Identifying more reliable parameters for the detection of change during the follow-up of mild to moderate keratoconus patients
Guber et al. Eye and Vision
Identifying more reliable parameters for the detection of change during the follow-up of mild to moderate keratoconus patients
Ivo Guber 3
Colm McAlinden 1 2
François Majo 0
Ciara Bergin 0
0 Jules-Gonin Eye Hospital, University of Lausanne, Fondation Asile des Aveugles , Lausanne , Switzerland
1 School of Ophthalmology and Optometry, Wenzhou Medical University , Wenzhou, Zhejiang , China
2 Department of Ophthalmology, Glangwili Hospital, Hywel Dda University Health Board , Carmarthen , UK
3 Department of Ophthalmology, University of Geneva , Geneva , Switzerland
Background: Reaching a consensus on which parameters are most reliable at detecting progressive keratoconus patients with serial topography imaging is not evident. The aim of the study was to isolate the parameters best positioned to detect keratoconus progression using the Pentacam HR® measures based on the respective limits of repeatability and range of measurement. Method: Using the Pentacam HR®, a tolerance index was calculated on anterior segment parameters in healthy and keratoconic eyes. The tolerance index provides a scale from least to most affected parameters in terms of measurement noise relative to that observed in healthy eyes. Then, based on the “number of increments” from no disease to advanced disease, a relative utility (RU) score was also calculated. RU values close to 1 indicate parameters best positioned to detect a change in keratoconic eyes. Results: The tolerance index values indicated that 36% of ocular parameters for keratoconic eyes had repeatability limits which were wider than normative limits (worse), but 28% of the ocular parameters were narrower than normative limits (better). Considering only those parameters with a RU greater than 0.95, a small number of parameters were within this range, such as corneal curvature and asphericity indices. Conclusions: This study demonstrates that measurement error in keratoconic eyes is significantly greater than healthy eyes. Indices implemented here provide guidance on the levels of expected precision in keratoconic eyes relative to healthy eyes to aid clinicians in distinguishing real change from noise. Importantly maximal keratometry (Kmax), central corneal thickness (CCT) and thinnest corneal thickness (TCT) were highlighted as problematic indices for the follow-up of keratoconus in terms of repeatability.
Pentacam; Keratoconus; Progression; Repeatability; Precision; Corneal crosslinking
The clinician who follows keratoconus patients with serial
topography imaging desires to know which parameters are
most reliable at detecting progression. This is important as
the detection of progression will often determine treatment
choice e.g., collagen cross-linking (CXL). However, the
ability of a parameter to detect progression is decreased with
increased measurement noise (signal to noise ratio).
Previously, in healthy eyes the repeatability limit, of the maximal
corneal curvature Kmax (with the Pentacam HR®) were
reported to be 0.8 Dioptres (D), however, we found
repeatability limits in keratoconic eyes to be 1.97 D [
result means that the current main criteria for progression
detection and CXL is inadequate (i.e. a change of 1 D in
Kmax after one year of follow-up) [
To date, comparison of repeatability between subgroups
has been limited to a comparison of the repeatability
limits or the correlation of variation values within a given
]. Noting the important changes observed
in repeatability limits with keratoconus, we aimed to
determine which parameters were least affected. To isolate
these parameters, we employed the tolerance and relative
utility (RU) indices [
]. The tolerance index creates a
scale of least to most affected parameters and the RU
index highlights which parameters will theoretically
describe the most number of stages of severity of disease
and hence progression.
In this article, we aim to highlight the topographic
parameters obtained with the Pentacam HR® (V 1.20r02)
that are more reliable in detecting keratoconus
progression. We aim to achieve this by providing a table of the
associated tolerance and RU indices and demonstrating
This study was approved by the local cantonal ethics
committee and adhered to the tenets of Declaration of
Helsinki for research on human subjects. Informed
consent was obtained from all participants.
Ethical approval was granted by the Flinders clinical
research ethics committee. Data from a previous study by
McAlinden et al. were used as the healthy control group
]. This study reported the repeatability limits of
Pentacam HR parameters for 100 healthy eyes. These reported
repeatability limits were used to calculate the tolerance
index and RU index. The study by McAlinden et al.
involved the use of one randomly selected eye. For the
repeatability assessment, each eye was scanned twice with
the Pentacam HR in the 25 pictures per second mode
using automatic release by one observer. Participants
remained positioned during all repeated measurements.
Only scans that had an examination quality specification
graded as “OK” were saved. Fifty-three left eyes of 100
subjects (68 female) with a mean age of 33.7 years (range
19–68) were included. A sample size of 100 eyes will
give 99% confidence limits around estimates that are
within 13% of the true value. McAlinden et al. reported
an estimate of 95% limit of repeatability in K-max to be
0.8 D in normal subjects, therefore the 99% confidence
interval (CI) around the estimate of the 95% limit is 0.7
D and 0.9 D.
Keratoconus (KCN) group
Ethical approval was granted by the ethical commission
of the canton de Vaud, Switzerland under protocol
number 375/11. Thirty-three eyes of 20 patients with mild to
moderate KCN were recruited from a specialized
anterior segment unit at the Jules-Gonin eye hospital in
Lausanne, Switzerland. Tomography measurements were
obtained using the Pentacam HR® (V 1.20r02). Three
repeated measurements by two independent observers
were taken with the Pentacam HR in the 25 pictures per
second scanning automatic release mode by two
independent observers. Only measurements with a quality
factor (Q) “OK” or when over 95% of the data was
validated by the system were used for analysis. Images
from 32 eyes (16 right, 16 left) of 20 patients (6 females,
14 males) were taken. The mean age of patients was
31 years (range 18–47). Baseline mean and standard
deviation (SD) for thinnest corneal thickness (TCT),
maximal corneal curvature (Kmax), mean corneal curvature
anterior (Km ant), astigmatism, anterior chamber (AC)
depth and corneal volume (CV) at 7 mm were
482.1 ± 36.8 μm, 52.3 ± 3.7 D, 46.0 ± 2.2 D, −3.25 ± 1.6
D, 3.3 ± 0.3 mm, and 23.5 ± 1.6 mm3, respectively. A
sample size of 32 will give 99% confidence limits that are
within 23% of the true value; here we have reported that
K max has a repeatability of 1.97 D, therefore the 99%
CI of this estimate is 1.5 D and 2.4 D.
Repeatability (Sr) and reproducibility (SR) were assessed
based on the recommendations from the British
Standards Institute and the International Organization for
]. Repeatability and reproducibility
limits from the normal population are denoted as rN and
]. Repeatability and reproducibility limits derived
from our KCN population are denoted as rK and RK [
These were used to calculate the tolerance index,
denoted as Tr and TR for repeatability and reproducibility
limits, respectively [
rKi ; TRi ¼ Logn RNi
Tri ¼ Logn rNi
Where i represents the ith parameter e.g., Kmax, K1
etc. A tolerance index value of 0 represents perfect
agreement with normal limits; the larger the difference
from 0 the greater divergence from normative limits.
Negative numbers indicate narrower (better) CI limits in
the pathological group relative to normal subjects and
positive numbers indicate wider (worse) CI limits.
Based on the estimates of repeatability of each parameter
(e.g., K-max) in both populations, healthy (n = 100) and
keratoconic (n = 32), the respective CI around each
estimate can be calculated and CI overlap can be assessed.
In this way, any significant changes in repeatability can
be detected and highlighted. The tolerance index allows
us to summarize this information systematically. Based
on the central limit theorem, with a sample size of 32
and 100, a │tolerance value│of >0.24 indicates that the
confidence limits do not overlap and there is a
statistically significant difference at the 5% level.
Relative utility index
To derive the RU, the within-subject standard deviation
for repeated measures that is derived by a one-way
analysis of variance (ANOVA)(Sri), the between observer
standard deviation that is derived by ANOVA (SRi), and
the between patient standard deviation (SPi) were
calculated using the data in keratoconus eyes (Eq. 2).
The RU scale is from 0 to 1, with poor latent ability
nearer 0 and good latent ability nearer to 1. Analysis was
performed with R software version 2.15.1 [
Repeatability and tolerance index
The tolerance index values reported for anterior and
posterior curvatures were on average greater than +0.35,
in particular, Kmax had a Tr of 0.90 indicating a much
wider repeatability limit in keratoconus eyes compared
to normal eyes (Table 1). On the other hand, anterior
and posterior axis values were found to demonstrate
better repeatability limits (r = 11°; 23° respectively), with
better (high negative) Tr values (Tr < −1.7). Summary
data in terms of keratometric power deviation (KPD),
AC depth, AC volume and AC angle estimates were all
greater than normative values (Table 1; Tr > 0). Front
surface elevation maps at TCT were more repeatable
than back surface elevation maps at TCT. Pachymetry
estimates had good repeatability limits for pupil centre,
corneal apex, and TCT, with most measures inside
normal limits (Table 1). Corneal volume measurements at
all diameters were repeatable and had similar or better
than normative limits of repeatability (Tr < 0.2). The
topometric Q-values were repeatable, however, anterior
Q-value repeatability limits were outside normal limits.
Centre keratoconus index (CKI) and index of height
decentration (IHD) were repeatable with tighter limits of
repeatability (Tr < −1.1) but index of surface variance
(ISV), index of vertical asymmetry (IVA) and particularly
index of height asymmetry (IHA) were markedly less
repeatable and significantly outside normative limits
(Tr > 1.0).
Reproducibility and tolerance index
With a single image, Kmax had reproducibility limits
well outside normal with a TR value of 1.06, but when
the average of three images was used instead,
reproducibility was similar to normal limits (TR = 0.12). Of the
pachymetry estimates, apex measures were the least
reproducible followed by those at the TCT. The measures
at pupil centre had the best R-value (R-values, Table 1).
R-values of corneal volume increased with increasing
diameter, however central corneal volume R-limits were
greater than any of the peripheral estimates. Anterior
Qvalues had worse reproducibility than normal limits and
did not markedly improve when estimates from pairs or
triplets of images were used. IHD and CKI had tight
reproducibility limits, remaining within normative limits,
suggesting these are among the most reproducible
parameters in KCN patients.
Relative utility index
RU was used to indicate which parameters are less
variable relative to the respective dynamic range of that
parameter in our cohort (Table 2). Pachymetry at the
corneal apex, for example, is unlikely to be useful
clinically, as this parameter has an RU of 0.42, suggesting that
58% of the differences in CT apex between any two
keratoconic eyes from the study cohort can be attributed to
measurement variability (Table 2). On the other hand,
corneal curvature estimates all have RU values above
0.94, except for Kmax that has an RU of 0.88 (Table 2).
Considering only those parameters with a RU value
greater than 0.95, a small number of parameters within
the acceptable range were identified, namely: K1, K2 and
Km; Q-value (anterior), R-peripheral posterior, CKI, ISV,
IVA, IHD, AC depth, the back-elevation map at TCT
and ectasia map indices D and Db (Table 2).
Clinically, it is difficult to choose which parameter to
use to determine whether disease progression has
occurred, a consensus on the accepted parameters is
emerging but there is still significant divergence between
]. This article provides an overview
of the reliability of these parameters, removing the
clinical interpretation component. We have summarized the
differences in measurement noise between healthy and
keratoconus patients across all topographic parameters
from the Pentacam HR device using the tolerance index.
Comparing “r” and “R” reported by McAlinden et al. in
healthy eyes to our data in keratoconic eyes, 36%/44%
(n = 13/36; 16/36) of parameters were significantly
worse (Tr/TR > 0.45), and 28%/36% (n = 11/36; 13/36)
were significantly better (Tr/TR < −0.45) (e.g., axis is
more repeatable in KCN patients) [
Furthermore, our study data demonstrates that
averaging across several images significantly improves the
tolerance values, or results in lower level of
measurement noise; some parameters recovering to those levels
observed in healthy eyes [
]. For example, using the
average of three images instead of a single image
reduced reproducibility limits of Kmax to be in line with
normal values (Table 1). These results indicate that if
the average of three topographies instead of a single
topography was automatically calculated, the ability to
detect keratoconus progression could be significantly
Table 1 The tolerance indices (Tr, TR) (Continued)
IHA 2.09 2.41 2.49
K1, K2 = Keratometry readings 1,2; Km = Mean keratometry reading;
Rper = Mean radius of curvature in the 7-9 mm area of the cornea; Rmin =
Minimum radius of curvature; KPD = Keratometric power deviation; AC = Anterior
chamber; ISV = Index of surface variance; IVA = Index of vertical asymmetry;
KI = Keratoconus index; CKI = Centre keratoconus index; IHA = Index of height
asymmetry; IHD = Index of height decentration; Sr = Within-subject standard
deviation; r = The limits of repeatability; Tr = The log of the ratio between the
limits of repeatability of keratoconus patients and normal subjects; −0.45 < Tr/
TR < 0.45 is within normative limits
Example of reading the table: Taking the line Kmax, r is 1.97 D, therefore it has
a Tr value of 0.9, which means that r limit of 1.97 is well outside normal limits,
R is 2.3 D, therefore it has a TR value of 1.06 is reported when a single image
is used, again indicating that this is well outside normal limits, TR reduces to
0.12 when the average of three images was used, which is not significantly
different than normal limits
Using this information, the RU index isolated the
group of parameters theoretically best positioned to
detect progression. Summarizing the RU values: 37%
(n = 15/41) of parameters had an RU greater than 0.95,
indicating good ability to detect progression, 29%
(n = 12/41) of parameters had an RU <0.80 indicating
poor ability to detect progression. It may seem
counterintuitive, but it is possible that a parameter has poor TI
but still a good RU. This is because some parameters
have large differences between mild and moderate KCN
or in other words has a large dynamic range, and it is
the balance between the limits of repeatability and the
size dynamic range that determines the RU.
Clinically, there are three primary motivations for
collecting serial topography images in keratoconus patients:
to help distinguish healthy from early keratoconus, to
detect progression of keratoconus, or to determine the
effectiveness of treatments for keratoconus. Regardless
of the motivation, when comparing the RU values
reported in this article with the area under the curve
(AUC) values reported in the literature, we observe that
there is notable agreement [
4, 5, 7–15, 24
In studies which attempt to distinguish between
healthy and keratoconic eyes, the pachymetry values,
posterior elevations maps, keratometry asymmetry and
decentration indices have been mainly reported [
4, 5, 7–
10, 13, 14
]. Pachymetry at centre and thinnest location
have good sensitivity and specificity, however, the AUC
is lower than that reported with the asymmetry indices
7, 8, 25
]. Comparing the parameters with >0.90 AUC
values reported by Correia et al. to those parameters
with >0.95 RU values reported here, there is good
agreement . Likewise, comparing the poorest AUC results
(<0.85) reported by Uçakhan et al. to the poorest RU
values (<0.8) reported here, there is good agreement in
majority of parameters [
There are several articles examining keratoconus
5, 11, 12, 15
]. The corneal curvature
parameters perform well in distinguishing between different
stages of the disease , furthermore progressing eyes
have significantly different change rates in these
parameters than in non-progressing eyes [
corresponds well with RU values recorded here for K1, K2
and Km. Despite central corneal thickness (CCT) and
TCT being well established clinically and both
demonstrating significant difference in mean values for
different stages of the disease [
], the annual change rates
are not significantly different between progressing and
stable eyes for these parameters [
], which corresponds
to the poor RU values for pachymetry reported in this
study (RU < 0.75).
There are a small number of studies that have
examined topographic parameters following CXL: those
parameters with positive outcomes in these studies
correspond well with the better RU values reported in
this study [
]. In our study, the large change in
repeatability in eyes with keratoconus versus healthy eyes
indicates that repeatability in eyes following CXL should
be critically examined, as there are many possible
additional confounders. A change in repeatability in eyes
following CXL could be important, as currently there is
more than 70 clinical trials listed on the National
Institute for Health Research (NIHR) clinical trial registry
examining the effectiveness of CXL, where the primary
or secondary outcome is a change in corneal curvature.
Therefore, the parameters used to validate keratoconus
progression in these clinical trials may require updating.
This agreement between RU and AUC values is of
significance as the data required to calculate RU values is
collected at one sole visit, while the AUC data requires
data from several years of clinical observation. RU values
are not a replacement for AUC values, but they can be
used to help optimize clinical trials, by helping to
provide guidelines on the parameters of interest, the
optimal number of scans and the frequency of consultation.
Some of the differences in precision noted between
keratoconic and normal eyes are likely to be related to
the fitting algorithm used by the Pentacam HR device.
Alignment algorithms rely on alignment markers such
as pupil centre, thinnest corneal location, and corneal
apex. Some alignment markers will be less evident in
normal eyes than keratoconic eyes. For example, due to
the conical shape of the cornea in keratoconic eyes, the
location of Kmax is clear in most images, therefore the
same x, y coordinates will be calculated between images.
Furthermore, the fitting algorithm uses a model of the
smooth spherical cornea in the form of a “best fit
sphere” more akin to the normal cornea than the conical
cornea observed in keratoconic eyes. With this
technique, the presence of the cone is unexpected and likely
distorts estimates of many of the topographic parameters
]. Lastly, in eyes with a steep cone, the eye movements
associated with the loss of fixation have the potential to
cause much larger errors in the estimation of parameters
such as Kmax and TCT. This may be exacerbated by
multifocality associated with these “steep cones”, thus
greater higher intraocular straylight [
], and poorer
fixation. Lastly, this study examined only early to
moderate KCN, those parameters identified as useful in this
group may differ from those used in more advanced
The indices implemented in this article were designed to
provide an “at a glance” guideline on the levels of
expected precision in keratoconic eyes relative to healthy
eyes to aid clinicians in distinguishing real change from
]. Furthermore, the RU index isolates
topographic parameters with a large dynamic range in
comparison to measurement noise. This index gives an
indication of those parameters with the potential for
detecting a change when no longitudinal data are available
e.g. when a new device/software is released. Our
hypothesis is that parameters with high RU are best positioned
to detect change, whether it is disease progression or
assessing the efficacy of a therapeutic intervention. For
example, the Kmax and CCT parameters, which are
currently the standard measures used for the monitoring
of keratoconus have been shown to have poor RU in our
study, indicating that these parameters are not best
positioned to detect change. Further investigation is required
to verify these results and develop this methodology for
AC: Anterior chamber; AUC: Area under the curve; CKI: Centre keratoconus
index; CXL: Collagen cross-linking; D: Belin/Ambrosio ectasia total deviation
value; D: Dioptre; Da: Deviation of the apex thickness; Db: Deviation of the
back-elevation map; Df: Deviation of the front elevation map; Dp: Deviation
of average pachymetric progression; Dt: Deviation of the minimum thickness;
IHA: Index of height asymmetry; IHD: Index of height decentration; ISV: Index
of surface variance; IVA: Index of vertical asymmetry; K1, K2: Keratometry
readings 1 and 2; KCN: Keratoconus; KI: Keratoconus index; Km: Mean central
keratometry; KPD: Keratometric power deviation; r: Limits of repeatability;
R: Limits of reproducibility; Rmin: Minimum radius of curvature; Rper: Mean
radius of curvature in the 7-9 mm area of the cornea; RU: Relative utility;
Sr: Repeatability; SR: Reproducibility; TR: Tolerance index (the log of the ratio
between the limits of reproducibility of keratoconus patients and normal
Availability of data and materials
The datasets used and/or analysed during the current study are available
from the corresponding author on reasonable request.
IG and CM collected the data, CB and IG analysed and interpreted the
patient data. IG and CB were the major contributors in writing the
manuscript. All authors read and approved the final manuscript.
Ethics approval and consent to participate
This study was approved by the local cantonal ethics committee and
adhered to tenets of Declaration of Helsinki for research on human subjects.
Healthy group: Ethical approval was granted by the Flinders clinical research
Keratoconus (KCN) group: Ethical approval was granted by the ethical
commission of the canton de Vaud, Switzerland under protocol number
Consent for publication
All patients gave informant consent.
The authors declare that they have no competing interests.
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