Sample Size Planning for Estimating Prevalence of Sensitive Attributes Using a Non-Randomized Response Model

It is well known that prevalence of a sensitive attribute may be underestimated based on direct inquiry of subjects. A non-randomized response model has thus been proposed and shown to be efficient in estimating the prevalence of sensitive attributes in surveys. Since most surveys are conducted to obtain precise estimates, herein we derive a sample size formula for this model based on confidence interval estimation rather than hypothesis testing as estimation is of most relevance in this context. In contrast to the conventional approach to sample size estimation, which does not explicitly consider the chance of achieving the precision, we incorporate an assurance probability into the formula by treating confidence interval width as random. Exact evaluation demonstrates that our formula performs well.