Design of two-phase prevalence surveys of rare disorders

Two-phase medical surveys, in which a large sample is assessed with an inexpensive screening instrument and a subsample is selected for a more thorough diagnostic evaluation, appear to have great merit in the epidemiolgoic study of certain rare disorders. We present the optimal design of two-phase surveys when resources are fixed and when 100% of those screened positive in the first phase must be included in the second-phase evaluation. We go on to examine the relative efficiency of this two-phase design compared to a single-phase design in which all resources are used in a survey that employs the diagnostic evaluation. Given information on the accuracy of the screen and the prevalence of the disorder, the utility of the two-phase design depends on the relative cost of the screening to the diagnostic assessments.