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Ophthalmic Statistics Note 11: logistic regression
1. John Stephenson1,
2. Catey Bunce2,3,
3. Caroline J Doré4,
4. Nick Freemantle5
5. on behalf of the Ophthalmic Statistics Group
1. 1School of Human and Health Sciences, University of Huddersfield, Queensgate, Huddersfield, UK
2. 2NHR Biomedical Research Centre at Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology, London, UK
3. 3Reader in Medical Statistics, Department of Primary Care & Public Health Sciences, King's College London, 4th Floor, Addison House, Guy's Campus, London, SE1 1UL
4. 4Comprehensive Clinical Trials Unit, University College London, London, UK
5. 5Medical School, University College London, London, UK
1. Correspondence to Dr John Stephenson, School of Human and Health Sciences, University of Huddersfield, Queensgate, Huddersfield GB-HD1 3DH, UK; J.Stephenson{at}hud.ac.uk

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## Logistic regression

Previous notes in this series have been concerned with the common situation in ophthalmic and other clinical fields of describing relationships between one or more ‘predictors’ (explanatory variables) and, usually, one outcome measure (response variable). A classic method used in deriving relationships between outcomes and predictors is linear regression analysis. Linear regression is a member of a family of techniques known as general linear models, which also include analysis of variance and analysis of covariance; the latter of which was covered in a previous Ophthalmic Statistics Note.1

A key feature of all these models is that the outcome measure—for example, postoperative refractive prediction error or intraocular pressure—is continuous. While other notes in the series2 warn of the dangers of unnecessary dichotomisation of variables, sometimes outcomes naturally fall into two categories.

• Example 1: A study was conducted on 137 patients to identify risk factors for intraoperative retinal breaks caused by induction of a posterior hyaloid face separation during 23-gauge pars plana vitrectomy.3 Putative risk factors for breaks were age at surgery, axial length of the operated eye and diagnosis, but the outcome variable here was whether or not the patient suffered a retinal break—a yes/no or dichotomous outcome.

• Example 2: A study was conducted on 58 patients undergoing surgery for idiopathic macular hole identifying whether or not a patient develops an outer foveal defect (OFD).4 Putative risk factors were age at surgery, characteristics of the macular hole such as base diameter and whether or not there was ocular comorbidity, but the outcome was whether or not the patient developed an OFD in their operated eye—a yes/no or dichotomous outcome.

In both examples, our objective is to examine …

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## Footnotes

• Contributors JS drafted the paper. CB, CJD and NF critically reviewed and revised the paper. JS and CB redrafted the paper after review. JS, CB and CJD critically reviewed the redraft.

• Funding CB is partly funded by the National Institute of Health Research (NIHR) Biomedical Research Centre at Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology.

• Competing interests None declared.

• Provenance and peer review Not commissioned; externally peer reviewed.