Is it better to use OLS here? We would argue that it is not. Warton et al.
9 point out that it is inappropriate to use OLS when the variance in the
x- and
y-variables differs and when noise is not Gaussian. Furthermore, they also state that an errors-in-variables method like major axis regression or standardized major axis regression should be used if one wishes to determine the slope parameter
after establishing a significant association, which, as already pointed out, is an assumption of the method described by Bablok et al.
8 Furthermore, part of our motivation for performing Passing–Bablok regression on our data came from analysis of 200,000 simulated data sets with Deming regression and Passing–Bablok regression. These simulated data sets comprised total deviation values (standard automated perimetry) and retinal nerve fiber layer thickness (optical coherence tomography), based on the data of Hood et al.,
3 and the aim was to determine how well each regression technique performed at estimating the true underlying slope in the simulated data. Marin-Franch and colleagues previously showed,
10 also using simulations, that estimating linear relationships between structure and function measurements in glaucoma may be improved by the use of Deming regression compared with OLS, major-axis, and standardized major-axis regression techniques. However, unlike Passing–Bablok regression, Deming regression requires the investigator to input the ratio of variance in the two measurements of interest from population data. In practice, this information is often unavailable, as was the case for peripheral grating resolution acuity in our study; moreover, the variance ratio may change with the extent of damage.
Figure (a) shows that for all simulations, Passing–Bablok regression yielded a slope parameter that was closer to the true underlying slope compared with that yielded by Deming regression (where the variance ratio was assumed to be equal to 1). The intercept parameter was estimated equally well with each technique, but the confidence interval was narrower for Passing–Bablok regression for all true underlying slopes (Fig. b). Moreover, performing Passing–Bablok regression on the data of Hood and Kardon
11 for healthy observers (we initially find a significant Kendall's tau;
P < 0.05 following Holm–Bonferroni correction) reveals a slope of 13.7 and 18.7 for the upper and lower hemifields, respectively. One can see from Figure (a) that Passing–Bablok slopes in this region approximate the true underlying slope rather well.