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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Heterogeneity in
meta-analysis
Dr. S. A. Rizwan M.D.,
Public Health Specialist & Lecturer,
Saudi Board of Preventive Medicine – Riyadh,
Ministry of Health, KSA
25.11.2019 1
With thanks to Martin Bland
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Outline
• What is heterogeneity?
• Sources of heterogeneity
• Impact of heterogeneity on different parameters
• Quantification of heterogeneity
• Dealing with heterogeneity
25.11.2019 2
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
What do we mean by Heterogeneity?
25.11.2019 3
It’sthe variance in trueeffects(not observed effects) that we careabout
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Where does it arise from?
• Studies differ in terms of
• Patients
• Interventions
• Outcome definitions
• Design
• This is called Clinical heterogeneity
• Variation in true treatment effects in magnitude or direction
• This is called Statistical heterogeneity
25.11.2019 4
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Where does it arise from?
• Statistical heterogeneity may be caused by
• clinical differences between trials
• methodological differences between trials
• unknown trial characteristics
• Even if studies are clinically homogeneous there may be statistical
heterogeneity
25.11.2019 5
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Why estimate heterogeneity?
It affects weight, mean, SE and utility of effects
25.11.2019 6
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Impact on Weight
25.11.2019 7
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
It affects the weights
25.11.2019 8
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
W = 1/ (V1)
Weights when T2 = 0
25.11.2019 9
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Weights when T2 > 0
25.11.2019 10
1W = 1/ (V +T 2
)
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Impact on Standard Error
25.11.2019 11
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
It affects the standard error
25.11.2019 12
… the confidence interval, and thep-value
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 13
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 14
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 15
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
140
25.11.2019 16
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Precision ofthe
mean effect
25.11.2019 17
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Precision ofthe
mean effect
25.11.2019 18
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Precision ofthe
mean effect
25.11.2019 19
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Impact on Mean ES
25.11.2019 20
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
It affects the mean ES
25.11.2019 21
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
It affects the mean ES
• As heterogeneity increases, mean effect shifts away from larger
studies and towards smaller studies
25.11.2019 22
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 23
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 24
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Impact on substantive utility
25.11.2019 25
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
It affects the substantive utility
25.11.2019 26
Is the treatment effectivefor everyone, or
effectivefor some and harmful for others?
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 27
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 28
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
150
25.11.2019 29
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 30
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 31
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 32
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 33
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Dispersion ofthe
individual effects
25.11.2019 34
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Dispersion ofthe
individual effects
25.11.2019 35
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
How do we quantify
heterogeneity?
25.11.2019 36
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Two-step process
• Isolate the real dispersion
• Translate this into useful indices
25.11.2019 37
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
1. Isolate the real dispersion
25.11.2019 38
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
What we’d like to see if the true effect is the
same in all studies
25.11.2019 39
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
What we might see if the true effect is the
same in all studies
25.11.2019 40
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Is there real dispersion?
25.11.2019 41
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
It depends on the precision
25.11.2019 42
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
It depends on the precision
25.11.2019 43
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Key point
• We can easily compute variance of observed effects
• But this is due partly to real differences in effects and partly to
sampling error within studies
• We need to isolate the between-studies variance
25.11.2019 44
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 45
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 46
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 47
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
170
To assess heterogeneity
• Compute observed variance
• Estimate how much variance would be expected if true effect is
identical in all studies
• Observed minus expected is estimate of true variance
25.11.2019 48
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Q df Q-df
Isolating the real dispersion
25.11.2019 49
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
2. Translate into useful indices
25.11.2019 50
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Indices related to heterogeneity
25.11.2019 51
Q−df Basis for all indices
p Test of null
T Standard deviation of true effects
T2 Variance of true effects
I2 Proportion of true/total variance
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
P-value
• Can we conclude that there is some variance in true effects
• Depends on amount of excess variance and the amount of evidence
25.11.2019 52
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 53
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 54
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 55
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Statistics apply to both models
25.11.2019 56
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
I square – an alternative of Q
• Q is statistically under-powered when the number of studies is low
and when the sample size within the studies is low
• Larger values of I2, the more heterogeneity
• 75%: large heterogeneity
• 50%: moderate heterogeneity
• 25%: low heterogeneity
25.11.2019 57
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Caution!
• I2 is NOT a measure of absolute heterogeneity
• I2 tells us what proportion of the observed dispersion reflects
differences in true scores rather than random sampling error
25.11.2019 58
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
What proportion
of the observed variance is real?
25.11.2019 59
I2
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Test for heterogeneity: χ2 = 4.91, df = 2, P=0.086
Heterogeneity
25.11.2019 60
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
What happens when heterogeneity is not
significant
• No statistical evidence for difference between trials
• But, test for heterogeneity has low power – the number of studies is
usually low - and may fail to detect heterogeneity as statistically
significant when it exists.
• This cannot be interpreted as evidence of homogeneity.
• To compensate for the low power of the test a higher significance
level is sometimes taken, P < 0.1 for statistical significance.
25.11.2019 61
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
What happens when heterogeneity is
significant
• Differences between trials exist
• It may be invalid to pool the results and generate a single summary
result
• Describe variation
• Investigate sources of heterogeneity
• Account for heterogeneity
25.11.2019 62
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Dealing with heterogeneity
• Do not pool — narrative review.
• Ignore heterogeneity and use fixed effect model:
• confidence interval too narrow,
• difficult to interpret pooled estimate,
• may be biased.
• Explore heterogeneity, can we explain it and remove it?
• Allow for heterogeneity and use random effects model
• Change the ES measure
• Exclude extreme outlier studies (caution!)
25.11.2019 63
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating sources of heterogeneity
• Subgroup analysis:
• subsets of trials,
• subsets of patients,
• subsets should be pre-specified to avoid bias.
• Relate size of effect to characteristics of the trials, e.g.:
• average age,
• proportion of females,
• intended dose of drug,
• baseline risk.
• ‘Meta-regression’ can be used.
25.11.2019 64
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating heterogeneity – Subgroups
• Split into 26 sub-studies with
more uniform age groups.
• Before adjustment for age: X2 =
127, df=9, P<0.001.
• After adjustment for age: X2 =
45, df=23, P=0.005.
• A considerable improvement,
but still some heterogeneity
present.
25.11.2019 65
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating heterogeneity – Subgroups
• We want to see if the mean effect sizes for studies grouped by age of
student differ from each other
• Question: What are our assumptions about τ2 ?
• Option 1: We assume that each group has its own underlying distribution
of effect sizes, so that we are really estimating μ and separate variance
components for each category of the age.
• Usually we don’t have a large number of studies within each group, and our estimates
of the variance components will not be precise
• Option 2: Assume that we have a common variance component τ2
25.11.2019 66
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating heterogeneity – meta-regression
• Line fitted by meta-regression.
• Odds ratios of ischemic heart
disease (and 95% CI) according to
the average extent of serum
cholesterol reduction achieved in
each of 28 trials.
• Overall summary of results is
indicated by sloping line.
• Results of the nine smallest trials
have been combined.
25.11.2019 67
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating heterogeneity - Galbraith plot
• Alternative graphical representation to forest plot.
• Horizontal axis: 1/standard error.
• Horizontal axis will be zero if standard error is infinite, a study of zero size.
• Vertical axis: effect/standard error.
• This is the test statistic for the individual study.
• For 95% of studies, we expect this to be within 2 units of the true effect.
25.11.2019 68
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating heterogeneity - Galbraith plot
• Corticosteroids for severe sepsis
and septic shock (Annane et al.,
2004)
-4
-2
0
2
Difference/standarderror
0 2 4 6
1/standard error
Long, low dose trials
25.11.2019 69
Galbraith plot for log OR
Low doses & long duration trials
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating heterogeneity - Galbraith plot
• We can add a line representing
the pooled effect.
• Plot (pooled effect)/se against
1/se.
-4
-2
0
2
Difference/standarderror
0 2 4 6
1/standard error
Pooled effect
25.11.2019 70
Galbraith plot for log OR
Low doses & long duration trials
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating heterogeneity - Galbraith plot
• We can add a line representing the
pooled effect.
• Plot (pooled effect)/se against 1/se.
• 95% limits will be 2 units above and
below this line.
• We expect 95% of points to be
between these limits if there is no
heterogeneity.
• This is true for low dose, long duration
trials.
-4
-2
0
2
Difference/standarderror
0 2 4 6
1/standard error
Pooled effect 95% limits
25.11.2019 71
Galbraith plot for log OR
Low doses & long duration trials
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating heterogeneity - Galbraith plot
• We have two points outside the
95% limits and one on the line.
• We can investigate them to see
how these trials differ from the
others.
• The pooled effect is smaller so the
line is less steep. -4
-2
0
2
Difference/standarderror
0 2 4 6
1/standard error
Pooled effect 95% limits
25.11.2019 72
Galbraith plot for log OR
All trials
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating heterogeneity - Galbraith plot
• We could reanalyse taking
dosage and duration separately.
• These trials are all of high dose
or short duration treatments.
-4
-2
0
2
Difference/standarderror
0 2 4 6
1/standard error
Long, low dose Short, high dose Other
25.11.2019 73
Galbraith plot for log OR
All trials
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Galbraith plot or Forest plot?
Wagner
CSG
Klatersky
Schumer
Lucas
Sprung
Bone
VASSCSG
Luce
Slusher
Bollaert
Briegel
Chawla
AnnaneYildiz
-4
-2
0
2
Difference/standarderror
0 2 4 6
1/standard error
Pooled effect 95% limits
Pooled
Yildiz
Annane
Chawla
Briegel
Bollaert
Slusher
Luce
VASSCSG
Bone
Sprung
Lucas
Schumer
Klatersky
CSG
Wagner
.01 .1 1 10 100
Odds ratio of death
25.11.2019 74
“Conventional meta-analysis diagrams . . . are not very useful for investigating heterogeneity. A
better diagramfor this purpose was proposed by Galbraith . . .” (Thompson, 1994). Is this really
true?
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Galbraith plot or Forest plot?
Wagner
CSG
Klatersky
Schumer
Lucas
Sprung
Bone
VASSCSG
Luce
Slusher
Bollaert
Briegel
Chawla
AnnaneYildiz
-4
-2
0
2
Difference/standarderror
0 2 4 6
1/standard error
Pooled effect 95% limits
Pooled
Yildiz
Annane
Chawla
Briegel
Bollaert
Slusher
Luce
VASSCSG
Bone
Sprung
Lucas
Schumer
Klatersky
CSG
Wagner
.01 .1 1 10 100
Odds ratio of death
25.11.2019 75
Trials outside the Galbraith limits will be trials where the 95% confidence interval
does not contain the pooled estimate. We can spot them from the forest plot.
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
L’ abbe plot
25.11.2019 76
• Ideally a L'Abbé plot should have the
symbols appropriate to the size of the
trials.
• There is an inset for the symbol size, and
the two colours show trazodone used for
erectile dysfunction in two different
conditions (and with clear clinical
heterogeneity).
Trazodone for erectile dysfunction in psychogenic
erectile dysfunction (dark symbols) and with
physiological or mixed aetiology (light symbols)
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating sources of heterogeneity
• Cannot always explain
heterogeneity
• Example: Effect of breast
feeding in infancy on blood
pressure in later life (Owen
et al., 2003)
• *In parenthesis: age at
which blood pressure
measured
25.11.2019 77
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Investigating sources of heterogeneity
• Cannot always explain
heterogeneity
• X2=59.4, 25df, P<0.001
• Three age groups: P=0.6.
• Born before or after 1980: P=0.8.
• Have to accept it and take it into
account by using a random effects
model.
25.11.2019 78
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Take home messages
• Heterogeneity is not a bad thing
• It should not be ignored
• It should be understood, explored and quantified
• And it should be properly handled in analysis
• Discussion of meta-analysis findings should include a major note on
heterogeneity of effects
25.11.2019 79
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Thank you
Kindly email your queries to sarizwan1986@outlook.com
25.11.2019 80

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Heterogeneity in meta-analysis

  • 1. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Heterogeneity in meta-analysis Dr. S. A. Rizwan M.D., Public Health Specialist & Lecturer, Saudi Board of Preventive Medicine – Riyadh, Ministry of Health, KSA 25.11.2019 1 With thanks to Martin Bland
  • 2. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Outline • What is heterogeneity? • Sources of heterogeneity • Impact of heterogeneity on different parameters • Quantification of heterogeneity • Dealing with heterogeneity 25.11.2019 2
  • 3. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What do we mean by Heterogeneity? 25.11.2019 3 It’sthe variance in trueeffects(not observed effects) that we careabout
  • 4. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Where does it arise from? • Studies differ in terms of • Patients • Interventions • Outcome definitions • Design • This is called Clinical heterogeneity • Variation in true treatment effects in magnitude or direction • This is called Statistical heterogeneity 25.11.2019 4
  • 5. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Where does it arise from? • Statistical heterogeneity may be caused by • clinical differences between trials • methodological differences between trials • unknown trial characteristics • Even if studies are clinically homogeneous there may be statistical heterogeneity 25.11.2019 5
  • 6. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Why estimate heterogeneity? It affects weight, mean, SE and utility of effects 25.11.2019 6
  • 7. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Impact on Weight 25.11.2019 7
  • 8. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It affects the weights 25.11.2019 8
  • 9. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course W = 1/ (V1) Weights when T2 = 0 25.11.2019 9
  • 10. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Weights when T2 > 0 25.11.2019 10 1W = 1/ (V +T 2 )
  • 11. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Impact on Standard Error 25.11.2019 11
  • 12. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It affects the standard error 25.11.2019 12 … the confidence interval, and thep-value
  • 13. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 13
  • 14. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 14
  • 15. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 15
  • 16. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 140 25.11.2019 16
  • 17. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Precision ofthe mean effect 25.11.2019 17
  • 18. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Precision ofthe mean effect 25.11.2019 18
  • 19. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Precision ofthe mean effect 25.11.2019 19
  • 20. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Impact on Mean ES 25.11.2019 20
  • 21. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It affects the mean ES 25.11.2019 21
  • 22. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It affects the mean ES • As heterogeneity increases, mean effect shifts away from larger studies and towards smaller studies 25.11.2019 22
  • 23. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 23
  • 24. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 24
  • 25. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Impact on substantive utility 25.11.2019 25
  • 26. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It affects the substantive utility 25.11.2019 26 Is the treatment effectivefor everyone, or effectivefor some and harmful for others?
  • 27. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 27
  • 28. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 28
  • 29. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 150 25.11.2019 29
  • 30. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 30
  • 31. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 31
  • 32. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 32
  • 33. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 33
  • 34. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Dispersion ofthe individual effects 25.11.2019 34
  • 35. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Dispersion ofthe individual effects 25.11.2019 35
  • 36. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course How do we quantify heterogeneity? 25.11.2019 36
  • 37. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Two-step process • Isolate the real dispersion • Translate this into useful indices 25.11.2019 37
  • 38. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 1. Isolate the real dispersion 25.11.2019 38
  • 39. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What we’d like to see if the true effect is the same in all studies 25.11.2019 39
  • 40. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What we might see if the true effect is the same in all studies 25.11.2019 40
  • 41. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Is there real dispersion? 25.11.2019 41
  • 42. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It depends on the precision 25.11.2019 42
  • 43. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It depends on the precision 25.11.2019 43
  • 44. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Key point • We can easily compute variance of observed effects • But this is due partly to real differences in effects and partly to sampling error within studies • We need to isolate the between-studies variance 25.11.2019 44
  • 45. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 45
  • 46. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 46
  • 47. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 47
  • 48. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 170 To assess heterogeneity • Compute observed variance • Estimate how much variance would be expected if true effect is identical in all studies • Observed minus expected is estimate of true variance 25.11.2019 48
  • 49. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Q df Q-df Isolating the real dispersion 25.11.2019 49
  • 50. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 2. Translate into useful indices 25.11.2019 50
  • 51. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Indices related to heterogeneity 25.11.2019 51 Q−df Basis for all indices p Test of null T Standard deviation of true effects T2 Variance of true effects I2 Proportion of true/total variance
  • 52. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course P-value • Can we conclude that there is some variance in true effects • Depends on amount of excess variance and the amount of evidence 25.11.2019 52
  • 53. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 53
  • 54. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 54
  • 55. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 55
  • 56. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Statistics apply to both models 25.11.2019 56
  • 57. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course I square – an alternative of Q • Q is statistically under-powered when the number of studies is low and when the sample size within the studies is low • Larger values of I2, the more heterogeneity • 75%: large heterogeneity • 50%: moderate heterogeneity • 25%: low heterogeneity 25.11.2019 57
  • 58. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Caution! • I2 is NOT a measure of absolute heterogeneity • I2 tells us what proportion of the observed dispersion reflects differences in true scores rather than random sampling error 25.11.2019 58
  • 59. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What proportion of the observed variance is real? 25.11.2019 59 I2
  • 60. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Test for heterogeneity: χ2 = 4.91, df = 2, P=0.086 Heterogeneity 25.11.2019 60
  • 61. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What happens when heterogeneity is not significant • No statistical evidence for difference between trials • But, test for heterogeneity has low power – the number of studies is usually low - and may fail to detect heterogeneity as statistically significant when it exists. • This cannot be interpreted as evidence of homogeneity. • To compensate for the low power of the test a higher significance level is sometimes taken, P < 0.1 for statistical significance. 25.11.2019 61
  • 62. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What happens when heterogeneity is significant • Differences between trials exist • It may be invalid to pool the results and generate a single summary result • Describe variation • Investigate sources of heterogeneity • Account for heterogeneity 25.11.2019 62
  • 63. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Dealing with heterogeneity • Do not pool — narrative review. • Ignore heterogeneity and use fixed effect model: • confidence interval too narrow, • difficult to interpret pooled estimate, • may be biased. • Explore heterogeneity, can we explain it and remove it? • Allow for heterogeneity and use random effects model • Change the ES measure • Exclude extreme outlier studies (caution!) 25.11.2019 63
  • 64. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating sources of heterogeneity • Subgroup analysis: • subsets of trials, • subsets of patients, • subsets should be pre-specified to avoid bias. • Relate size of effect to characteristics of the trials, e.g.: • average age, • proportion of females, • intended dose of drug, • baseline risk. • ‘Meta-regression’ can be used. 25.11.2019 64
  • 65. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity – Subgroups • Split into 26 sub-studies with more uniform age groups. • Before adjustment for age: X2 = 127, df=9, P<0.001. • After adjustment for age: X2 = 45, df=23, P=0.005. • A considerable improvement, but still some heterogeneity present. 25.11.2019 65
  • 66. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity – Subgroups • We want to see if the mean effect sizes for studies grouped by age of student differ from each other • Question: What are our assumptions about τ2 ? • Option 1: We assume that each group has its own underlying distribution of effect sizes, so that we are really estimating μ and separate variance components for each category of the age. • Usually we don’t have a large number of studies within each group, and our estimates of the variance components will not be precise • Option 2: Assume that we have a common variance component τ2 25.11.2019 66
  • 67. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity – meta-regression • Line fitted by meta-regression. • Odds ratios of ischemic heart disease (and 95% CI) according to the average extent of serum cholesterol reduction achieved in each of 28 trials. • Overall summary of results is indicated by sloping line. • Results of the nine smallest trials have been combined. 25.11.2019 67
  • 68. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • Alternative graphical representation to forest plot. • Horizontal axis: 1/standard error. • Horizontal axis will be zero if standard error is infinite, a study of zero size. • Vertical axis: effect/standard error. • This is the test statistic for the individual study. • For 95% of studies, we expect this to be within 2 units of the true effect. 25.11.2019 68
  • 69. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • Corticosteroids for severe sepsis and septic shock (Annane et al., 2004) -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Long, low dose trials 25.11.2019 69 Galbraith plot for log OR Low doses & long duration trials
  • 70. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • We can add a line representing the pooled effect. • Plot (pooled effect)/se against 1/se. -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Pooled effect 25.11.2019 70 Galbraith plot for log OR Low doses & long duration trials
  • 71. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • We can add a line representing the pooled effect. • Plot (pooled effect)/se against 1/se. • 95% limits will be 2 units above and below this line. • We expect 95% of points to be between these limits if there is no heterogeneity. • This is true for low dose, long duration trials. -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Pooled effect 95% limits 25.11.2019 71 Galbraith plot for log OR Low doses & long duration trials
  • 72. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • We have two points outside the 95% limits and one on the line. • We can investigate them to see how these trials differ from the others. • The pooled effect is smaller so the line is less steep. -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Pooled effect 95% limits 25.11.2019 72 Galbraith plot for log OR All trials
  • 73. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • We could reanalyse taking dosage and duration separately. • These trials are all of high dose or short duration treatments. -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Long, low dose Short, high dose Other 25.11.2019 73 Galbraith plot for log OR All trials
  • 74. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Galbraith plot or Forest plot? Wagner CSG Klatersky Schumer Lucas Sprung Bone VASSCSG Luce Slusher Bollaert Briegel Chawla AnnaneYildiz -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Pooled effect 95% limits Pooled Yildiz Annane Chawla Briegel Bollaert Slusher Luce VASSCSG Bone Sprung Lucas Schumer Klatersky CSG Wagner .01 .1 1 10 100 Odds ratio of death 25.11.2019 74 “Conventional meta-analysis diagrams . . . are not very useful for investigating heterogeneity. A better diagramfor this purpose was proposed by Galbraith . . .” (Thompson, 1994). Is this really true?
  • 75. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Galbraith plot or Forest plot? Wagner CSG Klatersky Schumer Lucas Sprung Bone VASSCSG Luce Slusher Bollaert Briegel Chawla AnnaneYildiz -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Pooled effect 95% limits Pooled Yildiz Annane Chawla Briegel Bollaert Slusher Luce VASSCSG Bone Sprung Lucas Schumer Klatersky CSG Wagner .01 .1 1 10 100 Odds ratio of death 25.11.2019 75 Trials outside the Galbraith limits will be trials where the 95% confidence interval does not contain the pooled estimate. We can spot them from the forest plot.
  • 76. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course L’ abbe plot 25.11.2019 76 • Ideally a L'Abbé plot should have the symbols appropriate to the size of the trials. • There is an inset for the symbol size, and the two colours show trazodone used for erectile dysfunction in two different conditions (and with clear clinical heterogeneity). Trazodone for erectile dysfunction in psychogenic erectile dysfunction (dark symbols) and with physiological or mixed aetiology (light symbols)
  • 77. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating sources of heterogeneity • Cannot always explain heterogeneity • Example: Effect of breast feeding in infancy on blood pressure in later life (Owen et al., 2003) • *In parenthesis: age at which blood pressure measured 25.11.2019 77
  • 78. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating sources of heterogeneity • Cannot always explain heterogeneity • X2=59.4, 25df, P<0.001 • Three age groups: P=0.6. • Born before or after 1980: P=0.8. • Have to accept it and take it into account by using a random effects model. 25.11.2019 78
  • 79. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Take home messages • Heterogeneity is not a bad thing • It should not be ignored • It should be understood, explored and quantified • And it should be properly handled in analysis • Discussion of meta-analysis findings should include a major note on heterogeneity of effects 25.11.2019 79
  • 80. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Thank you Kindly email your queries to sarizwan1986@outlook.com 25.11.2019 80