Appendix: derivation of sensitivity formula

N=number of women having triple test; p=prevalence of Down's syndrome; p*N=total number of fetuses with Down's syndrome; DR=detection rate; FPR=false positive rate; p*N*DR*AR=number of women with true positive results who have amniocentesis; (1-p)*N*FPR*AR=number of women with false positive results who have amniocentesis; p*N*DR*AR=number having an abortion (all positive amniocentesis results); TT=cost of triple test per person; Am=cost of amniocentesis; Ab=cost of abortion; AR= amniocentesis acceptance rate. The total cost of avoiding the birth of all detected fetuses with Down's syndrome has three components: the cost of the triple test (TT*N); the cost of amniocentesis in all women with true positive results or false positive results; and the cost of abortion. Total cost =TTF*N+Am*[p*N*DR+(1-p)*N*FPR]*AR +Ab*p*N*DR*AR Average cost =Total cost/Number of births avoided =TT*N+Am*[p*N*DR+(l-p)*N*FPR)]*AR +Ab*p*N*DR*AR p*N*DR*AR =TTr(1/AR) Am*FPR P*DR +Am p*DR +Ab The only term that varies as the acceptance rate (AR) changes is the one on the left. Assuming an acceptance rate of 75% as in table III this term is: TT(l/AR) TT(1/075) TTF(133) PR P * DR p*DR Thus changes in acceptance rate affect the average cost according to the formula given in the text: Change in average cost=(cost per triple test) (1/AR-1-33)/ (prevalence rate) (detection rate).