CONSTRUCTION OF HEARING PERCENTILES IN WOMEN WITH NONCONSTANT VARIANCE FROM THE LINEAR MIXED-EFFECTS MODEL

Current age-specific reference standards for adult hearing thresholds are primarily cross-sectional in nature and vary in the degree of scre ening of the reference sample for noise-induced hearing loss and other hearing problems, We develop methods to construct age-specific percen tiles for longitudinal data that have been modelled using the linear m ixed-effects model, We apply these methods to construct percentiles of hearing level using data from a carefully screened sample of women fr om the Baltimore Longitudinal Study of Aging, However, the variation i n the residuals and random effects from the linear mixed-effects model does not remain constant with age and frequency of the stimulus tone. In addition, the distribution of the hearing levels is not symmetric about the mean, We develop a number of methods to use the output from the linear mixed-effects model to construct percentiles that do not ha ve constant variance. We use a transformation of the hearing levels to provide for skewness in the final percentile curves. The change in th e variation of the residuals and random effects is modelled as a funct ion of beginning age and frequency and we use this variance function t o construct the hearing percentiles, We present a number of approaches , First, we use the absolute values of the population residuals to mod el the total deviation about the mean as a function of beginning age a nd frequency, Second, we model the standard deviation in the person-sp ecific (cluster) residuals as well as the standard deviation in the es timated random effects. Finally, we use weighted least squares with th e regressions on the absolute cluster residuals and absolute estimated random effects where the weights are the reciprocal of the standard d eviations of their estimates. (C) 1997 by John Wiley & Sons, Ltd.