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Patrick Johnston, Lisa Smith, John Rodriguez, Keith Lane, George Ousler, Richard Abelson; Modeling Blink: Blink Rate or Interblink Interval?. Invest. Ophthalmol. Vis. Sci. 2013;54(15):967.
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© ARVO (1962-2015); The Authors (2016-present)
Blink activity is commonly assessed in subjects with dry eye via blink rate (BR) or interblink interval (IBI). As data the two measurements are equivalent in the sense that one is the reciprocal of the other (a subject with N blinks over time period T has a BR of N/T and an average IBI of T/N). As means, however, they are not equivalent since the reciprocal of mean BR does not equal the mean of IBI, and this raises the question of preference. We consider two aspects. First, if a particular blink measurement is desired (BR or IBI), we assess the merits of normal versus gamma models. Second, in cases where an investigator is interested in blink frequency but is not committed to a particular measurement, we propose a novel method to compare the appropriateness of the two measurements.
For a particular measurement (BR or IBI), two-mean models were fit assuming both normal and gamma distributions and these were compared using the Akaike information criterion (AIC). Differences in AIC compare the relative goodness of fit of two statistical models, the model with the lower AIC being preferred. Importantly (because normal and gamma models are not special cases of each other), models compared by AIC need not be nested. BR and IBI cannot be compared directly because comparisons of AIC require models with identical outcomes. However, the functional relationship between BR and IBI permits comparison based on a generalization of the Box-Cox transformation method. For example, estimates with outcome IBI = 1/BR using a gamma model are identical to estimates based on BR using an inverse gamma model, and it is the latter model that provides the appropriate AIC for comparison.
The gamma model was preferred to the normal model for BR by 10 units of AIC, and for IBI by 7 units of AIC. In cases where either measurement is allowed to represent blink frequency, BR was preferred to IBI by 4 units of AIC (in both cases using a gamma model).
It is not uncommon for t-tests to be used in the analysis of BR and IBI, and while these tests are optimal under normality, they are not optimal under the superior gamma approximation indicated by this study. In addition, we have proposed a novel method to compare BR and IBI, in effect selecting the preferred scale on which to measure blink frequency. In the present study BR was preferred to IBI.
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