Modelling hearing thresholds in the elderly

This paper concerns a linear mixed-effects repeated measures model in the analysis of a large data set with over 17,000 observations in a longitudinal study of pure-tone hearing perception in the elderly. The repeated measurements are described by fixed and random components in the model. The fixed effects include the age at entry, time of follow-up, a quadratic component in natural logarithm of frequency, a component to allow for participants with hearing impairments, as well as interaction terms between age and frequency and between impairment and frequency. The random factors include a term for subject, a time component and a frequency component. The analysis shows that hearing impaired individuals have similar patterns of hearing loss over time but, on average, have higher hearing thresholds than normal individuals. Estimation of the random effects in the model by restricted maximum likelihood (REML) using the Newton-Raphson method made possible the analysis of this large data set with speed and efficiency.