Cochi et al. (1989) recorded data on congenital rubella syndrome from two sources. The National Congenital Rubella Syndrome Registry (NCRSR) obtained data through voluntary reports from state and local health departments. The Birth Defects Monitoring Program (BDMP) obtained data from hospital discharge records from a subset of hospitals. Below are data from 1970 to 1985, from the two systems:

a. The authors state that the NCRSR and the BDMP are independent sources of information. Do you think that is plausible? What about the other assumptions for capture–recapture?
b. Use Chapman’s estimate (13.2) to find ˜N for each year for which you can calculate the estimate. What estimate will you use for the years in which Chapman’s estimate cannot be calculated?
c. Now aggregate the data for all the years, and estimate the total number of cases of congenital rubella syndrome between 1970 and 1985. How does your estimate from the aggregated data compare with the sum of the estimates from (b)? Which do you think is more reliable?
d. Is there evidence of a decline in congenital rubella syndrome? Provide a statistical analysis to justify your answer.