Design Considerations for a Two-stage Study with a Continuous Outcome and a Rare Exposure

We consider the scenario in which the severity of a disease is characterized by a normally distributed response and the chance of being exposed (yes/no) to the risk factor is extremely rare. A screening test is employed to oversample subjects who may be at risk for the disease because expensive laboratory tests are needed to measure the outcome of interest and to confirm the true exposure status. Considerations of sample size and cost are discussed for this type of two-stage design with the objectives of 1) minimizing the number of subjects in the Stage II, and 2) overcoming the problem of a rare exposure. In particular, with an imperfect screening tool, one must take into account the sensitivity and specificity of the screening test, and the uncertainty of the estimates of the exposure prevalence in the survey population. The Penn State Children Sleep Disorder Study (PSCSDS) is used for illustration.