Latent dry eye disease state variable

Abstract

Purpose: Evidence is growing that dry eye represents a common disease process resulting from a number of underlying pathologies that impact the ocular surface and that clinical estimates of dry eye severity reflect the magnitude of a single dry eye disease state variable, Θ. A theory for estimating Θ from scaled clinical observations is developed, and the hypothesis is tested that Θ exists.

Methods: The theory is developed around three assumptions: (1) a monotonic function unique to each person and indicator maps the indicator onto Θ, (2) between-person differences in mapping functions are random, and (3) observed indicator values include random perturbations. Data recently published by Sullivan and his colleagues were digitized from scatter plots of seven different indicators versus a composite severity score (square root of summed weighted squared indicator scores).

Results: The data were analyzed with a model derived under the specific assumptions that between-person variance in mapping functions is independent of the indicator value and random perturbations in observed indicator values are normally distributed. Tear osmolarity was the most sensitive indicator, and tear breakup time was the least. The distribution of residuals (squared difference between observed and predicted indicator values) agreed with model expectations for all indicators except tear osmolarity, which had larger residuals than expected, and the composite severity score, which had smaller residuals than expected.

Conclusions: The results are consistent with the existence of a single latent dry eye disease state variable. Only tear osmolarity does not appear to map monotonically and/or unidimensionally onto the latent variable.