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BiostatisticsBiostatistics

Univ.-Prof. DI Dr. Andrea Berghold

Institute for Medical Informatics, Statisticsand Documentation

Medical University of Graz

andrea.berghold@medunigraz.at

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ContentContent

• Introduction to Medical Statistics

• Study designs in medical research with emphasis on clinical trials

• Exploring and summarizing data

• Populations and samples

• Statements of probability and confidence intervals

• Drawing inferences from data - Hypothesis testing

• Estimating and comparing means

• Proportions and chi-square tests

• Correlation and regression

• Diagnostic tools

• Methods for analysing survival data

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LiteratureLiterature

• Martin Bland: An Introduction to Medical Statistics. 3rd ed. Oxford University Press, 2000.

• Douglas Altman: Practical Statistics for Medical Research. Chapman & Hall.

• Aviva Petrie and Caroline Sabin: Medical Statistics at a Glance.Blackwell Science, 2000

• …

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NEJM June 2001: Methods Section of Full-Length Original Articles(by article, in column inches)

StatisticalStatistical MethodsMethods -- medicalmedical literatureliterature

PercentageAll methodsStatisticalMethods

12.9 %35.74.6

14.7 %53.67.9

23.6 %51.612.2

19.8 %36.87.3

18.0 %177.732.0

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In the same issue the following statistical methods were mentioned:

StatisticalStatistical MethodsMethods -- medicalmedical literatureliterature

• Bonferroni method

• Chi-square test for independence

• Chi-square test for goodness-of-fit

• Confidence intervals

• Cox proportional hazards models

• Cumulative mortality

• Fisher's exact test

• Intention-to-treat analysis

• Interim analysis

• Kaplan-Meier survival curves

• Logistic regression

• Logrank test

• Mantel-Haenszel adjusted relative risks

• Noninferiority testing

• Odds ratio

• Power Analysis

• P-values

• Randomization

• Relative risk reduction

• Repeated measures ANOVA

• Sample size estimation

• Spearman correlation

• t-tests

• Wilcoxon test

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Is it worth to struggle with statistics?

Bad statistics leads to bad research,

and bad research is unethical

Altman (1982)

StatisticsStatistics

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• Design of studies- How do I get adequate data?

• Data analysis using statistical methods- What do I do with the data?

• Critical appraisal- How do I interpret study results?

BiostatisticsBiostatistics -- MedicalMedical StatisticsStatistics

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A A StudyStudy

interpret

analyse data

collect data

plan trial

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1. Stating the problem

• Major objective of the study -determine relevant variables und factors

• Search the literature, discussion with experts

A A StudyStudy

2. Designing the study

• Study design, sample size calculation etc.

• Statistical analysis plan

• Study protocol

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A A StudyStudy

3. Collecting data

• Collecting data and plausibility checks

4. Data analysis

• Graphs and summary statistics

• Statistical inference

5. Interpretation of results and conclusions

• Discussion of new information

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Some questions which should be answered in advance:

StatingStating thethe problemproblem

• What is the major objective of the study?

• Is the question clearly defined?

• Is it also relevant?

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• Are there differences in the one-year rate of restenosis usingstents or PTA with stenosis of arteria iliaca?

• Does a betablocker decrease all-cause mortality in patientswith chronic heart failure?

• Have cancer patients who have anemia a worse prognosisthan patients without anemia?

• Which method should be used for training of laparascopicsurgery?

• …

ExamplesExamples

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• Primary variable, endpointBsp.: rate of restenosis;all-cause mortality;5 year disease-specific survival;number of stitches per minute; …

• FactorsBsp.: Stage (NYHA); Anemia, size of tumour, lymph nodes;Method, playing an instrument; ...

• Other factorsBsp.: Age, sex, smoking ....

VariablesVariables

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TypesTypes of of studiesstudies

• Experimental studies

• Observational studies

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TypesTypes of of studiesstudies

Main types of studiesin medical research

Observational studies Experimental studies

Cross-sectionalstudiy

case-controlstudy

cohortstudy Clinical trial Laboratory

experiments

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Comparison of the efficacy of different drugs, therapies, vaccines etc. after controlling for confounders (e.g. age, sex, stage of disease).

ClinicalClinical trialtrial

Aim:

Observed differences in success rates betweentreatment groups can exclusively be put down to thefact that differences are caused by the efficacy of the

different treatments.

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Comparable treatment groups

random allocation

chance (e.g. toss a coin or random numbergenerator) decides, which group a patient will berandomized to.

RandomizationRandomization

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20 patients will be allocated at random to two groupsPatients:1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20We throw the die oncefor each patient:odd number: Gruppe Aeven nuumber: Gruppe B

Group A: Group B:

Result: ?2

1

?5

2

?3

, 3

?

, 4, 5, 6 , 7, 8, 910

,, 11

, 1213

,, 14, 15, 16, 17

18,, 19

, 20

RandomizationRandomization

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RandomizationRandomization

Different methods: simple randomizationpermuted blocksminimization …

Stratified randomization (multicentre studies, age, sex)

• To prevent bias: compare treatments between groups whichdo not differ in any systematic way

• Statistical theory is based on the idea of random sampling

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Pat. Pat. allocationallocation therapytherapy

11 AA RadiatioRadiatio22 AA RadiatioRadiatio33 BB Rad.+ Chem.Rad.+ Chem.44 BB Rad.+ Chem.Rad.+ Chem.

55 AA RadiatioRadiatio66 BB Rad.+ Chem.Rad.+ Chem.77 AA RadiatioRadiatio88 BB Rad.+ Chem.Rad.+ Chem.

99 BB Rad.+ Chem.Rad.+ Chem.1010 AA RadiatioRadiatio1111 AA RadiatioRadiatio1212 BB Rad.+ Chem.Rad.+ Chem.

1313 BB Rad.+ Chem.Rad.+ Chem.1414 BB Rad.+ Chem.Rad.+ Chem.1515 AA RadiatioRadiatio1616 AA RadiatioRadiatio.... .... .......... .... ......

randomizationrandomization listlistblock block randomizationrandomization::1:1: AABBAABB2:2: ABABABAB3:3: ABBAABBA4:4: BABABABA5:5: BAABBAAB6:6: BBAABBAA

n! 4!n! 4!nn11! n! n22! 2! 2!! 2! 2!

= = 6= = 6

Randomization list(only at study coordinating centreand not for the researcher)

IfIf itit isis a a doubledouble--blind blind studystudy

thethe studystudy coordinatingcoordinating centrecentretellstells onlyonly thethepackagepackage labellabel..

RandomizationRandomization

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ImplementationImplementation

• Sealed envelopes

• Trial coordination centre via telephone or fax

• Interactive Voice Response Systems

• Internet-based Systems

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Randomizer for Clinical TrialsRandomizer for Clinical Trials

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Online Online RandomizationRandomization

www.randomizer.at

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Treating patients the same way – avoidassessment bias

Blinding

Blinding Blinding -- MaskingMasking

In an open study the patient and researcher knowto which group the patient belongs to.

Which therapy a patient gets, is

not known for the patient: single blindnot known for the patient and researcher: double blind

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RandomizedRandomized controlledcontrolled trialstrials

• Choice of target population

Selection of patients: Definition of target population usinginclusion and exclusion criteria

• Trial Design

• Parallel – Design

• Cross-Over – Design

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Parallel Parallel -- DesignDesign

Elig

ible

and

will

igin

gsu

bjec

ts

Con

trol

Ran

dom

izat

ion

Ass

essm

ent

TestA

sses

smen

t

Pop

ulat

ion

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Cross Cross –– OverOver -- DesignDesign

Ran

dom

izat

ion

Ass

essm

ent

Pop

ulat

ion

Ass

essm

ent

Ass

essm

net

Con

trol

Con

trol

Elig

ible

and

will

iing

subj

ects

Test

Test

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IntentionIntention--toto TreatTreat

all randomized patients must be included in the analysis -

they have to be included in the group theywere randomised to, independent of whathappened after randomization.

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IntentionIntention--toto--TreatTreat (ITT) Analysis (ITT) Analysis

Randomization

Treatment A Treatment B

Treatment Aper protocol

Treatmentwithdrawal

Treatment Bper protocol

Treatmentwithdrawal

Intention-to-Treat: 1+2 vs 3+4Per-Protocol (PP): 1 vs 3

1 2 3 4

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IllustrationIllustration

11,6%8,7%7,6%ITT – Analysis

12,5%17,6%15,9%Withdrawal

11,2%2,6%3,4%PP - Analysis

PlaceboAtenololPropanolol

Percentage of patients who died within 6 weeks after heartinfarction (Wilcox et. al.)

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EfficacyEfficacy and and EffectivenessEffectiveness

Efficacyeffect under optimal conditions

All patients are included in the analysis, who were treated per protocol.

Per-Protocol Analysis

Effectivenesseffect under „real“ conditions.

All patients are included in the analysis, who were included in thestudy (Withdrawal, changing treatment etc.).

Intention-to-treat Analysis

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RandomizedRandomized controlledcontrolled trialtrial

prospective: 4 years follow-upstandard therapy: drug for 6 months, new therapy: long term therapy

22720126total

1161133Long termtherapy

11188236 months

totalnoyes

RelapseTherapy

95% confidence interval RR: [2,5;25,9]

RR = = 8,023 / 1113 / 116

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ObservationalObservational StudiesStudies

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CohortCohort StudyStudy

PopulationCohort

selected forstudy

exposed(subjects)

unexposed(controls)

with outcome

without outcome

with outcome

without outcome

Onset of study Time

Direction of inquiry

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ExamplesExamples of of cohortcohort studiesstudies

e.g. Framingham study

Prognostic study

risk factors"Start" of observation

Epidemiological study

prognostic factorstime of diagnosis

orstart of therapye.g. influence of anemia on

survival

ExposureOnset of study

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ExampleExample

Relationship between cigarette smoking and incidence rate of strokein a cohort of 118 539 women (age 30-55 Jahre) – follow-up 8 years

27.923271265Ex-smoker

17.7

49.6

Incidence(per 100 000 person-years)

39559470Never-smoked

280141139Smoker

Person-yearsNo. of casesof strokeExposure

RR = = 2.8

95% confidence interval RR: [2.1; 3.7]

139 / 28014170 / 395594

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Relative Relative RiskRisk

c+ddcNot exposed

a+bbaExposed

totalnoyes

ExposureDisease

RR =a / (a+b)c / (c+d)

RR =Incidence rate of exposedIncidence rate of not-exposed

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CaseCase--ControlControl studystudy

cases

controls

exposed

unexposed

exposed

unexposed

Onset of studyTime

Direction of inquiry

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ExampleExample

824422402total

231132= d

99= cSun protection

593290= b

303= a

no sunprotection

totalcontrolscases

Exposure(during

childhood)

DiseaseMelanoma

OR = = = 1.39

95% confidence interval: [1.02; 1.89]

a / c 303 / 99b / d 290 / 132

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OddsOdds

The Odds of a probability P is defined by

It is the chance, that an event happens.

•Example:

P = 0,5 : an event will happen with a probability of 50%

Odds(P) = 0,5/0,5 = 1 (chance of 1:1)

P = 0,8

Odds(P) = 0,8/0,2 = 4 (chance of 4:1)

Odds (P) = P1-P

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OddsOdds Ratio Ratio

dcNot exposed

baexposed

no(controls)

yes(cases)

ExposureDisease

OR = =a / c adb / d bc

OR =Chance, that case was exposed

Chance, that control was exposed

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Cross Cross SectionalSectional StudyStudy

Populationsubjects

selected forstudy

with outcome

without outcome

Onset of study Time

no direction of inquiry