Population screening for carrier status: effects of test limitations on precision of carrier prevalence rates

Because of genetic heterogeneity and ambiguity of test results, only rarely will carrier screening identify all carriers of a given autosomal recessive disorder. However, the fraction of carriers identified by the test can be estimated in a case frequency study. The population carrier rate then is the rate observed in a population screening study divided by the fraction of all defective alleles detected by the screening test, estimated in the case frequency study. For example, suppose 3% of a population are found to carry the delta F508 mutation for cystic fibrosis (CF) during population screening. If a case frequency study in this same population finds that 75% of the alleles of CF cases represent the delta F508 mutation, then the estimated population carrier rate is 4% (= .03/.75). The precision of this estimate involves the precision of both the fraction of carriers detected in the case frequency study and the proportion of carriers observed in the population screening study. Standard formulae for estimating the confidence interval and sample size consider only the variability in the population screening study. Since these formulae underestimate the true variability of the estimate of the population carrier rate, the sample size calculated for a population screening study is also underestimated. We present formulae which incorporate the variability in both factors, and illustrate the effect of this additional variability on confidence limits for estimates and sample size when planning a study.