used a hypothetical two-guaiacprotocolwouldhaveatrue-positive.rate(sensi-tivity)of99.31percentandafalse-positiverate(specifici-.situationinwhichoneguaiactestinasix-guaiacscreeningprotocolwoulddetectonly60percent(asopposedto99 tivity)of99.31percentandafalse-positiverate(specifici-ty)of59.69percent.ThevaluesinTable1indicatelittleprotocolwoulddetectonly60percent(asopposedto92percent)ofthecasesofcancer(thirdcolumnofTable3). ty)of59.69percent.ThevaluesinTable1indicatelittlegaininthetrue-positiveratefromtestingbeyondthesec-percent)ofthecasesofcancer(thirdcolumnofTable3).Similarly,wecalculatedmarginalcostforahypothetical ond guaiac examination. On the other hand a steadily ris- population in which prevalence of colonic cancer would ing rate in the false-positive group occurs with more fre- be only 11 cases per 10,000 people screened as opposed to quent testing. 72 (fourth column of Table 3 ). Comparison of the marginal cost of the third column to Marginal Cost of Cancer Detection from Multiple Testing the second column in Table 3 indicates that marginal cost In Table 2 cancer detection is compared to the cost in- rises less rapidly with sequential testing when the one-test 228 THE NEW ENGLAND JOURNAL OF MEDICINE July 31, 1975 Table 3. Effect of Test Sensitivity and Cancer Prevalence on might not be excessively expensive if the test-response WHAT DO WE GAIN FROM THE SIXTH STOOL GUAIAC? Duncan Neuhauser, Ph. D., and AnN M. Lewicki, M.D. Abstract The six sequential stool guaiac protocol creased with lower prevalence of colonic cancer. This has been advocated for screening of colonic cancer. result shows that even an inexpensive test can beAnalysis of the expenditures involved in such a pro- come quite costly in terms of cases detected. The margram shows that the cost of detecting cancer rises ex- ginal cost per case detected depends on the prevaponentially so that the marginal cost of the sixth test lence of the condition in the population screened and may be 20,000 times the average cost. The marginal the sensitivity of the test applied. ( N Engl J Med cost is decreased with lower test sensitivity and in- 293:226228,1975 ) From the Center for the Analysis of Health Practices, Harvard School of Public Health, and the Department of Radiology, Harvard Medical School and Peter Bent Brigham Hospital (address reprint requests to Dr. NeuhausPractices and in part by a grant (GM 1-8674) from the U. S. Public Health least once on six sequential tests. In the initial 278 people Service. Marginal cost refers to the extra effort required to produce one extra unit batic cancers were eventually found by barium-enema study. This rate is equivalent to finding 72 cases among Table 1 was constructed by calculation of the expected yield from six sequential guaiac tests. It expresses the ingly. Incremental cost also decreased. Thus, the increpercentage and the case rate when the six tests are applied mental cost for the sixth stool guaiac test over the fifth is to a population of 10,000 people of whom 72 are assumed $13,190 as compared to $17,917 for the fourth over the tohavecoloniccancer.Undersuchconditions,forexam-ple,ifoneguaiactestdetects91.67percentofthecasesofthirdexamination.Thisdeclineisdueinparttothehigh-ercostthatweassumedforthefirsttestandalsotoade- cancer, and a second examination will detect an additional clining rate of false-positive results (fewer people who 91.67 per cent of the remainder, the total proportion of need further screening by barium-enema examination). cases detected by the two tests would be equal to 99.31 per One should note, however, the staggering rise in the cent (10091.67=8.33;8.330.9167=7.6491.67+ marginal cost calculated from the above-mentioned valcent (10091.67=8.33;8.330.9167=7.64;91.67+ marginal cost calculated from the above-mentioned val- 7.64=99.31). 7.64=99.31).scuredintheaveragecostfigure(Table2,column7)cancerdetection(Table2,column6).Thisexpenseisob- Table 1. True-Positive and False-Positive Rates with Sequen- tial Guaiac Tests. The percentage and number of people without cancer who can be expected to test positively on sequential testing were calculated in a similar manner. Effect of Test Sensitivity and Cancer Prevalence on Marginal Cost In interpreting the results, we assumed that the six- guaiac screening protocol represents one laboratory pro- To evaluate what effect lower one-test sensitivity of a cedure with six possible distinct cutoff points. Thus, a screening test has on marginal cost, we used a hypothetical two-guaiacprotocolwouldhaveatrue-positive.rate(sensi-tivity)of99.31percentandafalse-positiverate(specifici-.situationinwhichoneguaiactestinasix-guaiacscreeningprotocolwoulddetectonly60percent(asopposedto99 tivity)of99.31percentandafalse-positiverate(specifici-ty)of59.69percent.ThevaluesinTable1indicatelittleprotocolwoulddetectonly60percent(asopposedto92percent)ofthecasesofcancer(thirdcolumnofTable3). ty)of59.69percent.ThevaluesinTable1indicatelittlegaininthetrue-positiveratefromtestingbeyondthesec-percent)ofthecasesofcancer(thirdcolumnofTable3).Similarly,wecalculatedmarginalcostforahypothetical ond guaiac examination. On the other hand a steadily ris- population in which prevalence of colonic cancer would ing rate in the false-positive group occurs with more fre- be only 11 cases per 10,000 people screened as opposed to quent testing. 72 (fourth column of Table 3 ). Comparison of the marginal cost of the third column to Marginal Cost of Cancer Detection from Multiple Testing the second column in Table 3 indicates that marginal cost In Table 2 cancer detection is compared to the cost in- rises less rapidly with sequential testing when the one-test 228 THE NEW ENGLAND JOURNAL OF MEDICINE July 31, 1975 Table 3. Effect of Test Sensitivity and Cancer Prevalence on might not be excessively expensive if the test-response