Background: The technique of sampling is a particularly important aspect of sampling surveys, and the method of determining sample size is the key link in sampling technique. However, a sample size determination method for complex sampling surveys of sensitive issues using a randomized response model is not yet available.
Methods: In this work, we drew from the theory of probability and mathematical statistics, and developed a series of formulas for sample size determination that are required to estimate the overall proportion and mean on dichotomous sensitive questions in 3-stage sampling using Simmons models.
Results: Shortly after generating the formulas, we successfully applied them to a pre-survey regarding sensitive issues among female sex workers (FSWs) in Xichang, and found their practical application to achieve satisfactory effects. By using a large number of Monte Carlo simulation sampling tests, the reliability of the survey methods and formulas for sensitive question surveys were found to be high, but the randomized response technique (RRT) cannot completely eliminate the possibility of social acceptability bias.
Conclusions: RRT is an acceptable method for sensitive question surveys within sensitive populations, and this new sampling method is liable to be used for sensitive question surveys of large populations. We believe that the results obtained in the field of public health can provide some data support for clinical practice.
Keywords: Randomized response technique (RRT); female sex worker (FSW); sensitive question survey.