Berghold, IMI, MUG

Biostatistics

Univ.-Prof. DI Dr. Andrea Berghold

Institute for Medical Informatics, Statisticsand Documentation

Medical University of Graz

andrea.berghold@medunigraz.at

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Content

• 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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Literature

• 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)

Statistical Methods - medical literature

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:

Statistical Methods - medical literature

• 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)

Statistics

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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?

Biostatistics - Medical Statistics

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Study

interpret

analyse data

collect data

plan study

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1. Stating the problem

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

• Search the literature, discussion with experts

Study

2. Designing the study

• Study design, sample size calculation etc.

• Statistical analysis plan

• Study protocol

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A Study

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:

Stating the problem

• What is the major objective of the study?

• Is the question clearly defined?

• Is it also relevant?

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

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

3. Have cancer patients who have anemia a worse prognosisthan patients without anemia?

4. Which method should be used for training of laparascopicsurgery?

5. …

Examples

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• Primary variable, endpoint1. rate of restenosis;2. all-cause mortality;3. 5 year disease-specific survival;4. number of stitches per minute; …

• Factors1. none2. stage (NYHA); 3. anemia, size of tumour, lymph nodes;4. method, playing an instrument; ...

• Other factorsAge, sex, smoking ....

Variables

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• Random error

• inter- and intraindividual variability

• Systematic error - Bias

• Selection bias

• Assessment bias

• Information bias

• …

Try to avoid bias and reduce random error as much as possible.

Errors

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Types of studies

• Observational studies

• Experimental studies

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Types of studies

Main types of studiesin medical research

Observational studies Experimental studies

Cross-sectionalstudiy

case-controlstudy

cohortstudy Clinical trial Laboratory

experiments

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Observational Studies

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Cross Sectional Study

Populationsubjects

selected forstudy

with outcome

without outcome

Onset of study Time

no direction of inquiry

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Example

565 / 10237= 0,055

221 / 5008= 0,044

344 / 5229= 0,066prevalence

102375008= (b+d)

5229= (a+c)total

9672= (c+d)

4787= d

4885= cno

565= (a+b)

221= b

344= ayes

totalgirlsboysdisease – asthma

Exposure

OR = = = 1.53a / b 344 / 221c / d 4885 / 4787

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Case-Control study

cases

controls

exposed

unexposed

exposed

unexposed

Onset of studyTime

Direction of inquiry

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Example

824422402total

231132= d

99= csun protection

593290= b

303= a

no sunprotection

totalcontrolscases

Exposure(during

childhood)

Disease- Melanoma

OR = = = 1.39

95% confidence interval: [1.02; 1.89]

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

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Odds

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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Odds 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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Cohort Study

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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Examples of cohort studies

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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Example

Association between cigarette smoking and incidence of stroke in 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 Risk

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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Experimental Studies

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

Clinical trial

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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Statistical issues

• The efficacy and safety of treatments have to be judgedagainst a background of biological variability

• In designing studies, two main points have to be kept in mind:

• the effect of bias

• the effect of chance

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Focus

• Comparative trials:

• Interested in treatment effect and treatment comparisons

• Concurrent control group• Investigate a new experimental intervention versus placebo or a

“standard” intervention• compare two alternative commonly-used interventions with each

other• Study the result of adding an additional agent to a standard regimen• Compare different doses or intensities of an intervention

• Pre-defined study objective

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Design techniques to avoid bias

• Randomization

• Blinding

„The most important design techniques for avoiding bias in clinical trials are blinding and randomisation.“ (ICH E9: Statistical Principles in Clinical Trials)

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Randomization

• To allocate treatments to subjects in a trial at random (usingcoins, dice, random number tables or generators)

• Allocation concealment

• Neither the subject nor the investigator knows ahead of time what treatment the subject will receive

• Benefits:

• Eliminates assignment basis – avoids selection bias

• Tends to produce comparable groups

• Statistical basis for a valid treatment comparison

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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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A BA B

1 31 32 52 54 64 677889910 10

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Restricted randomization

• Disadvantages of simple randomization:

• No guarantee of equal or approximately equal sample size in eachtreatment group at any stage of the trial

• With n = 20 on two treatments A and B, the chance of a 12:8 split or worse is approximately 0.19

• No protection against long runs of one treatment• Subject characteristics may change over time

• Restricted randomization:

Permuted blocks (Matts & Lachin)Biased coin (Efron)Urn design (Wei)Big Stick (Soares & Wu)…

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Pat. allocation therapy

1 A Radiatio2 A Radiatio3 B Rad.+ Chem.4 B Rad.+ Chem.

5 A Radiatio6 B Rad.+ Chem.7 A Radiatio8 B Rad.+ Chem.

9 B Rad.+ Chem.10 A Radiatio11 A Radiatio12 B Rad.+ Chem.

13 B Rad.+ Chem.14 B Rad.+ Chem.15 A Radiatio16 A Radiatio.... .... ......

randomization listblock randomization:1: AABB2: ABAB3: ABBA4: BABA5: BAAB6: BBAA

n! 4!n1! n2! 2! 2!!

= = 6= = 6

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

Randomization

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Stratified randomization

• Balance treatment groups with respect to prognostic factors

• For large studies, randomization “tends” to give balance

• For smaller studies a better guarantee may be needed

• Common factors used for stratification - e.g. clinical centre, age, sex, disease severity

• Define strata – e.g. Age: < 40, 40-60, > 60;Sex: M, F (3 x 2 strata)

• Randomization is performed within each stratum and is usually blocked

• Rule of thumb – use as few stratification factors as possible

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Randomized controlled trials

The trial carried out by the Medical Research Council (MRC, 1948) to test the efficacy of streptomycin for the treatment of pulmonarytuberculosis is generally considered to be the first randomizedexperiment in medicine.

target population: patients with progressive bilateral pulmonarytuberculosis (bacterially proven), aged 15-30 years

107 patients in 3 centers were allocated by a series of randomnumbers drawn up for each sex at each centre.

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Implementation

• Sequenced sealed envelopes

• Phone call / fax to trial coordination centre

• Interactive Voice Response Systems

• Internet-based Systems (e.g. Randomizer for Clinical Trials)

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Randomizer for Clinical Trials

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Online Randomization

www.randomizer.at

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Blinding - Masking

• To limit the occurrence of bias in the conduct and interpretation of the trial (in the care, the assessment of endpoints, the attitude of subjects to treatments etc.)

• Double-blind: neither subject nor investigator/staff are awareof the treatment received

• placebo, “double dummy”, masked vials

• blinding may not be possible• surgical versus medical intervention• one intervention has obvious side-effect

• Outcome assessed by masked observer

• Single-blind

• Open-label trial

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Randomized controlled trials

• 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 - Design

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 – Over - Design

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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• The statistical analysis has to be defined before the study iscarried out

• Statistical analysis plan (SAP)

• Population used for analysis:

• All-Randomized patients

• Per-Protocol patients

• Safety population

Statistical analysis

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Intention-to-Treat

all randomized patients must be included in the analysis -

they have to be included in the group they were randomised to, independent of what happened after randomization.

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Intention-to-Treat (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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Illustration

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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Efficacy and Effectiveness

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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Main points RCTs

• Randomization – concealed allocation

• Blinding – double blind study

• Minimal loss in follow up

• Intention to treat Analyse

• Carry out specified analysis