Estimating reference ranges from stratified two-stage samples

We present methodology for estimating age-specific reference ranges by using data from two-stage samples. On the basis of the information obtained in the first stage, the initial sample is stratified and random subsamples are drawn from each stratum, where the selection probabilities in this second-stage sampling may be different across strata in the population. The variable for which the reference ranges are to be established is measured at the second phase. The approach involves maximum likelihood estimation of the parameters of the age-specific distributions and separate estimation of the population stratum probabilities. These are combined to yield estimates of the quantiles of interest. The issue of variance estimation for the estimated quantiles is also addressed. The methodology is applied to the estimation of reference ranges for a cognitive test score in a study of non-demented older Japanese-Americans.