Article Text

## Statistics from Altmetric.com

In the recent paper by Feltgen and colleagues,^{1} the intraocular pressure (IOP) was measured by Goldmann applanation tonometry and by using a cannula inserted into the anterior chamber connected with a pressure transducer. Thus, the measurement took place omitting a possible influence of the cornea on the result. Marx *et al*^{2} believed that by intracameral measurement the “true” intraocular pressure may be measured. Feltgen *et al* share his opinion. They believe, therefore, that they have compared the intraocular pressure measured with and without the possible influence of the cornea.

Feltgen *et al* write in their conclusion: “There is no systematic error of applanation tonometry with increasing central corneal thickness (CCT). Therefore it is inadequate to recalculate IOP based on regression formula of applanatory IOP versus CCT.” They base their conclusion on their results. In our opinion their paper shows the following methodological deficits: (1) Both methods used for measuring IOP are not up to the demands of the scientific technique of measurement; (2) their intracamerally measured IOP values do not reflect the true IOP because of bias; (3) a non-significant regression coefficient does not prove that the slope is actually 0 and, therefore, by a non-significant regression coefficient it is not proved that applanatory readings are not influenced by CCT; (4) the goodness of fit of the linear regression model is insufficient; and (5) an important covariate (true IOP value) was omitted in the linear regression. We would like to discuss these points in detail.

In the study of Feltgen *et al* the only criterion for the quality of measurement is the stability of the readings on the monitor. However, it is not sufficient to conclude from the presence of stability that the scale readings represent the “true” pressure value that is at the tip of the cannula. If there were a barrier inside the cannula the reading on the monitor would also be stable but would not represent the pressure at the tip. There are many pitfalls in pressure measurements by thin tubes that we know from our own studies.^{3,}^{4} Minute air bubbles or tiny particles influence the result a great deal. If we want to know that a display reading represents the quantity in question then we have to guarantee that the measurement system has the opportunity to react freely to changes in the quantity. This guarantee can be obtained by feeding a known signal to the input of the system and by observing the output. If the output reacts in the expected way then the guarantee is given. Ehlers *et al*^{5} realised this in their rabbit experiments and we in electrophysiology.^{6–}^{9} As long as this demand is not met the results are not definitive, giving cause for criticism and leading to misinterpretations.

Feltgen *et al* write in their paper (p 86): “ …however, we believe intracamerally measured IOP values reflect the `true' IOP more accurately.” Scientific facts should not be a matter of belief. The belief of the authors in the values they measured is not justified. In the study under discussion their figure 2 shows the scatter plot of the pressure differences versus central corneal thickness. From this diagram and from their statistical calculations the authors draw their conclusions. Their results are quite different from those of Ehlers *et al*^{5} shown in figure 4 of their paper. Thus we must compare these two data sets. To facilitate this task, we have digitised the data presented in the figures of Feltgen *et al* and of Ehlers *et al.* They are shown here in Figures 1 and 2 on the same scale. The difference is striking.

Let's first consider a possible reason from the physical point of view. Ehlers *et al*^{5} reduced the pressure measurement to a basic physical quantity, here to the length of a water column. We can, therefore, trust the results of Ehlers *et al* more than the results of Feltgen *et al* who used a pressure transducer which has a zero point fluctuation up to 4.5 mm Hg (Abbott GmbH, data file). It is recommended also by the manufacturer that the zero point of the measurement system has to be determined for each patient by comparison with a water column (Dr Beer, Abbott GmbH, Wiesbaden, personal communication). This procedure is not described by Feltgen *et al.*

Therefore, none of the methods used in the article by Feltgen *et al* may be called a reference method and all methods may be prone to error and bias. Hence, analysis of differences in IOP between these models is inappropriate in order to decide on the necessity of a conversion formula.

Further, the variability of differences is large, which is probably the result of errors in the intracameral measurement of IOP. Regression lines with a small non-significant slope (0.38 mm Hg IOP difference per 0.1 mm cornea thickness in the article by Feltgen *et al* may occur in both situations where variability is both high and low. Only, in the latter case, when—as a consequence of the small variability—the confidence interval for the slope is narrow, may this be interpreted in the way that the covariate included in the model (that is, CCT) has no effect. If the variability is high and the slope is approximately 0, this may lead to the conclusion that IOP measurement is inappropriate because of too large an error. This conclusion is allowed if no other essential covariates were overlooked. If variability is high and the slope of the regression line is near 0, a large p value may not be interpreted as a proof of no effect of the covariate considered in the regression model. For better interpretation of the results a confidence interval for the estimated slope would have been much more appropriate than a p value.

As a consequence, the differences between measurements from applanation tonometry and a reference method, like the intraocular hydrostatic pressure done by Ehlers *et al*, should be evaluated first. If measurements by applanatory IOP are highly correlated with measurements by the reference method a conversion formula may be derived from linear regression. Under the assumption of small variability of residuals (difference between observed value and regression line)—that is, a satisfactory goodness of fit (for example, *r*^{2}≥60%), results may lead to the recommendation of the use of a conversion formula. In contrast, Feltgen *et al* report an *r*^{2} of 0.2%. Only for small residuals, a slope approximately 0, and a confidence interval with limits near to 0, may the recommendation that a conversion formula is not necessary be given.

Moreover, the large variability in IOP differences may occur because Feltgen *et al* did not adjust for “true” intraocular hydrostatic pressure as Ehlers *et al* did. Since Ehlers *et al* calculated separate linear regression models for 10 mm Hg and 30 mm Hg which resulted in different intercepts and slope parameters, this might be another source of variation in the IOP differences from Feltgen *et al* which were unadjusted.

We hope our arguments are convincing and ask that you bring them to the attention of your readers.

## References

# Authors' reply

In reply to the comments of Stodtmeister and colleagues on our recent paper,^{1} we won't argue about the correlation between central corneal thickness (CCT) and intraocular pressure (IOP), but we mistrust the clinical application of correcting factors. Stodtmeister *et al* compare our study to that of Ehlers *et al*^{2} which is often cited to prove an influence of corneal thickness on applanatory measurement.

In our paper simultaneous IOP measurement by applanation and intracameral tonometry was performed. Assuming a normal CCT of 520 μm, an IOP correction for every 10 μm change in corneal thickness is recommended. But in the Ehlers paper, there are some confusing arguments.

Ehlers *et al*^{2} describe a very good correlation between direct and intracameral IOP measurement (correlation coefficient approximated 1). Unfortunately, they didn't give the measured IOP values. In figure 2, the slopes of correlation lines at different CCT are presented for rabbits (not for human eyes!). The increase of the slopes are less than 45°. With the paper of Bland and Altman^{3} in mind, a minor methodological agreement is very likely. It is therefore not allowed to recalculate the values P10 and P30 (applanatory versus intracamerally IOP, measured at an adjusted IOP of 10 and 30 mm Hg) for a relevant IOP level of 20 mm Hg (P20). It is indeed very interesting that the group didn't measure at an IOP level of 20 mm Hg.

The equipment for intracameral measurement is comparable to our device. We also calibrated the transducer before each measurement. When we tested our device on enucleated human eyes in a preclinical study, a very sensitive change of IOP values was noted when touching the eyeball. We therefore decided not to measure the IOP simultaneously. We also confirmed these findings in vivo. For these reasons, we expected an unpredictable increase of applanatory measurement during intracamerally IOP in the study of Ehlers.^{2} Unfortunately, there is no comment about this problem.

Stodtmeister and colleagues pointed out the “pitfalls in pressure measurement” (bubbles or tiny particles) without mentioning that Ehlers had not solved these problems in his trial on human eyes. We are also missing any information about the cannula size. Additionally, the device used resembles an “open system” where fluid could circulate through the anterior chamber and trabecular meshwork. This can generate a noticeable change in intraocular pressure.

Ehlers *et al*^{2} measured IOP in patients with an acute eye disease (glaucoma patients requiring surgery) and cataract patients. He changed the IOP to 10 and 30 mm Hg. This method is questionable especially in glaucoma patients, because an acute IOP change could also entail endothelial alterations which could alter CCT. Unfortunately, he didn't measure the CCT after IOP change. We have no information about the influence of IOP alterations on CCT.

In summary, the above mentioned study gives a hint on the influence of CCT on IOP measurement, but does not prove this assumption. It is amazing that within the last 25 years nearly 50 published papers refer to the Ehlers study^{2} without checking the results by intracameral measurement themselves.

All papers measuring CCT and applanatory IOP renouncing intracameral measurement described an increasing IOP with increasing CCT. We could also confirm this finding in our study (y = 14.5 + 8.4 × CCT, where y is applanatory IOP in mm Hg). Of course, it would be easiest to claim the cornea for this correlation. But it is also conceivable that eyes with thick corneas (for example, OHT) have a reduced ocular outflow facility and consequently elevated IOP—for instance, because of a “thick” trabecular meshwork.

With the present study ^{1} we tried to find out if the above recommended correcting factors are clinically applicable or not. According to our findings they are not. We found quite variable and unpredictable differences between intraocular pressure and applanatory measurement in an individual patient. Interestingly, the same results can be found in the Ehlers study.^{2} Therefore, we renew our warning to recalculate the IOP depending on central corneal thickness.