Circular statistics for analyzing changes in retinal nerve fiber layer
To evaluate the use of circular statistics to analyze retinal nerve fibre layer (RNFL) thickness in eyes with and without a prior history of optic neuritis (ON). Single-centre consecutive study. Twenty-two multiple sclerosis patients and 20 healthy control subjects. Data on 28 eyes with a history of...
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| Published in: | Canadian journal of ophthalmology Vol. 59; no. 6; pp. e737 - e741 |
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| Language: | English |
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01.12.2024
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| Abstract | To evaluate the use of circular statistics to analyze retinal nerve fibre layer (RNFL) thickness in eyes with and without a prior history of optic neuritis (ON).
Single-centre consecutive study.
Twenty-two multiple sclerosis patients and 20 healthy control subjects.
Data on 28 eyes with a history of ON of 22 multiple sclerosis patients and 40 eyes of 20 healthy control subjects collected in 2010 and 2015. RNFL thickness was measured separately in 12 sectors around the optic nerve head. We used circular statistics to calculate the mean weighted vector of RNFL thickness for each sector and eye in 2 measurements made 5 years apart (2010 and 2015). Comparisons of weighted mean vectors between groups were made using a paired Mardia–Watson–Wheeler test.
The directions of the mean weighted vectors for ON eyes were 45.8º in 2010 and 56.0º in 2015, whereas in control eyes the directions were 319.4º in 2010 and 188.9º in 2015. No significant differences were found between 2010 and 2015 in any of the 2 groups. However, significant differences were found between ON and control eyes in 2010 and 2015.
This paper provides an example of how to use circular statistics in cases of directional data in ophthalmology and demonstrates that circular statistics are a suitable tool for this purpose.
Évaluer l'intérêt des statistiques circulaires dans l'analyse de l’épaisseur de la couche de fibres nerveuses rétiniennes (RNFL, pour retinal nerve fiber layer) en présence ou en l'absence d'antécédents de névrite optique (NO).
Étude sur des patients consécutifs réalisée dans un établissement unique.
Vingt-deux patients atteints de sclérose en plaques et 20 sujets témoins en bonne santé.
Les données portant sur 28 yeux ayant des antécédents de NO (22 patients atteints de sclérose en plaques) et sur 40 yeux de 20 sujets témoins en bonne santé ont été recueillies en 2010 et en 2015. On a mesuré l’épaisseur de la RNFL dans 12 secteurs distincts autour de la papille. Les statistiques circulaires ont servi à calculer le vecteur moyen pondéré de l’épaisseur de la RNFL dans chaque secteur et dans chaque œil lors de 2 mesures réalisées à 5 années d'intervalle (2010 et 2015). C'est le test de Mardia-Watson-Wheeler pour mesures appariées qui a été utilisé pour comparer les vecteurs moyens pondérés entre les groupes.
Les directions des vecteurs moyens pondérés dans les yeux du groupe NO se chiffraient à 45,8° en 2010 et à 56,0° en 2015, tandis que les directions dans les yeux témoins étaient de 319,4° en 2010 et de 188,9° en 2015. Il n'y avait pas de différence significative entre les valeurs de 2010 et de 2015 dans ni l'un ni l'autre des groupes. Cela dit, des différences significatives ont été observées entre les yeux du groupe NO et ceux du groupe témoin, tant en 2010 qu'en 2015.
Notre article peut servir d'exemple de la façon dont les statistiques circulaires peuvent être utilisées pour traiter des données directionnelles en ophtalmologie et démontre que les statistiques circulaires conviennent à cette fin. |
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| AbstractList | To evaluate the use of circular statistics to analyze retinal nerve fibre layer (RNFL) thickness in eyes with and without a prior history of optic neuritis (ON).OBJECTIVETo evaluate the use of circular statistics to analyze retinal nerve fibre layer (RNFL) thickness in eyes with and without a prior history of optic neuritis (ON).Single-centre consecutive study.DESIGNSingle-centre consecutive study.Twenty-two multiple sclerosis patients and 20 healthy control subjects.PARTICIPANTSTwenty-two multiple sclerosis patients and 20 healthy control subjects.Data on 28 eyes with a history of ON of 22 multiple sclerosis patients and 40 eyes of 20 healthy control subjects collected in 2010 and 2015. RNFL thickness was measured separately in 12 sectors around the optic nerve head. We used circular statistics to calculate the mean weighted vector of RNFL thickness for each sector and eye in 2 measurements made 5 years apart (2010 and 2015). Comparisons of weighted mean vectors between groups were made using a paired Mardia-Watson-Wheeler test.METHODSData on 28 eyes with a history of ON of 22 multiple sclerosis patients and 40 eyes of 20 healthy control subjects collected in 2010 and 2015. RNFL thickness was measured separately in 12 sectors around the optic nerve head. We used circular statistics to calculate the mean weighted vector of RNFL thickness for each sector and eye in 2 measurements made 5 years apart (2010 and 2015). Comparisons of weighted mean vectors between groups were made using a paired Mardia-Watson-Wheeler test.The directions of the mean weighted vectors for ON eyes were 45.8º in 2010 and 56.0º in 2015, whereas in control eyes the directions were 319.4º in 2010 and 188.9º in 2015. No significant differences were found between 2010 and 2015 in any of the 2 groups. However, significant differences were found between ON and control eyes in 2010 and 2015.RESULTSThe directions of the mean weighted vectors for ON eyes were 45.8º in 2010 and 56.0º in 2015, whereas in control eyes the directions were 319.4º in 2010 and 188.9º in 2015. No significant differences were found between 2010 and 2015 in any of the 2 groups. However, significant differences were found between ON and control eyes in 2010 and 2015.This paper provides an example of how to use circular statistics in cases of directional data in ophthalmology and demonstrates that circular statistics are a suitable tool for this purpose.CONCLUSIONSThis paper provides an example of how to use circular statistics in cases of directional data in ophthalmology and demonstrates that circular statistics are a suitable tool for this purpose. To evaluate the use of circular statistics to analyze retinal nerve fibre layer (RNFL) thickness in eyes with and without a prior history of optic neuritis (ON). Single-centre consecutive study. Twenty-two multiple sclerosis patients and 20 healthy control subjects. Data on 28 eyes with a history of ON of 22 multiple sclerosis patients and 40 eyes of 20 healthy control subjects collected in 2010 and 2015. RNFL thickness was measured separately in 12 sectors around the optic nerve head. We used circular statistics to calculate the mean weighted vector of RNFL thickness for each sector and eye in 2 measurements made 5 years apart (2010 and 2015). Comparisons of weighted mean vectors between groups were made using a paired Mardia–Watson–Wheeler test. The directions of the mean weighted vectors for ON eyes were 45.8º in 2010 and 56.0º in 2015, whereas in control eyes the directions were 319.4º in 2010 and 188.9º in 2015. No significant differences were found between 2010 and 2015 in any of the 2 groups. However, significant differences were found between ON and control eyes in 2010 and 2015. This paper provides an example of how to use circular statistics in cases of directional data in ophthalmology and demonstrates that circular statistics are a suitable tool for this purpose. Évaluer l'intérêt des statistiques circulaires dans l'analyse de l’épaisseur de la couche de fibres nerveuses rétiniennes (RNFL, pour retinal nerve fiber layer) en présence ou en l'absence d'antécédents de névrite optique (NO). Étude sur des patients consécutifs réalisée dans un établissement unique. Vingt-deux patients atteints de sclérose en plaques et 20 sujets témoins en bonne santé. Les données portant sur 28 yeux ayant des antécédents de NO (22 patients atteints de sclérose en plaques) et sur 40 yeux de 20 sujets témoins en bonne santé ont été recueillies en 2010 et en 2015. On a mesuré l’épaisseur de la RNFL dans 12 secteurs distincts autour de la papille. Les statistiques circulaires ont servi à calculer le vecteur moyen pondéré de l’épaisseur de la RNFL dans chaque secteur et dans chaque œil lors de 2 mesures réalisées à 5 années d'intervalle (2010 et 2015). C'est le test de Mardia-Watson-Wheeler pour mesures appariées qui a été utilisé pour comparer les vecteurs moyens pondérés entre les groupes. Les directions des vecteurs moyens pondérés dans les yeux du groupe NO se chiffraient à 45,8° en 2010 et à 56,0° en 2015, tandis que les directions dans les yeux témoins étaient de 319,4° en 2010 et de 188,9° en 2015. Il n'y avait pas de différence significative entre les valeurs de 2010 et de 2015 dans ni l'un ni l'autre des groupes. Cela dit, des différences significatives ont été observées entre les yeux du groupe NO et ceux du groupe témoin, tant en 2010 qu'en 2015. Notre article peut servir d'exemple de la façon dont les statistiques circulaires peuvent être utilisées pour traiter des données directionnelles en ophtalmologie et démontre que les statistiques circulaires conviennent à cette fin. To evaluate the use of circular statistics to analyze retinal nerve fibre layer (RNFL) thickness in eyes with and without a prior history of optic neuritis (ON). Single-centre consecutive study. Twenty-two multiple sclerosis patients and 20 healthy control subjects. Data on 28 eyes with a history of ON of 22 multiple sclerosis patients and 40 eyes of 20 healthy control subjects collected in 2010 and 2015. RNFL thickness was measured separately in 12 sectors around the optic nerve head. We used circular statistics to calculate the mean weighted vector of RNFL thickness for each sector and eye in 2 measurements made 5 years apart (2010 and 2015). Comparisons of weighted mean vectors between groups were made using a paired Mardia-Watson-Wheeler test. The directions of the mean weighted vectors for ON eyes were 45.8º in 2010 and 56.0º in 2015, whereas in control eyes the directions were 319.4º in 2010 and 188.9º in 2015. No significant differences were found between 2010 and 2015 in any of the 2 groups. However, significant differences were found between ON and control eyes in 2010 and 2015. This paper provides an example of how to use circular statistics in cases of directional data in ophthalmology and demonstrates that circular statistics are a suitable tool for this purpose. |
| Author | Gonzalez, Francisco Arias-Gomez, Manuel Abalo-Lojo, Jose M. |
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| Cites_doi | 10.1177/1352458508091367 10.1016/j.ophtha.2005.10.040 10.1167/iovs.15-19047 10.1111/j.1460-9568.2007.05507.x 10.1016/j.msard.2017.11.017 10.1098/rspa.1953.0064 10.1167/iovs.12-10362 10.1212/01.wnl.0000260612.51849.ed |
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| References | Batschelet (bib0003) 1981 Fisher (bib0002) 1953; 217 Herrero, Garcia-Martin, Almarcegui (bib0004) 2012; 53 Fisher, Jacobs, Markowitz (bib0006) 2006; 113 Sepulcre, Murie-Fernandez, Salinas-Alaman (bib0008) 2007; 68 Gonzalez, Romero, Castro, Bermudez, Perez (bib0001) 2007; 55 Abalo-Lojo, Treus, Arias (bib0005) 2018; 19 Costello, Hodge, Pan (bib0007) 2008; 14 Graham, You, Yiannikas (bib0009) 2016; 57 Fisher (10.1016/j.jcjo.2024.03.002_bib0002) 1953; 217 Herrero (10.1016/j.jcjo.2024.03.002_bib0004) 2012; 53 Costello (10.1016/j.jcjo.2024.03.002_bib0007) 2008; 14 Graham (10.1016/j.jcjo.2024.03.002_bib0009) 2016; 57 Batschelet (10.1016/j.jcjo.2024.03.002_bib0003) 1981 Gonzalez (10.1016/j.jcjo.2024.03.002_bib0001) 2007; 55 Fisher (10.1016/j.jcjo.2024.03.002_bib0006) 2006; 113 Abalo-Lojo (10.1016/j.jcjo.2024.03.002_bib0005) 2018; 19 Sepulcre (10.1016/j.jcjo.2024.03.002_bib0008) 2007; 68 |
| References_xml | – volume: 55 start-page: 2536 year: 2007 end-page: 2546 ident: bib0001 article-title: Sensitivity to direction and orientation of random dot stereobars in the monkey visual cortex publication-title: Eur J Neurosci – volume: 19 start-page: 124 year: 2018 end-page: 128 ident: bib0005 article-title: Longitudinal study of retinal nerve fiber layer thickness changes in a multiple sclerosis patient cohort: a long term 5 year follow-up publication-title: Mult Scler Relat Disord – volume: 68 start-page: 1488 year: 2007 end-page: 1494 ident: bib0008 article-title: Diagnostic accuracy of retinal abnormalities in predicting disease activity in MS publication-title: Neurology – volume: 57 start-page: 2311 year: 2016 end-page: 2317 ident: bib0009 article-title: Progressive loss of retinal ganglion cells and axons in non–optic neuritis eyes in multiple sclerosis: a longitudinal optical coherence tomography study publication-title: Invest Ophthalmol Vis Sci – volume: 14 start-page: 893 year: 2008 end-page: 905 ident: bib0007 article-title: Tracking retinal nerve fiber layer loss after optic neuritis: a prospective study using optical coherence tomography publication-title: Mult Scler – volume: 113 start-page: 324 year: 2006 end-page: 332 ident: bib0006 article-title: Relation of visual function to retinal nerve fiber layer thickness in multiple sclerosis publication-title: Ophthalmology – volume: 217 start-page: 295 year: 1953 end-page: 305 ident: bib0002 article-title: Dispersion on a sphere publication-title: Proc R Soc Lond A – year: 1981 ident: bib0003 article-title: Circular statistics in biology – volume: 53 start-page: 8344 year: 2012 end-page: 8349 ident: bib0004 article-title: Progressive degeneration of the retinal nerve fiber layer in patients with multiple sclerosis publication-title: Invest Ophthalmol Vis Sci – year: 1981 ident: 10.1016/j.jcjo.2024.03.002_bib0003 – volume: 14 start-page: 893 year: 2008 ident: 10.1016/j.jcjo.2024.03.002_bib0007 article-title: Tracking retinal nerve fiber layer loss after optic neuritis: a prospective study using optical coherence tomography publication-title: Mult Scler doi: 10.1177/1352458508091367 – volume: 113 start-page: 324 year: 2006 ident: 10.1016/j.jcjo.2024.03.002_bib0006 article-title: Relation of visual function to retinal nerve fiber layer thickness in multiple sclerosis publication-title: Ophthalmology doi: 10.1016/j.ophtha.2005.10.040 – volume: 57 start-page: 2311 year: 2016 ident: 10.1016/j.jcjo.2024.03.002_bib0009 article-title: Progressive loss of retinal ganglion cells and axons in non–optic neuritis eyes in multiple sclerosis: a longitudinal optical coherence tomography study publication-title: Invest Ophthalmol Vis Sci doi: 10.1167/iovs.15-19047 – volume: 55 start-page: 2536 year: 2007 ident: 10.1016/j.jcjo.2024.03.002_bib0001 article-title: Sensitivity to direction and orientation of random dot stereobars in the monkey visual cortex publication-title: Eur J Neurosci doi: 10.1111/j.1460-9568.2007.05507.x – volume: 19 start-page: 124 year: 2018 ident: 10.1016/j.jcjo.2024.03.002_bib0005 article-title: Longitudinal study of retinal nerve fiber layer thickness changes in a multiple sclerosis patient cohort: a long term 5 year follow-up publication-title: Mult Scler Relat Disord doi: 10.1016/j.msard.2017.11.017 – volume: 217 start-page: 295 year: 1953 ident: 10.1016/j.jcjo.2024.03.002_bib0002 article-title: Dispersion on a sphere publication-title: Proc R Soc Lond A doi: 10.1098/rspa.1953.0064 – volume: 53 start-page: 8344 year: 2012 ident: 10.1016/j.jcjo.2024.03.002_bib0004 article-title: Progressive degeneration of the retinal nerve fiber layer in patients with multiple sclerosis publication-title: Invest Ophthalmol Vis Sci doi: 10.1167/iovs.12-10362 – volume: 68 start-page: 1488 year: 2007 ident: 10.1016/j.jcjo.2024.03.002_bib0008 article-title: Diagnostic accuracy of retinal abnormalities in predicting disease activity in MS publication-title: Neurology doi: 10.1212/01.wnl.0000260612.51849.ed |
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| SubjectTerms | Adult Female Humans Male Middle Aged Multiple Sclerosis - diagnosis Nerve Fibers - pathology Optic Disk - pathology Optic Neuritis - diagnosis Retinal Ganglion Cells - pathology Retrospective Studies Tomography, Optical Coherence - methods |
| Title | Circular statistics for analyzing changes in retinal nerve fiber layer |
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