Improving population-level refractive error monitoring via mixture distributions

Introduction

Sampling and describing the distribution of refractive error in populations is critical to understanding eye care needs, refractive differences between groups and factors affecting refractive development. We investigated the ability of mixture models to describe refractive error distributions.

Methods

We used key informants to identify raw refractive error datasets and a systematic search strategy to identify published binned datasets of community-representative refractive error. Mixture models combine various component distributions via weighting to describe an observed distribution. We modelled raw refractive error data with a single-Gaussian (normal) distribution, mixtures of two to six Gaussian distributions and an additive model of an exponential and Gaussian (ex-Gaussian) distribution. We tested the relative fitting accuracy of each method via Bayesian Information Criterion (BIC) and then compared the ability of selected models to predict the observed prevalence of refractive error across a range of cut-points for both the raw and binned refractive data.

Results

We obtained large raw refractive error datasets from the United States and Korea. The ability of our models to fit the data improved significantly from a single-Gaussian to a two-Gaussian-component additive model and then remained stable with ≥3-Gaussian-component mixture models. Means and standard deviations for BIC relative to 1 for the single-Gaussian model, where lower is better, were 0.89 ± 0.05, 0.88 ± 0.06, 0.89 ± 0.06, 0.89 ± 0.06 and 0.90 ± 0.06 for two-, three-, four-, five- and six-Gaussian-component models, respectively, tested across US and Korean raw data grouped by age decade. Means and standard deviations for the difference between observed and model-based estimates of refractive error prevalence across a range of cut-points for the raw data were −3.0% ± 6.3, 0.5% ± 1.9, 0.6% ± 1.5 and −1.8% ± 4.0 for one-, two- and three-Gaussian-component and ex-Gaussian models, respectively.

Conclusions

Mixture models appear able to describe the population distribution of refractive error accurately, offering significant advantages over commonly quoted simple summary statistics such as mean, standard deviation and prevalence.