- Email: [email protected]
Lens Dysfunction through Aging
Lens Dysfunction through Aging Dear Editor: Alió et al1 measured optical density of human lenses in vivo using Scheimpflug densitometry. They reported that the results were analyzed for the entire population and then for 4 arbitrarily selected age groups. They state that “the relationship between all variables and age was modeled using the bivariate correlation model and Pearson correlation (r).” In “Results,” they report that “densities of embryonic, anterior fetal, and posterior fetal nuclei show a positive correlation with aging after the age of 40 (r ⫽ 0.762, P⬍0.0001; r ⫽ 0.764, P⬍0.0001; and r ⫽ 0.756, P⬍0.0001, respectively).” They state several times in the article that a positive correlation was found after the age of 40 years. They also state that “the scatterplots of embryonic and anterior fetal nuclei clearly show a turning point around the age of 40 years, after which densities of the nuclei show an increase with age.” Further, in “Discussion” they write “in our study, nucleus density showed a positive correlation with age, after 40 years, for embryonic, anterior fetal, and posterior fetal nuclei. When different age groups are analyzed, we can see that nucleus density does not increase before the age of 40, after which nucleus density increases linearly with age.” Evidently, the authors have used a linear regression analysis and have divided their data arbitrarily into 4 groups and then used an analysis of these subdivisions to draw conclusions regarding a break point in the data. A Pearson correlation linear regression analysis is inappropriate on data that are clearly not linearly related. It appears that an arbitrary cutoff was made at 40 years of age and then the remaining data were fitted with a linear regression. Even the data after 40 years are clearly not linearly related. A formal statistical break-point analysis would be required on their
618.e1
entire data set to determine the existence of a break point and, if it exists, at what age it occurs. If the analysis described above serves as the basis for their conclusion that there is no change in lens optical density before age 40, this is an inappropriate analysis and an unsubstantiated conclusion. There is no justification for excluding the data below 40 years of age in the analysis or for using a linear regression analysis on data that are clearly not linearly related. I have extracted their data from the published graphs (an inexact exercise to say the least, not only in terms of the absolute values obtained, but also in terms of the number of data points extracted) and, by way of an example, fitted these data with a nonlinear Hill 4 parameter function (SigmaPlot, SPSS, Chicago, IL) as has been used to describe other age changes in the lens.2 In each case, these functions show significant fits to the entire data set and clearly show no constancy below 40 years of age, but rather a progressive increase in lens optical density (Fig 1 [available at http://www.aaojournal.org]). Will the authors please undertake an appropriate reanalysis of the full age range of their original data set using an appropriate function and reevaluate their conclusions regarding age changes in optical density of the lens below 40 years of age? I look forward to their reanalysis and the conclusions they reach. ADRIAN GLASSER Houston, Texas References 1. Alió JL, Schimchak P, Negri HP, Montés-Micó R. Crystalline lens optical dysfunction through aging. Ophthalmology 2005; 112:2022–9. 2. Heys KR, Cram SL, Truscott RJ. Massive increase in the stiffness of the human lens nucleus with age: the basis for presbyopia? Mol Vis 2004;10:956 – 63.
Letters to the Editor
Figure 1. Replots of the data extracted from Alio et al fit, by way of an example, with nonlinear Hill 4 parameter functions. A, Data from their Figure 4a for the embryonic nucleus (a ⫽ 2122.8065, b ⫽ 3.9115, c ⫽ 170.5028, y0 ⫽ 20.1403, r2 ⫽ 0.78, P⬍0.0001). B, Data from their Figure 5a for the anterior fetal nucleus (a ⫽ 1041.2361, b ⫽ 2.7270, c ⫽ 183.9502, y0 ⫽ 21.0180, r2 ⫽ 0.82, P⬍0.0001). C, Data from their Figure 6a for the posterior fetal nucleus (a ⫽ 918.3773, b ⫽ 1.8915, c ⫽ 256.0855, y0 ⫽ 22.7347, r2 ⫽ 0.82, P⬍0.0001).
618.e2
618.e1
entire data set to determine the existence of a break point and, if it exists, at what age it occurs. If the analysis described above serves as the basis for their conclusion that there is no change in lens optical density before age 40, this is an inappropriate analysis and an unsubstantiated conclusion. There is no justification for excluding the data below 40 years of age in the analysis or for using a linear regression analysis on data that are clearly not linearly related. I have extracted their data from the published graphs (an inexact exercise to say the least, not only in terms of the absolute values obtained, but also in terms of the number of data points extracted) and, by way of an example, fitted these data with a nonlinear Hill 4 parameter function (SigmaPlot, SPSS, Chicago, IL) as has been used to describe other age changes in the lens.2 In each case, these functions show significant fits to the entire data set and clearly show no constancy below 40 years of age, but rather a progressive increase in lens optical density (Fig 1 [available at http://www.aaojournal.org]). Will the authors please undertake an appropriate reanalysis of the full age range of their original data set using an appropriate function and reevaluate their conclusions regarding age changes in optical density of the lens below 40 years of age? I look forward to their reanalysis and the conclusions they reach. ADRIAN GLASSER Houston, Texas References 1. Alió JL, Schimchak P, Negri HP, Montés-Micó R. Crystalline lens optical dysfunction through aging. Ophthalmology 2005; 112:2022–9. 2. Heys KR, Cram SL, Truscott RJ. Massive increase in the stiffness of the human lens nucleus with age: the basis for presbyopia? Mol Vis 2004;10:956 – 63.
Letters to the Editor
Figure 1. Replots of the data extracted from Alio et al fit, by way of an example, with nonlinear Hill 4 parameter functions. A, Data from their Figure 4a for the embryonic nucleus (a ⫽ 2122.8065, b ⫽ 3.9115, c ⫽ 170.5028, y0 ⫽ 20.1403, r2 ⫽ 0.78, P⬍0.0001). B, Data from their Figure 5a for the anterior fetal nucleus (a ⫽ 1041.2361, b ⫽ 2.7270, c ⫽ 183.9502, y0 ⫽ 21.0180, r2 ⫽ 0.82, P⬍0.0001). C, Data from their Figure 6a for the posterior fetal nucleus (a ⫽ 918.3773, b ⫽ 1.8915, c ⫽ 256.0855, y0 ⫽ 22.7347, r2 ⫽ 0.82, P⬍0.0001).
618.e2