www.ophtalmique.ch

Dr Ciara Bergin PhD

Jules-Gonin Eye Hospital

Lausanne

Statistics in ophthalmology

Basic Science Course

Neuchâtel 2017

Overview

• Motivation

• Review of

– Types of data

– Mean vs Median

– Normal vs non-normal distributed data

– Statistical tests

– Survival analysis

• Common Pitfalls

Motivation:

• Why should an

Ophthalmologist care

about statistics?

– Helps make informed

decisions

– Helps individualize care

based on patient

characteristics

Bias ++

Stats ++

Basic statistics

• Descriptive statistics – Collecting, presenting and describing data

• Inferential statistics – Drawing conclusion and or making decision

concerning a population based only on sample data

Data

Quantitative

Discrete

Eg number of clock hrs of

retinal detachment

Continous

Age, months follow-up, amount of

subretinal fluid

Qualitative

Catagorical

Eg Race, sex, eye colour

Data types

Understanding Catagorical/

Nominal data

Understanding continous data

Understanding Dichotomised data

Understanding Ordinal data

Normal distribution

Revision : Data types Example Dichotomised

Ordinal Continous Nominal/

categorical

Low vision

IOP

Eye Color

Central macular

thickness

High IOP

Thin Cornea

Pachymetry

Logmar

Vital status

Mean vs Median

• Mean is useful to describe normally

distributed data, but less informative than

median for a lot of measures in

ophthalmology.

– Visual acuity

– IOP

– Visual field sensitivity

Median vs Mean

Normally distributed?

• Does the frequency of the data have a bell

shape?

Pachymetry in normal population:

Shapiro-Wilks

test for normality

Visual acuity

Mean =0.4

SD=± 0.4

Incorrect summary!

No data Data

Normal vs non-normally distributed

• Normally distributed – Pachymetry

– Retinal thickness

POPULATION DEPENDANT!!!

Can be normally distributed in the healthy population but not with the presence of disease

• Non-normally distributed – VA –LogMAR

– Visual sensitivity (dB) (visual fields)

– IOP

Summary measures: useful

functions in excel: (en/fr/al)

• Normally distributed

– Mean: mean(data)/moyenne(data)/mittelwert(data)

– Standard deviation:

stdev(data)/ecartype(data)/stabw(data)

• Non-normally distributed

– Median: median(data)/mediane(data)/median(data)

– Range: =min(data) : =max(data)

Open the appendix

• 4 Excel work sheets of typical clinical data

each contains

– A worksheet of raw clinical data

– A worksheet with summary tables

• Please check you have the following files

Example 1: Retinal Detachment

Summary measures on IOP

Number of eyes 108

Mean IOP

SD

95% CI ( , )

Median IOP

IQR IOP [ , ]

Range IOP [ , ]

Nom:

Example 2: Pachy

Corneal

curvature

Kmax<40D Kmax 40-42D K-max>40D

Number of

eyes

Males

Left eyes

Age

Mean Pachy

SD

Median Pachy

Range Pachy [ , ] [ , ] [ , ]

Example 3: Phacoemulsification

Timepoint M1 M3 M6

Number of

eyes

Males

Left eyes

SF6

Mean VA

SD VA

Median VA

Range VA [ , ] [ , ] [ , ]

Narrow angles

% On treatment

Example 4: Uveal melanoma

Group Adult Juvenile P-values

Number of eyes 129 43

Males

Left eyes

Enucleation

Mean time to

enuc

SD time to enuc

Median time to

enuc

Range time to

enuc

[ , ] [ , ]

Metastatis

Population

Sample

Inferential statistics Sample statistics

Known Population statistics

Unknown Inference

Eg. In 50 patients with open

angle glaucoma a reduction

of 1.5mmHg in IOP was

observed 1 month following

phacoemulsification

We infere that patients with open

angle glaucoma 1 month

following phacoemulsification

will have a reduction of

1.5mmHg in IOP

Inference

Design type

• Paired

– Same measure on a

patient/animal/subject

before and after an

intervention/ time

period

• Non-paired

– Same measure on a

between two matched

groups of patients/

animal/ subjects

Which test when? Data type Distribution type Paired or non-

paired

Test type

Dichotomised Fisher test

Catagorical Chi-squared test

~ Continous Normal Paired Paired student t-test

Non-paired Non-paired student

t-test

Non-normal Paired Paired Wilcoxon

test

Non-paired Mann-Whitney U-

test

Test your knowledge: Which test?

Comparison Data type: Dichotomised,

catagorical, continous

normal, continous non-

normal

Paired or

non-paired

Test type

Are there more blue

eyed patients?

Does cataract

surgery lower IOP?

Are cornea of

keratoconus

patients thinner

than normals?

Is the number of

quandrants of

retinal detachment

associated with low

vision?

Survival data

• Take the example of Oncology

– Did the patient survive? – dichotomisation

– If not how long after did they die

• “have an event”

– If they have survived, for how long?

• “time of censoring”

→Two parameters, time and event (yes/no)

Survival analysis

Time E

vent

Common pitfalls

• Using one eye or two

– These are not independent • i.e. if a patient is a steroid responder, likely both eyes

will be affected

• Dichotomizing data unnecessarily

– Reduces the quality of the data

• Absence of evidence is not evidence of absence

– No statistical difference observed does not imply that there is no difference, eg anti-vegf trials

For the interested reader:

• Analysing follow-up data – linear regression vs ANOVA

• Sensitivity and specificity – We can detect all AMD if we diagnose everyone with AMD

• Power and effect size – – statistically significant is not immediately clinically

significant

• Multiple hypothesis testing on the same dataset – Ask enough questions you will finally just by chance get the

answer you want