Vector analysis of clinical refractive agreement between autorefraction, retinoscopy, and subjective refraction in non-cycloplegic patients
Keywords:
Ocular refraction, Autorefractometry, Static retinoscopy, Subjective refraction, Thibos vector notation, Refractive concordanceAbstract
Background: Refractive errors are among the leading causes of visual impairment worldwide. In clinical practice, refraction can be determined by objective methods such as autorefraction and static retinoscopy, or by subjective refraction, which is considered the reference standard. The vector notation proposed by Thibos and Horner (M, J0, and J45) provides a more robust comparison between these techniques. Objective: To analyze the clinical refractive agreement among autorefraction, retinoscopy, and subjective refraction in non-cycloplegic patients using vector notation. Material and methods: A cross-sectional study was conducted in 254 patients examined at the Centro Regional de Salud Valencia, University of El Salvador. Right-eye refraction data were obtained using the three methods mentioned. Refractive errors were transformed into vector notation (M, J0, and J45). Variables were expressed as medians and interquartile ranges (IQR). The Kruskal–Wallis test was used to compare methods, the intraclass correlation coefficient (ICC) was used to assess agreement, and Spearman’s correlation was used to determine relationships between vectors. Bland–Altman plots were used to explore systematic biases. Results: The spherical equivalent (M) showed similar medians among methods (p = 0.861) and excellent agreement (ICC = 0.958). The astigmatic vectors (J0, J45) showed good agreement (ICC ≈ 0.88) and greater dispersion. All correlations were statistically significant (p < 0.001). Conclusion: The three methods yielded comparable results, with excellent agreement for M and good agreement for J0 and J45. Autorefraction proved to be a reliable tool for refractive screening in high-demand clinical settings, although subjective refraction remains recommended in cases of significant astigmatism or discrepancies between methods.
Downloads
References
1. World Health Organization. World report on vision. Geneva: WHO Press; 2019 [citado 2025 nov 10]. Disponible en: https://www.who.int/publications
2. Leasher JL, Lansingh VC, Flaxman SR, Jonas JB, Keeffe J, Naidoo K, et al. Prevalence and causes of vision loss in Latin America and the Caribbean: 1990–2010. Br J Ophthalmol. 2014;98(5):619–28. doi:10.1136/bjophthalmol-2013-304013
3. Jorge J, Queirós A, González-Méijome JM, Fernandes P, Almeida JB, Parafita MA. The influence of cycloplegia on objective refraction. Ophthalmic Physiol Opt. 2008;28(5):412–9. doi:10.1111/j.1475-1313.2008.00587.x
4. Sheppard AL, Davies LN. Clinical evaluation of the Shin-Nippon NVision-K 5001 autorefractor. Ophthalmic Physiol Opt. 2010;30(2):143–51. doi:10.1111/j.1475-1313.2009.00700.x
5. Kinge B, Midelfart A, Jacobsen G, Rystad J. The relationship between visual acuity, refraction, and instrument measurements. Acta Ophthalmol Scand. 1999;77(3):302–5. doi:10.1034/j.1600-0420.1999.770314.x
6. Elliott DB. Clinical Procedures in Primary Eye Care. 5th ed. Edinburgh: Elsevier; 2021.
7. Rosenfield M, Chiu NN, Fogt N. Borish’s Clinical Refraction. 3rd ed. Philadelphia: Elsevier; 2022.
8. Thibos LN, Wheeler W, Horner D. Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error. Optom Vis Sci. 1997;74(6):367–75. doi:10.1097/00006324-199706000-00019
9. Harris WF. Representation of dioptric power in Euclidean 3-space. Ophthalmic Physiol Opt. 1991;11(2):130–6. doi:10.1111/j.1475-1313.1991.tb00212.x
10. Zhou Y, Wang J, Zhang X, Yu X, Jin J, et al. Vector analysis of high astigmatism (≥2.0 D) correction in refractive surgery. BMC Ophthalmol. 2022; 22:384. doi:10.1186/s12886-022-02640-y
11. Chen AH, O’Leary DJ. A comparison of autorefraction and subjective refraction in young myopes. Am J Ophthalmol. 2006;142(1):157–9. doi:10.1016/j.ajo.2006.01.084
12. Oral Y, Günaydin N, Ozgur O, Arsan AK, Oskan S. A comparison of different autorefractors with retinoscopy in children. J Pediatr Ophthalmol Strabismus. 2012;49(6):370–7. doi:10.3928/01913913-20120821-04
13. Guo R, Shi L, Xu K, Hong D. Clinical evaluation of autorefraction and subjective refraction with and without cycloplegia in Chinese school-aged children: a cross-sectional study. Transl Pediatr. 2022;11(6):933–46. doi:10.21037/tp-22-226
14. Mallen EA, Wolffsohn JS, Gilmartin B, Tsujimura S. Clinical evaluation of the Shin-Nippon NVision-K 5001 autorefractor in adults. Ophthalmic Physiol Opt. 2001;21(2):101–7. doi:10.1046/j.1475-1313.2001.00552.x
15. Tan HK, Ang JJ. Evaluation of the correlation between retinoscopy, autorefractometry, and subjective refraction in adults. Ophthalmic Physiol Opt. 2015;35(6):707–12. doi:10.1111/opo.12236
16. Hernández Sampieri R, Mendoza Torres C. Metodología de la investigación: las rutas cuantitativa, cualitativa y mixta. 7ª ed. Ciudad de México: McGraw-Hill; 2022.
17. Scheaffer RL, Mendenhall W, Ott RL. Elementary Survey Sampling. 7th ed. Boston: Cengage Learning; 2011.
18. Shapiro SS, Wilk MB. An analysis of variance test for normality (complete samples). Biometrika. 1965;52(3–4):591–611. doi:10.1093/biomet/52.3-4.591
19. Kruskal WH, Wallis WA. Use of ranks in one-criterion variance analysis. J Am Stat Assoc. 1952;47(260):583–621. doi:10.1080/01621459.1952.10483441
20. Spearman C. General intelligence, objectively determined and measured. Am J Psychol. 1904;15(2):201–93. doi:10.2307/1412107
21. Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Hillsdale (NJ): Lawrence Erlbaum; 1988.
22. Shrout PE, Fleiss JL. Intraclass correlations: uses in assessing rater reliability. Psychol Bull. 1979;86(2):420–8. doi:10.1037/0033-2909.86.2.420
23. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;1(8476):307–10. doi:10.1016/S0140-6736(86)90837-8
24. Giavarina D. Understanding Bland–Altman analysis. Biochem Med (Zagreb). 2015;25(2):141–51. doi:10.11613/BM.2015.015
25. Krouwer JS. Why Bland–Altman plots should use X-axis means and not differences vs. a reference method. Clin Chem. 2008;54(5):1020–2. doi:10.1373/clinchem.2007.100909
26. The jamovi project. Jamovi (Version 2.5). 2024 [citado 2025 nov 10]. Disponible en: https://www.jamovi.org
27. McKinney W. Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython. 3rd ed. Sebastopol (CA): O’Reilly Media; 2022.
28. Virtanen P, Gommers R, Oliphant TE, Haberland M, Reddy T, Cournapeau D, et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat Methods. 2020;17(3):261–72. doi:10.1038/s41592-019-0686-2
29. Vallat R. Pingouin: statistics in Python. J Open Source Softw. 2018;3(31):1026. doi:10.21105/joss.01026
30. Hunter JD. Matplotlib: a 2D graphics environment. Comput Sci Eng. 2007;9(3):90–5. doi:10.1109/MCSE.2007.55
31. Atchison DA, Schmid KL, Edwards KP. The effect of accommodation on autorefraction: a review. Ophthalmic Physiol Opt. 2018;38(5):407–20. doi:10.1111/opo.12561
32. Atchison DA, Thibos LN. Optical models of the human eye. Clin Exp Optom. 2016;99(2):99–106. doi:10.1111/cxo.12308
33. Musa M, et al. The importance of retinoscopy in modern optometric practice: a narrative review. Cureus. 2024;16(2):e54076. doi:10.7759/cureus.54076
34. Şimşek M, Aksoy B, Kural G, Eren S, Akman M. Comparison of the results of four different autorefractometers with retinoscopy in children. Indian J Ophthalmol. 2022;70(8):2958–64. doi:10.4103/ijo.IJO_1534_22
35. Ramírez D, Arévalo JF. Prevalence and correction of refractive errors in Latin America: a regional overview. Clin Ophthalmol. 2020;14:3095–104. doi:10.2147/OPTH.S263902
36. World Medical Association. Declaration of Helsinki: ethical principles for medical research involving human subjects. JAMA. 2013;310(20):2191–4. doi:10.1001/jama.2013.281053
37. World Health Organization. Ethical standards for research in health care and public health. Geneva: WHO Press; 2018 [citado 2025 nov 10]. Disponible en: https://www.who.int/publications/i/item/9789241550086
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Salud Integral

This work is licensed under a Creative Commons Attribution 4.0 International License.
