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Regression to the Mean Could Account for This Discrepancy
Author Response: Regression to the Mean Could Account for This Discrepancy
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Michael D. Crossland UCL Institute of Ophthalmology, London, UK, Kavitha Thayaparan, and Gary S. Rubin
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m.crossland{at}ucl.ac.uk Michael D. Crossland, et al.
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We read with interest the paper by Haymes et al.1 on the reliability and validity of the Mars Contrast Sensitivity Test. We were surprised that the absolute values for the Mars chart were not comparable to the Pelli-Robson chart as this conflicts with data from our group and others (Thayaparan K, et al. IOVS 2006;47:ARVO E-Abstract 3480).2,3 We speculate that the data presented in Figure 3 of Haymes's paper may be confounded by a regression-to-the-mean problem: high readings on one chart are likely to be followed by lower results on a second chart and vice versa. This phenomenon has been well described in the literature4,5 and is one of the reasons for the widespread use of the Bland-Altman technique, whereby the mean of the values from both tests is plotted on the abscissa rather than the result of only one test.6 Indeed, Bland and Altman state that "[i]t would be a mistake to plot the difference against either value separately because the difference will be related to each, a well-known statistical artefact."6 Although it may be that the Mars chart measured lower contrast sensitivity values than the Pelli-Robson chart for people with better contrast sensitivity (and higher values for those with poor contrast sensitivity), the methods used by Haymes and colleagues are not sufficient for this conclusion to be made. Michael D. Crossland1,2 1Division of Vision Rehabilitation, UCL Institute of Ophthalmology, London, UK Acknowledgment: We have no commercial interest in the Mars Letter Contrast Sensitivity Test or the Pelli-Robson chart. References 1. Haymes SA, Roberts KF, Cruess AF, et al. The letter contrast sensitivity test: clinical evaluation of a new design. Invest Ophthalmol Vis Sci. 2006;47:2739-2745. |
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Sharon A. Haymes
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sharon.haymes{at}dal.ca Sharon A. Haymes
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We appreciate the thoughts of Crossland et al. regarding our article.1 However, we believe that regression-to-the-mean effects made a negligible contribution to the discrepancies between the Mars Letter Contrast Sensitivity (CS) Test and the Pelli-Robson CS Chart that were found in our study. Crossland et al. suggest that we should have used Bland-Altman analysis,2 plotting the difference as a function of the average of both tests. However, we suggest that the average of two tests with systematically different results is difficult to interpret and not clinically meaningful, whereas the Pelli-Robson CS Chart provides a well-accepted and valid reference standard.3-5 As stated in the legend of Figure 3,1 we derived the difference between the tests from the average of two measurements with the Mars Test and two measurements with the Pelli-Robson Chart, and plotted this as a function of the latter. Averaging repeated measurements reduces random measurement error as well as regression-to-the-mean effects related to such errors. The figure shows that Mars CS was less than Pelli-Robson CS at the upper end of the range and greater at the lower end of the range, with the relationship between difference in tests and magnitude of Pelli-Robson CS being non-zero and statistically significant (r = -0.82, P < 0.001). Given the low test-retest variability of both tests and the fact that our comparison was based on repeated estimates, we consider the observed differences were much larger than those expected from regression-to-the-mean effects. Indeed, even if we re-plot the difference between Mars and Pelli-Robson CS as a function of average Mars and Pelli-Robson CS, as suggested by Crossland et al., the same pattern of discrepancy between the tests is evident and remains highly significant (r = -0.61, P < 0.001; an anonymized data set is available from the corresponding author upon request). Although Thayaparan et al.6 did not find such a discrepancy between these two tests, our findings are supported in part by those of Dougherty et al.7 They also observed higher CS measures with the Mars test compared to the Pelli-Robson test at the lower end of the CS range and proposed that this was likely to be because the actual Mars contrast values in this range were on average 0.07 log units higher than stated.6 We conclude that our methods were robust to regression-to-the-mean effects and that the results observed in our study reflect true discrepancies between the Mars and Pelli-Robson CS test charts used. Whether or not the small discrepancies are of clinical significance will depend on the purpose for which the Mars test is being used. Sharon A. Haymes1 1Department of Ophthalmology and Visual Sciences, Dalhousie University, Halifax, Nova Scotia, Canada Acknowledgement: We have no commercial interest in the Mars Letter Contrast Sensitivity Test or the Pelli-Robson Contrast Sensitivity Chart. References 1. Haymes SA, Roberts KF, Cruess AF, et al. The letter contrast sensitivity test: clinical evaluation of a new design. Invest Ophthalmol Vis Sci. 2006;47:2739-2745. |
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