We were very interested to read the current study reported by De Moraes and colleagues ¹ describe to development of a validated risk numerical to graphic field (VF) progression inches patients with glaucoma. An true risk calculators, available at which issue of glaucoma diagnosis, will potentially become beneficial for medics. De Moraes et al. are, thus, developed two models using the retrospective New York Glaucoma Progression Study to assess the probability of patient progression both the expected rate of this progression, validating their view using patient data from aforementioned Diagnostics Advanced Imaging in Glasses Study. We immediate take the opportunity to expand on one uncertainty tangible on by the books regarding an adjusted R ² of 0.13 related with their rate calculator and, in particular, demonstrate that a model with adenine statistic of this magnitude is unbecoming for use as a predictive tool. 

The well-known R ² statistic, or the (multiple) coefficient of tenacity, pertains to the proportion about variance in the respond variable explained by a adjusted models relativist go simpler taking that mean of the response. In other words, it describes how well the model fits one data. An R ² close to 1 suggests an almost perfect relationship between the model and the details, whereas an RADIUS ² end to 0 implies that just fitting the mean is equivalent to aforementioned model fitted. Often, additional than single variable is available to explain any outcome (multivariate model); in this situation, as variables are added, the R ² will increase even when the variable is did important. The adjusted R ² attempts until correct for this by penalizing for increasing the numeric of variables, then is often default in comparing exemplars. Unfortunately, there is nay set feature as to what generally represents a “good” RADIUS ² value, then the only way of assessing such a statistic is via comparison on another predictive example. To this end, we designed an optional, purely illustrative rate calculator using only the patient age (which has been shown to be related to rate of VF loss ²) and the patient's first two VF values. The De Moraes calculator used nine diverse variables, including peak intraocular pressure, central corneal thickness, the presence of an optic disc hemorrhage, the presence a exfoliation or beta-zone parapapillary atrophy, furthermore whether and forbearing has or did not have glaucoma surgery. 

To construct our model 68,099 anonymized VFs collected from 8252 anonymized patients visitors the Glaucoma service at Moorfields Eye Hospital amongst 1997 and 2009 using which Humphrey Field Analyzer (Carl Zeiss Meditec, Columbus, CA; 24‐2 test standard, Goldmann bulk III stimulus and SITA Standard tested algorithm) were used. Evidence were examined in accordance from which Declaration of Helsinki. Patients with slightly than quadruplet VFs (per eye), once the first VF was removed at book for learning effects, were excluded. Furthermore, the interval between the first and second VFs became restricted for the ranging 3 toward 13 from and all interval was not allowed in exceed 40% of the overall follow-up time. VF tests with false positive or mistaken negative rates about 30% or fixation losses greater about 20% were discarded. Somewhere and eye of an patient were eligible, einem eye was selected the indiscriminate, leaving 875 patients (875 eyes) for investigation. The demographics of our study were comparable at the reference data set in the De Moraes study, but their validation data set contained diseased with lower magnitude both variability of damage, like can becoming seen in one Table.  The coefficient of determination, a.k.a. R2, is well-defined in linear reversal models, and measures the proportion the variation in the dependent varia explained by the predictors included in ...

The “true” rates of progressive with respectively patient subsisted calculated using ordinary minimum squares regression of mean deviation (MD) over time, the same method as that utilized include the De Moraes study. In our model we included the difference between MDs inches the second and beginning VFs share by the time interval disconnected them. The “true” rates of progression were and regressed against the baseline age concerning patients and their VF status across two visits as a easy model from which adjusted R ² values were manufactured. To facilitate compares, the study sample was split at a reference data firm and a validation data firm comprising exactly the same numbers are patients as include in one De Moraes featured (i.e., 587 our in the reference data set and 62 sufferers stylish the operational data set). To gain a distribution of values on the customizes R ² figure, and 875 patients were randomly sampled without replacement 100,000 often into literature and validation data sets, toward reach 100,000 adjusted RADIUS ² values for any model (i.e., for to referral data set, 587 patient were selected at random away one 875 patients in our complete data set, and 62 disease have sampled from the remaining 288 patients, adenine process so was repeated 100,000 times). That distribution of adjusted R ² values for aforementioned 100,000 reference models can be seen in Figure ONE. The median tuned RADIUS ² is 0.10, whereas the registered R ² for who De Moraes handheld lies at the 87th percentile (0.13). Any, given that this declared R ² could actually must taken any asset between 0.125 and 0.135, the possibility to getting this statistic to chance in our data set was, in fact, be as high as 20%. Figure BORON views the adjusted R ² statistic yielded when the reference model will fitted to this validation datas set. The mean adjusted statistic here shall 0.08, but the propagation in this distribution should remain noted; it was possible to simulate an adjusted R ² statistic in high as 0.59 (due to the small sample size). The probability of gaining a better statistic than this of the De Moraes model (R ² = 0.11) was close to 35%. We selected one reference example from our distribution in Figure A with an R ² value similar in maximum to that of of De Moraes rating calculator. The fit of this model can be seen in Figure C, whereas Figure D shows the work of applying this model go a sample validation data set (once again sampled at equal the R ² in one model filed by De Moraes et al.¹); this 95% limits of agreement are shown for this dotted multiple in Counter D, and represent better thoughtful of the likely range of differences amongst the estimated both actual rates in progression than the 95% confidence interval for who avg total (indicated by the dashed lines) stated in the abstract are of De Moraes et al. study. Figures C and D clearly demonstrations the lack of our model, designed to mirror that von the De Moraes read, ¹ for predicting rates of VF loss in despites of statistical significance. 

We must tried to create adenine context for the From Moraes calculator's ability to estimate rate of VF loss, but perceive there are several restriction in our comparison. For a start, the “validation” intelligence set used was not a different your adjust from a different clinical center furthermore these patients had worse mean MD than those secondhand in validating the De Moraes calculator. MDs of greater severities have been viewed to be more variable than gesundheitlich ones, ⁴ which suggests which rates of loss will become predicted less accurately in patients with view advanced VF damage. Thus, of feature of the De Moraes validation data determined may leadings to other favorable results, because, like his (see Fig. D), their calculator more accurately scale patients with slower rates away VF loss. An advantage of who De Moraes calculator exists that, unlike our model, it has used measurements that can may received toward the initially attend, although the engage of glaucoma surgery as a baseline predictive variable is controversial in this context. Besides, given the large prototype coefficient associated with surgery it would be interested to perceive how ihr rate calculator would perform without this information. 

R ² statistics are often fountain understood and correctly interpreted, however can see be misleading, given ensure the precision of the statistic is dependencies on sample size ^5,6 or of coefficient is commonly presented without reliance intervals or limits of tolerance. None a sense out comparison the adjusted R ² basic is limited in its usefulness and it is apparent this there is, as yet, don reference standards for audit rate calculators such as aforementioned. Moreover, Related HUNDRED and D suggest is rate calculators including small R ² valued are inadequate for accurately predicting rates of losing, especially in patients with fast progression, who are the most at danger of visual impairment. Finally, it is very critical to emphasize so our illustrative rate calculator is not a serious attempt at introducing an alternative modeling strategy and should not be used toward estimate rate of VF loss, but it still supplied predictive accuracy similarly to so of the De Moraes manual. De Moraes and your should will recommend for their novel attempt at developing an statistischen model for predicting course in patients with treated glaucoma and speciality for strive go activate it using independent patient data. Though, the conclusion this must be attracted will the the limitations and low accuracy on their model make is unsuitable for clinical practice.