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Introduction on common statisticalmethods in clinical ophthalmologyGabriela Czanner PhD CstatDepartment of BiostatisticsDepartment of Eye and Vision ScienceEmail: [email protected] May 2012MERSEY POSTGRADUATE TRAINING PROGRAMMEWorkshop Series: Basic Statistics for Eye Researchers and Clinicians

Outline Why statistics? Main statistical principles: variables, sample andinference Summary of most common statistical methods inclinical ophthalmology Department of Biostatistics at U of Liverpool. Whatdo we do? References

Why is statistics needed? Statistics needed for objective evaluationof what is observed in clinical research What the clinical data sayHow certain we are of the messageHow to assure data qualityCost effectiveness of further studiesResearch questionDesign of studyCollecting dataData analysis Statistics as a communication tool Present findings convincingly Understand and evaluate the findings ofothersReportGeneral steps in aresearch project

Fundamental statistical concepts:VariablesWhat we measure on subjects?Variable It is something whose value can vary. E.g.age, gender, visual acuity, degree to whichlaser scars are visible on a scan.Data are values you get when you measure avariable. E.g. Age 0.2, 0.5, 1.1, 1.2, 1.2, 1.3, 1.3, 1.4, 1.4,2.3, 3.1, 3.3, 4.1, 4.6, 5.1,5.5, 5.6, 5.9, 6.1, 7.1, 7.3,8.6, 8.7, 15.5, 17.7, 22.0, 33.2, 35.1 years Genger: Male and Female Visibility of laser scars on a scan: Impossible, Poor,Good, Very Good. Distribution is a “picture or map of data”

Types of variables i.e. types of dataE.g.Male/FemaleVisibility of scarPoor/Good/Very GoodNumber of scarsin a retinaAge

Fundamental statistical concepts:Sampling and randomizationHow to choose subjects for investigation?In effectiveness studies how we allocatetreatments to subjects?Idea We choose a sample of objects (patients or eyes) andwe measure them to obtain dataCommon study designs Observational studies vs. randomized controlled trialsProspective vs. retrospectiveMatched case-controls design vs. cohort studiesMain factors for selection of study design Research question e.g. prevalence of disease,effectiveness of a treatment, factors related to AMDResources, sources of bias, clinical importanceThe objects who are studiedact as a proxy for the totalpopulation of interest.NB. In ophthalmology theobject can be: eyes or patients.

Common Study DesignsSource: from the workshop slides of Biostatistics department “Statistical issues inthe design and analysis of research projects”Prospective data collected prospectively, retrospective data are recolled

Fundamental statistical concepts:InferenceWhat the data say? How certain we are of the message?Idea We use data collected on the sample to makestatistical inference about the population of interest. i.e. from the sample we infer the properties of thepopulation of the interestData analysis method is based on Assumptions about study design Assumptions about type s of variables(categorical ) Assumption of a model of how variables may beassociated with each other (i.e. a model that hasbeen proved already or is to be investigated), Probability laws (e.g. Law of large numbers)Data analysismethodInference aboutpopulations of likeindividualsNB. Statistical data analysis (inference) methods however sophisticated cannot “rescue” a poor study design.

Example - Colour blindness We are interested in whether there is an associationbetween colour blindness and gender. We asked 240 men and 260 women about color-blindness.The results of a survey are as follows:MaleNormal colourvision221Colour blindTotal19240Female2546260Total47525500

Example - Colour blindnessIn sample 8% males and 2% females are colour blindDoes this mean that women are at less risk of becoming colour blindthan men?We rewrite research question into null hypothesis H0: there is no association between colour blindness and genderHow to test the null hypothesis? We can use a method of comparison of proportions Results reported as Confidence Interval or P-value

Example - Colour blindness Confidence interval: range of plausible values for the“true” difference (usually use 95% certainty) Method of comparison of proportions General formula (in large samples)estimate 1.96 · standard error95% CI for p1 – p2 is (2%, 9%) there is a significant difference in the proportion withcolour blindness between the 2 groups at a 95% confidencelevel (because value 0 is not in CI)

Choosing the right statistical methodfor data analysisSeveral factors to consider: Objective of the analysis e.g. Estimating prevalence, comparison of groups,association between measures, instruments comparisons, Type of data, i.e. categorical or continuous Observations, i.e. independent or paired Distribution of the data, i.e. symmetric or skewedNB. Always check if the assumptions of the statisticalmethod are satisfied

Comparisons of two groupsType of DataCategoricalContinuous NormalContinuous Skewed16e.g. Color blindness yes/noor 3 severity grades ofdiabetic maculopathy141210864Std. D ev 7.682M ean 11.4N 42.0000.05.010.015.020.025.030.035.0Tests for differences, independent data:Attendances at GP for chest proble msChi-square 2 testt-testMann-Whitney UFisher’s exact testTests for differences, non-independent (paired) data:McNemar’s testPaired (single sample) t-testWilcoxon

Comparisons of two or more groupswith respect to a continuous dataAnalysis of variance (ANOVA) One-way ANOVA It compares the 2 or more groups with respectto continuous data E.g. Compare 3 grades of diabetic retinopathywith respect to retinal blood flow Two-way ANOVA How is retinal blood flow varying across 3grades of diabetic retinopathy and gender?NB. Standard assumptions of ANOVA are Normal distribution of data and independent objects of analysis.The three groups of interestdefined by diabeticretinopathy stage.

Spearman rankcorrelationcoefficientPearson correlationcoefficientSimple linearregressionNB. Correlation does not mean causation.10090807060Continuous50Ordinal40Type of DataLeft Temporal Lobe volume (cm 3)Measuring association between two variables405060708090100Right Temporal Lobe volume (cm 3)Example of positivecorrelation in twocontinuous variables

Agreement between two alternative waysof measurementTest-retest or instrument comparisons Two typical questions How well a new instrument replicates themeasurements of other instrument? E.g.intraocular pressure measured via Goldmannapplanation tonometrry or Perkins tonometer Is there a good level of agreement between tworaters (clinicians) using the same instrument? What methods are most common? Kappa coefficient of agreement Bland–Altman plotNB. Pearson correlation coefficients is not applicable as it measure an associationand not the agreement. Two instruments can correlate well and still disagree greatly.

List of more advanced statistical methods used inophthalmic clinical research Repeated measures ANOVAComparison of groups (novel therapy vs traditional therapy) when outcome(visual acuity in logMAR) is measured repeatedly on same subjects. Multiple linear regressionHow visual acuity (logMAR) depends on age (in years) while controllingfor effect of other factors such as disease duration in years, and being onnovel or traditional therapy. Linear mixed models, General estimating equations, Longitudinal analysisSame goal as linear regression, but it allows for correlation between objectsof study i.e. correlation in measurements from two eyes Logistic regressionHow a visual acuity (dichotomously measured) depends on age whilecontrolling for effect of other factors. Survival analysis methodsStudy the time to development of blindness.

Most common statistical issues in clinicalophthalmology How to measure the primary outcome? E.g. How to measure visual acuity? Snellen Chart and Early Treatment DiabeticRetinopathy study Chart (ETDRS). No appropriate conversion exists. Dichotomizing the measurements? E.g. to dichotomize the visual acuity measurements It leads to loss of information, hence more patients needed for study. Eyes vs. patients as unit of randomization and analysis? Measurements from two eyes of same patient may be correlated andhence carry less information than two eyes from two different patients;and standard data analysis methods are not appropriate. Multiple measures and multiple comparisons? Performing statistical inference on multiple measures leads to significantresults by chance. This is overcome by using proper adjustments.

Department of Biostatistics at University of Liverpool.Some of the things that we do Teaching courses for NHS: http://www.liv.ac.uk/medstats/courses.htm Some courses: Statistical issues in the design and analysis of research projects;Advise on analysis at design stageAdvise on including funding for statistical support in grant applicationsMay collaborate on every stage of clinical researchWe have academic staff specializing in statistics for ophthalmologyNB. Most of our courses are relevant to clinical ophthalmologists.However, ophthalmology has specific issues and challenges for whichwe plan to develop devoted workshops.

ResourcesBooks Practical statistics for medical research by Douglas G. Altman Medical Statistics from Scratch by David BowersJournals’ with series on how to do statistics in clinical research American Journal of Ophthalmology has Series on Statistics British Medical Journal has series Statistics NotesGuide on how to do clinical research in ophthalmology Clinical Research. A primer for Ophthalmologists. InternationalCouncil of Ophthalmology. February 2009, http://www.icoph.org

Statistical papers with examples from ophthalmology Holopigian and Bach, A primer on common statistical errors in clinicalophthalmology, Doc. Ophthalmology, 2010 Fan, Teo and Saw. Application of advanced statistics in ophthalmology. InvOphth and Visual Science, p 6059-6065, 2011. Bunce. Correlation, Agreement, and Bland-Altman Analysis: StatisticalAnalysis of Method Comparison Studies. Am J O 2010. Boscardin. The Use and Interpretation of Linear Regression Analysis inOphthalmology Research. Am J O 2010. Wang and Attia. Study Designs in Epidemiology and Levels of Evidence.Am J O 2009Statistical papers for general clinical research (relevant to clinicalophthalmology) Bland and Altman. Statistical methods for assessing agreement between twomethods of clinical measurement, Lancet 1986.

Thank you for your attentionQuestions?Suggestions for topics for future workshops?Email: [email protected]

Ophthalmology Research. Am J O 2010. • Wang and Attia. Study Designs in Epidemiology and Levels of Evidence. Am J O 2009 Statistical papers for general clinical research (relevant to clinical ophthalmology) • Bland and Altman. Statistical methods for assessing agreement between two methods of clinical measurement, Lancet 1986.