Berghold, IMI, MUG
PhD Course inBiostatistics
Univ.-Prof. DI Dr. Andrea Berghold
Institute for Medical Informatics, Statisticsand Documentation
Medical University of Graz
Berghold, IMI, MUG
Content
• Introduction to Medical Statistics
• Study designs in medical research
• 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
Statistical Methods All methods Percentage
4.6 35.7 12.9 %
7.9 53.6 14.7 %
12.2 51.6 23.6 %
7.3 36.8 19.8 %
32.0 177.7 18.0 %
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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 of 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 class); 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!
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
disease – asthma
Exposure
totalboys girls
yes 344= a
221= b
565= (a+b)
no 4885= c
4787= d
9672= (c+d)
total 5229= (a+c)
5008= (b+d) 10237
prevalence 344 / 5229= 0,066
221 / 5008= 0,044
565 / 10237= 0,055
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
Exposure(during
childhood)
Disease- Melanoma
totalcases controls
no sun protection
303= a
290= b
593
sun protection 99= c
132= d
231
total 402 422 824
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
ExposureDisease
yes(cases)
no(controls)
exposed a b
not exposed c d
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
Onset of study Exposure
Prognostic study time of diagnosisor
start of therapyprognostic factors
e.g. influence of anemia on survival
Epidemiological study"Start" of
observation risk factorse.g. Framingham study
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Example
Association between cigarette smoking and incidence of stroke in a cohort of 118 539 women (age 30-55) – follow-up 8 years
Exposure No. of cases of stroke Person-years Incidence
(per 100 000 person-years)
Smoker 139 280141 49.6
Ex-smoker 65 232712 27.9
Never-smoked 70 395594 17.7
RR = = 2.8
95% confidence interval RR: [2.1; 3.7]
139 / 28014170 / 395594
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Relative Risk
ExposureDisease
totalyes no
exposed a b a+b
not exposed c d c+d
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 ofdisease, …).
Clinical trial
Aim:
Observed differences in success rates between treatment groups can exclusively be put down to the fact 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 judged against 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 (using coins, 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 once for each patient:odd number: group Aeven nuumber: group 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
Randomization
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A B
1 32 54 678910
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Restricted randomization
• Disadvantages of simple randomization:
• No guarantee of equal or approximately equal sample size in each treatment group at any stage of the trial
• With n = 20 on two treatments A and B, the probability 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 Radiatio 2 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
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 pulmonary tuberculosis is generally considered to be the first randomized experiment in medicine.
target population: patients with progressive bilateral pulmonary tuberculosis (bacterially proven), aged 15-30 years
107 patients in 3 centers were allocated by a series of random numbers 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 aware of 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 using inclusion and exclusion criteria
• Trial Design
• Parallel – Design
• Cross-Over – Design
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Parallel - Design
Elig
ible
an
d w
illig
ing
subj
ects
Con
trol
Ran
dom
izat
ion
Ass
essm
ent
Test
Scr
eeni
ng
Pop
ulat
ion
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Cross – Over - Design
Ran
dom
izat
ion
Ass
essm
ent
Pop
ulat
ion
Scr
eeni
ng
Ass
essm
net
Con
trol
Con
trol
Elig
ible
an
d w
illiin
g su
bjec
ts
Test
Test
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• The statistical analysis has to be defined before the study is carried out
• Statistical analysis plan (SAP)
• Population used for analysis:
• All-Randomized patients – Intention-to-treat analysis
• On-treatment patients – Per-protocol analysis
• 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
Propanolol Atenolol Placebo
ITT – Analysis 7.6% 8.7% 11.6%
PP - Analysis 3.4% 2.6% 11.2%
Withdrawal 15.9% 17.6% 12.5%
Percentage of patients who died within 6 weeks after heart infarction (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 the study (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
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Laboratory Experiments
Exactly the same principles apply to laboratory experiments on
animals or on biological specimens as for clinical trials
• Stricter control of extraneous factors is possible
• Effect of uncertainties is minimized – use of control group,
randomization, replication
• Principles of randomization is often not well understood
• Using genetically similar animals – little biological variablity