Age-related standards for ordinal data: modelling the changes in visual acuity from 2 to 9 years of age

The visual acuities of 1140 children between the ages of 2 and 9 years were measured using the Sonksen-Silver Acuity System (SSAS) from a distance of 3 metres. Ordered logistic regression was used to construct smoothly changing age-related reference ranges for the proportions of children at different ages expected to have acuities in each of three ordinal categories. Exponential functions of age fitted the data better than polynomials. The resulting reference ranges can be used to derive the ages at which a given percentage of children achieve each of the acuity cut-offs. However, since it is unlikely that all children will be available for testing at the exact appropriate age, two possible alternatives are introduced and discussed. First, a new ordinal category that would result in a chosen outcome at a pre-selected age is calculated. Secondly, because it may be more feasible to use the current SSAS system whilst varying the distance of measurement, age-related standards showing the distances required to give constant pass-rates with the usual letter-sizes are also presented.