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How to find your way through the jungle of statistics ...
Carl-Olav Stiller , associate professorClinical pharmacologyKarolinska University Hospital - Solna17176 Stockholm
Tel: 08-5177 [email protected]
Statistikens djungel - grunder
Why do we need statisticsHypothesis testing Hypothesis generating Common pitfallsParametric or non-parametric
statisticsIndependent or dependent
observations Planning of research
Why do we need statistics in research?
To test hypothesis To show similarities or differences To analyse correlations To describe findings / data
Differences or similarities ?
Do I want to show differences? Power analysis -
Which difference do I want to be able to detect?
Sensitivity and specificity
What can go wrong? We find a difference which is not true
Alpha problem We find similarity, but the groups are
different tBeta problem
Hypotes - endpointPrimary hypotesis
The aim of the study. Highest evidence
Secondary hypotesis / endpoint All other tests
Lower evidenceHypotesis generating
Lack of difference is not the same as similarity!
If you compare small groups it is hard to detect any difference.
In order to show similarities the groups have to have a certain size.
Prior to start of the study you have to define the interval for similarity.
Sensitivity or specificity
Sensitivity:May I trust a positive outcome? What is the likelyhood of a positive outcome
being true / correct ?
SpecificityMay I trust a negative outcome?What is the likelyhood of a negative
outcome being true / correct ?
Parametric or non- parametric statistics?
Non-parametric statistics: Rank order: Same, smaller, bigger
Parametric statistics: Based on normal distribution (Gauss curve)
What kind of data do I have?
Normal distribution: Parametric or non-parametric statistics
Normal distribution with cut off: Non-parametric statistics preferred If you use parametric statistics SD gets too low
and your precision seems to be higher than it is.
Rank order scale: Non-parametric statistics should be used (is
it ?) Assement scale:
Non-parametric statistics should be used (is it?)
Rank order scales: examples
Borg scale for excertion: 1-5 No to maximal excertion
Cardiac failure according to NYHA (New York heart association) 1-4
Pain intensity – for example migraine headace: 0 – no pain, 1 – some pain, 2 – moderate pain,
3 – severe pain, 4- very severe pain
Visual analog scalePain intensity
0: No pain 100: Worst imaginable pain
Problem: Subjective assessment, everyone has different
reference frames - 40 for one individual is not the same as 40 for another
Inter individual variation VAS data are often calculated with parametric
statistics - ”appropiate or not? ”
Combined assessment scales
Depressions skala - Montgomery - Åsberg Olika variabler slås ihop till ett värde
Alzheimer skala - ADAS cog, Olika förmågor som påverkas vid
Alzheimer skattas och slås ihopIntelligenskvot
Prestationer i olika test vägs samman
Parametric or non-parametric statistics ?
Common pit falls:Non-parametric data are calculated
with parametric statistics
But parametric data may also be calculated with non-parametric statistics
Control group or test before treatment and after treatment ?
Test before and after may be useful as pilot study to generate a hypothesis ”hypotesgenererande”
Control group is ”gold - standard” – better data and lower risk for false positive outcome.
Treatment of severe headache with opioids or NSAIDs i.m. at the emergency department
Harden RN, Gracely RH, Carter T, Warner G The placebo effect in acute headache management: ketorolac, meperidine,and saline in the emergency department.Headache 1996 Jun;36(6):352-6
Dependent or independent observations
Dependent observations Control before or after treatment Tissue from different regions of the
same individual
Independent observations Observations in separate individuals
Common staticaal tests comparing two or more groups
Parametric statistics Non-parametric statistics
Two groups
Independent obs. Dependent obs Independent obs. Dependent obs. Unpaired t-test Paired t-test Mann-Whitney test Wilcoxons test
Three or more groups
Independent obs. Dependent obs Independent obs. Dependent obs. One-way ANOVA (analys of variance)
Repeated measures ANOVA
Kruskall Wallis Friedman test
+ Tukey – alla par + Newman Keuls – alla par
+ Bonferroni – alla par + Bonferroni – selekterade par
+ Dunett – mot kontroll
+ Dunns test
Standard deviation SD
Standard deviation SD
Control Drug A Drug B0
20
40
60
80
Eff
ect
Standard error of the mean SEM = SD /√ n
SEM
Control Drug A Drug B0
20
40
60
80
Eff
ect
Confidence interval
Correct illustration av effect range
95 % konfidens-intervall
Control Drug A Drug B0
20
40
60
80
Eff
ect
What is a good clinical study?
Relevant patient population Sufficient size / powerClinically relevanta effect outcomeReference treatment using relevant
dosesDouble blind / randomisedSufficient follow up time Few withdrawals
Common pit falls …..
Preliminary data Limited number of participants No control groupOpen trial or single blind trials
Beware …..
... Control group with inadequate treatment.
Second best alternative Gold standard
Dose selection of drug and comparator ?
Beware …..
No randomisation
It is not the treatment, but the group selection which explains the outcome
Beware ..
Selection criteria
Hard selection: Results may not be generalisable.
No selection: The treament effect can be blurred by other aspects.
Beware …..
... Subgroup analysis not planned in advance
Large number of subgroups analysed Risk for difference just by chance
Beware…..
Outcome was analysed with unproven methods
Surrogate outcomeShort follow upDrop out
Beware …..
... Differences in adverse events were not analysed
Rare adverse events are not detected in RCT
Beware …..
... Results are only presented as percent change and not absolute difference
A large relative change – for example 50 % decreased may soud impressive, but may be not important if the risk is low
Summary
Select statistics before you start your experiment
Analyse your data Mind pit falls Good luck