Estimating the variance of disease-prevalence estimates from population-based registries

We propose a new Poisson method to estimate the variance for prevalence estimates obtained by the counting method described by Gail et al. (1999, Biometrics 55, 1137-1144) and to construct a confidence interval for the prevalence. We evaluate both the Poisson procedure and the procedure based on the bootstrap proposed by Gail et al. in simulated samples generated by resampling real data. These studies show that both variance estimators usually perform well and yield coverages of confidence intervals at nominal levels. When the number of disease survivors is very small, however, confidence intervals based on the Poisson method have supranominal coverage, whereas those based on the procedure of Gail et al. tend to have below-nominal coverage. For these reasons, we recommend the Poisson method, which also reduces the computational burden considerably.