|Year : 2021 | Volume
| Issue : 1 | Page : 15-20
Agreement between three methods for measuring near point of convergence among patients with different refractive errors
Antony A Baskaran1, Tanuja Britto2, Raja T Sowndher3, Philip A Thomas4
1 Assistant Professor, Department of Pediatric Ophthalmology, Institute of Ophthalmology, Joseph Eye Hospital, Melapudur, Trichy-1, India
2 Professor, Department of Pediatric Ophthalmology, Institute of Ophthalmology, Joseph Eye Hospital, Melapudur, Trichy-1, India
3 Department of Optometry, Institute of Ophthalmology, Joseph Eye Hospital, Melapudur, Trichy-1, India
4 Associate Director (Research) and Professor, Department of Ocular Microbiology and Clinical Research, Institute of Ophthalmology, Joseph Eye Hospital, Melapudur, Trichy-1, India
|Date of Submission||29-Aug-2019|
|Date of Decision||10-Dec-2020|
|Date of Acceptance||13-Dec-2020|
|Date of Web Publication||09-Sep-2021|
Dr. Antony A Baskaran
Department of Pediatric Ophthalmology, Institute of Ophthalmology, Joseph Eye Hospital, Melapudur, Trichy-1
Source of Support: None, Conflict of Interest: None
PURPOSE: To describe the agreement of three methods of Near Point of Convergence (NPC) measurement among patients with different refractive errors.
METHODS: 60 asymptomatic subjects, 18 – 25 yrs old, were included in 3 groups: emmetropes, myopes and hypermetropes. All subjects underwent NPC break point and recovery point measurement by Royal Air Force (RAF) rule, Pencil Rule (PR) and penlight with red green glasses (RG) using standard techniques. The values obtained were compared within each group by Friedman test. Bland Altman plots were constructed and Limits of Agreement calculated.
RESULTS: Hypermetropes performed poorly in RG test with significantly receded break point and recovery point values (10.30 ± 1.45cm, 13.13± 1.20cm) compared to RAF test (7.18 ± 1.86 cm, 10.15 ± 2.11cm ) and PR test (7.78 ± 1.75 cm, 10.75 ± 1.44cm). The recovery point values of the emmetropes with RG test (10.15 ± 2.32cm) was significantly receded compared to PR (9.30 ± 1.72 cm) and RAF test (Emm: 9.08 ± 2.30cm). The myopes performed better with PR test with significantly better recovery point values with PR test (8.70 ± 1.97 cm) compared to RAF (9.68 ± 2.08) and RG (9.45 ± 1.73) tests. The limits of agreement were wide suggesting disagreement between the tests.
CONCLUSION: The RG test yields more receded results in hypermetropes compared to the RAF and PR tests, and the PR test yields better results than the RAF test in myopes. Thus, the results obtained by these different methods show a lack of agreement. The variability is not uniform in patients with different refractive errors.
Keywords: Agreement, convergence, near point of convergence, pencil-ruler test, refractive errors, royal air force rule
|How to cite this article:|
Baskaran AA, Britto T, Sowndher RT, Thomas PA. Agreement between three methods for measuring near point of convergence among patients with different refractive errors. Saudi J Ophthalmol 2021;35:15-20
|How to cite this URL:|
Baskaran AA, Britto T, Sowndher RT, Thomas PA. Agreement between three methods for measuring near point of convergence among patients with different refractive errors. Saudi J Ophthalmol [serial online] 2021 [cited 2023 Mar 28];35:15-20. Available from: https://www.saudijophthalmol.org/text.asp?2021/35/1/15/325776
| Intaroduction|| |
The near point of convergence (NPC), the nearest point at which the lines of sight intersect when the eyes converge to the maximum, is a routinely performed and very useful test in the assessment and management of convergence insufficiency. Hussaindeen et al. found the average NPC break and recovery points in normal Indian children to be 3 ± 3 cm and 4 ± 4 cm when using accommodative targets, and 7 ± 5 cm and 10 ± 7 cm, respectively, when using penlight and red filter.
The NPC varies with the targets used and the methods employed for measurement. The variation with different targets used and the influence of royal air force (RAF) rule on the measurement of NPC have been well studied.,,, This difference in NPC between methods is said to be due to the differential accommodative demands, presence or absence of RAF rule, experience of the observer, and anticipation.
The previous literature on variation of NPC with targets usually employed emmetropes, those who read 20/20 with habitual correction,, and presbyopes. Ostadimoghaddam et al. measured NPC with an accommodative target and found hypermetropes to have receded values, as compared to myopes; however, this difference did not remain significant in multiple regression analysis.
Nevertheless, there are insufficient data regarding whether the different methods of NPC evaluation have similar variability in patients with different refractive errors. Understanding this variability may help the clinician to choose and interpret the results of orthoptic examination in a more meaningful manner.
Using Bland–Altman plots and measuring the limits of agreement (LOA) is one of the best methods to compare diagnostic tests with each other. Most of the studies on NPC have not used this statistical tool to study the degree of agreement between the different methods of NPC assessment.
By using Bland–Altman plots, the current study proposed to determine the extent of agreement between three different methods of NPC measurement in patients with different refractive errors.
| Methods|| |
This cross-sectional observational study was done from January 2014 to August 2014 at a tertiary eye care hospital in southern India. Sixty asymptomatic South Indian subjects, ranging in age from 18 to 25 years of age, with emmetropia, or a refractive error (simple myopia or simple hypermetropia [manifest hypermetropia corrected by fogging]) with best-corrected visual acuity 6/6 in each eye, were included by convenience sampling. None of the subjects had symptoms suggestive of convergence insufficiency. The sample size was decided based on the sample size calculated in similar studies by Siderov et al. and Adler et al.
All these patients underwent static and cycloplegic refraction prior to enrollment, a cover test to check for manifest strabismus, and a stereopsis assessment with TNO cards. The break and recovery points of NPC were assessed using the RAF rule, pencil-ruler (PR) method, and a penlight with red-green glasses; the average of three consecutive values was calculated for each method. The RAF rule test was done in a standard manner. The sharp tip of a pencil was used as the target for the PR method. Red-green glasses were worn by the patient, and a pen torch was used as a target in the red-green glass method. All the tests were done on every subject by the same person and over the RAF rule to ensure uniformity of measurement between methods. The point at which the subjects appreciated diplopia of the target was considered the end point. Three readings were taken consecutively for each method and the average was calculated. The tests were performed with full room illumination. All the above tests were performed with refractive correction in place for myopes and hypermetropes.
Patients above 25 years of age, those with anterior or posterior segment abnormalities, those with astigmatism (>0.5 D cyl), anisometropia (>1 D sphere difference between eyes), amblyopia, manifest squint, and those with poor near stereoacuity were excluded.
The study followed the tenets of the Declaration of Helsinki, and approval of the experimental protocol was obtained from the Institutional Ethics Committee. Informed consent was obtained from all subjects.
The mean values of the break and recovery points of the three tests were not found to be distributed normally by Shapiro–Wilk test (P < 0.01) [Supplementary Table 1] and [Supplementary Figure 1]. Hence, they were compared within each of the three refractive error groups by a nonparametric test for repeated measures, namely the Friedman test. Bland–Altman plots were constructed using SPSS (IBM Corp. Released 2011. IBM SPSS Statistics for Windows, Version 20.0. Armonk, NY: IBM Corp.) by plotting the differences between the tests in the Y-axis with the average of the readings in the X-axis. The LOA were calculated using Excel sheet 2007 by calculating the 5th and 95th percentile values of the differences and incorporated in the Bland–Altman plot, which gives a graphical representation of the degree of agreement between the tests. The LOA are a measure of the variability of the tests, with broader limits suggestive of a high variability between two tests.
| Results|| |
The demographic and baseline characters of the subjects are tabulated [Table 1]. There were 20 subjects in each group. There was no significant difference with regard to age or gender distribution between the groups [Table 1]. The mean NPC break and recovery points for the three tests for the three refractive error groups are tabulated [Table 2]. The stereopsis of all the participants was better than 240 arc sec by TNO cards.
|Table 1: Demographic factors and baseline data compared between patients and eyes in the three refractive error groups|
Click here to view
|Table 2: Break and recovery points of near points of convergence in emmetropes, myopes, and hypermetropes as measured by three different methods|
Click here to view
Among emmetropes (RAF: 7.75 ± 2.23 cm; PR: 7.65 ± 1.50; RG: 8.03 ± 1.13 cm) and myopes (RAF: 7.00 ± 1.26 cm; PR: 6.38 ± 0.74; RG: 7.03 ± 1.58 cm), the break points were not significantly different between the different methods. However, among the hypermetropes (RAF: 7.18 ± 1.86 cm; PR: 7.78 ± 1.75 cm; 10.30 ± 1.45 cm), there was a significant difference in the break points yielded by the three different methods.
The recovery points measured by the three methods differed significantly, with receded values consistently noted in the RG test among emmetropes and hypermetropes. However, the PR test gave better recovery values among the myopes, compared to the other tests [Table 2].
[Figure 1], [Figure 2], [Figure 3] give a pictorial representation of the differences in the break points between RAF/RG, RAF/PR, and PR/RG methods, and the relative variability of the same in the three different refractive error groups. The RG test appeared to yield consistently more receded values than did the RAF/PR tests among the hypermetropes. The PR test was found to have lesser receded values compared to the RAF test among myopes than in other groups. The LOA for the entire subset of observations were also plotted to show the values within which 95% of the differences fell.
|Figure 1: A Bland–Altman plot showing the difference between the royal air force/pencil-ruler break point measurements over the average of the break point of the two measurements. The large dotted lines indicate the upper (95%) and lower (5%) limits of agreement for royal air force and pencil-ruler test for all the subjects together. The small dotted line indicates the median of the differences. Most myopes were found to be above the median, suggesting that pencil-ruler yields better values compared to royal air force in myopes|
Click here to view
|Figure 2: A Bland–Altman plot showing the difference between the pencilruler/red-green glass break point measurements over the average of the break point of the two measurements. The large dotted lines indicate the upper (95%) and lower (5%) limits of agreement for royal air force and pencil-ruler test for all the subjects together. The small dotted line indicates the median of the differences. All the hypermetropes were at/below the median, suggesting that hypermetropes consistently yielded more receded values with the red-green glasses test than with the royal air force and pencil-ruler tests, compared to the values in myopes and emmetropes|
Click here to view
|Figure 3: A Bland–Altman plot showing the difference between the royal air force/red-green glass break point measurements over the average of the break point of the two measurements. The large dotted lines indicate the upper (95%) and lower (5%) limits of agreement for royal air force and pencil-ruler test for all the subjects together. The small dotted line indicates the median of the differences. All the hypermetropes were at/below the median, suggesting that hypermetropes consistently had a receded value in the red-green glasses test than in the royal air force test, compared to the values in myopes and emmetropes|
Click here to view
[Table 3] shows the LOA derived from the differences of the break points measured by the three methods for the three groups and all the study subjects together. LOA have to be interpreted based on the clinical scenario showing the extent of agreement between the tests. Considering all the subjects together, a difference of approximately 5 cm was found to exist between the different tests, when compared with each other.
|Table 3: Limits Of Agreement calculated for differences in the break points measured by different methods in the three different refractive error groups and in all the study subjects together|
Click here to view
Considering the individual refractive error subgroups, the LOA, although wide, appeared to vary symmetrically (both positive and negative differences) among the emmetropes. Among the hypermetropes, the LOA were consistently negative when the RG test was considered, suggesting that the RG test, compared to other tests, calculated receded values, especially in hypermetropes. However, among the myopes, except between RAF and PR test, the LOA appeared to be symmetrically distributed, although wide. Comparing the RAF/PR test, the LOA (‒0.1 cm to + 2.25 cm) were predominantly positive, suggesting that the myopes tended to overperform in the PR test, compared to others.
| Discussion|| |
Adler et al. calculated the NPC using different methods among emmetropic children, while Siderov et al. and Scheimann et al. calculated it including patients with refractive errors wearing habitual correction. In spite of having normal visual acuity wearing a spectacle prescription, the orthoptic status of a subject with refractive error may not be similar to that of an emmetrope. This could be due to various spectacle-related issues, such as prismatic effects of the glasses, centration of the glasses, and alteration in image size caused by the spectacles. This is evident from the change observed in orthoptic parameters, compared to the preoperative state, following laser corrective surgery in patients with refractive errors.
Thus, the NPC tests, owing to the differential accommodative demands, may not yield concordant results in patients with different refractive errors when tested with their habitual correction. Although it may be considered an artifact of spectacle correction, it is with their habitual correction that patients study and do near activities. Moreover, most orthoptists measure the orthoptic parameters in patients using their habitual correction. Hence, the variability of these tests among patients with refractive errors has to be considered.
Among the three methods studied, PR test can be easily done with a pencil and a ruler, unlike RG test, which requires anaglyph glasses, and RAF test, which requires RAF ruler. In this study, to standardize measurements, all the tests were done over RAF ruler. Schieman et al. and Pang et al. found break and recovery points measured using penlight with red-green glasses (PLRG) to be most accurate in differentiating symptomatic from asymptomatic patients. In these studies, among asymptomatic subjects, accommodative rule, penlight, and PLRG were not found to vary significantly. However, among the symptomatic ones, the PLRG test yielded remote values. In our study, even among asymptomatic subjects, the RG test yielded significantly remote values among hypermetropes and significantly receded recovery points among emmetropes and hypermetropes. However, this variability was not found among the myopes.
Siderov et al. concluded that although there were differences in the NPC values obtained by different targets, the difference was not clinically significant. Although we found similar results among emmetropes, significant variations could be seen among hypermetropes. However, PLRG was not included as a target in their study.
This variation also appeared to be present on the Bland–Altman plots, where the RG test was compared with other tests, that is, PR and RAF tests [Figure 2] and [Figure 3]; here, the majority of the hypermetropes had a “lesser than median” difference, compared to myopes and emmetropes, who were distributed symmetrically around the median. This was evident on the 95% LOA calculated among hypermetropes for RAF/RG (upper: ‒1.28 cm, lower: ‒5.05 cm) and PR/RG (upper: ‒4.05 cm, lower: ‒0.88 cm).
Possible reasons why RG tests yielded receded values among hypermetropes, and not to the same extent among emmetropes and myopes, could be the dissociativeness and the nonaccommodative nature of the test, and the probable prismatic effect of glasses in convergence.
Among myopes, the PR test yielded better break (marginal significance) and recovery points (significant difference), compared to the RG and RAF tests. When comparing the RAF/PR test, myopes tended to fall in the more positive side above the median consistently compared to emmetropes and hypermetropes [Figure 1]. The 95% LOA of the same was also more positive [lower: ‒0.1; upper: +2.25 cm].
The sharp tip of the pencil, being a three-dimensional object, can elicit a better convergence response. This phenomenon was markedly observed in the myopes consistently, compared to the other groups. This was possibly because of the base-out prism effect of myopic glasses when eyes converge, thereby seeing through the nasal part of the lenses rather than the center. The possible effects of glasses on measurement of NPC have also been stated by Adler et al.
That the values obtained using different targets are not in agreement with each other is evident from the results of previous studies [Table 4]; however, the results of the current study suggest that this variability is not uniform. The RG test showed a higher degree of disagreement among hypermetropes while the PR test showed a higher degree of disagreement among myopes.
|Table 4: Break and recovery points (mean±standard deviation) with different targets compared with other studies|
Click here to view
The limitations of this study include the small sample sizes in each subgroup, the use of nonparametric methods of measurement, and the nonrandomization of the order of the tests. Notwithstanding these, the use of RAF rule for all the targets may not reflect the real-life scenario where targets are moved in free space.
Further studies using contact lenses, rather than spectacles, may have to be performed to study the influence of refractive errors/spectacle correction on the variability of NPC using different methods.
| Conclusion|| |
In the current study, the NPC values obtained by the three methods studied were not in agreement with each other, although this variability was less among emmetropes. In myopes, the PR test gave better values, and in hypermetropes, the RG test yielded more remote values.
Financial support and sponsorship
Conflicts of interest
There are no conflicts of interest.
| References|| |
Hussaindeen JR, Rakshit A, Singh NK, George R, Swaminathan M, Kapur S, et al.
Prevalence of non-strabismic anomalies of binocular vision in Tamil Nadu: Report 2 of BAND study. Clin Exp Optom 2017;100:642-8.
Pang Y, Gabriel H, Frantz KA, Saeed F. A prospective study of different test targets for the near point of convergence. Ophthalmic Physiol Opt 2010;30:298-303.
Siderov J, Chiu SC, Waugh SJ. Differences in the nearpoint of convergence with target type. Ophthalmic Physiol Opt 2001;21:356-60.
Adler PM, Cregg M, Viollier AJ, Margaret Woodhouse J. Influence of target type and RAF rule on the measurement of near point of convergence. Ophthalmic Physiol Opt 2007;27:22-30.
Scheiman M, Gallaway M, Frantz KA, Peters RJ, Hatch S, Cuff M, et al.
Nearpoint of convergence: Test procedure, target selection, and normative data. Optom Vis Sci 2003;80:214-25.
Ostadimoghaddam H, Hashemi H, Nabovati P, Yekta A, Khabazkhoob M. The distribution of near point of convergence and its association with age, gender and refractive error: A population-based study. Clin Exp Optom 2017;100:255-9.
McAlinden C, Khadka J, Pesudovs K. Statistical methods for conducting agreement (comparison of clinical tests) and precision (repeatability or reproducibility) studies in optometry and ophthalmology. Ophthalmic Physiol Opt 2011;31:330-8.
[Figure 1], [Figure 2], [Figure 3]
[Table 1], [Table 2], [Table 3], [Table 4]