MetaAnalysis

1
Marjan Akbari Kamrani Students Scientific
Research Center Tehran university of medical
sciences
Meta-Analysis
2
Meta-Analysis

• Meta-analysis is a statistical analysis of a
  collection of studies
• Meta-analysis methods focus on contrasting and
  comparing results from different studies in
  anticipation of identifying consistent patterns
  and sources of disagreements among these results
• Primary objective
• Synthetic goal (estimation of summary effect)
• vs
• Analytic goal (estimation of differences)

3
Types of Information
In summarizing the results and facilitating their
analysis

• Key variables that characterize
• Participants
• Interventions
• Outcome Measures
• Internal validity of each study.
• Results in natural units that are easily
  understood
• Standardized results, if these can be derived in
  a way that will facilitate comparisons across
  studies without being misleading

4
Steps of a Systematic Review

• Well formulated question
• Comprehensive data search
• Unbiased selection and extraction process
• Critical appraisal of data
• Synthesis of data
• Perform sensitivity and subgroup analyses if
  appropriate and possible
• Prepare a structured report

5
Outcome
Discrete (event)
Continuous (measured)
Mean Standardized Difference Mean
Difference (MD) (SMD)
Odds Relative Risk Ratio Risk Difference (OR) (
RR) (RD)
(Basic Data)
(Basic Data)
Overall Estimate
Overall Estimate
6
Effect measures discrete data

• P1 event rate in experimental group
• P2 event rate in control
  group
• OR Odds ratio P1/(1-P1)/P2/(1-P2)
• RD Risk difference P2 - P1
• NNT No. needed to treat 1 / (P2-P1)

7
Discrete - Odds Ratio (OR)
Event No event Experimental a b ne Control c d n
c
Pea/ne
Pcc/nc
number of patients experiencing event number of
patients not experiencing event Odds in
Experimental group a.d Odds in Control
group b.c
Odds Odds ratio
8
Odds Ratio (1)
Odds (E) Odds (C) OR
13/33 0.394
7/31 0.226
0.394/0.226 1.743
9
Odds Ratio (2)
Odds (E) Odds (C) OR
14/119 0.118
128/20 6.4
0.118/6.4 0.018
10
Discrete - Relative Risk (RR)
Event No event Experimental a b ne Control c d n
c
Pea/ne
Pcc/nc
number of patients experiencing event number of
patients Risk in Experimental group Risk
in Control group
Risk Risk Ratio
RR Pe/Pc a(cd)/(ab)c
11
Relative Risk (1)
Risk (E) Risk (C) RR
13/46 0.283
7/38 0.184
0.283/0.184 1.538
12
Relative Risk (2)
Risk (E) Risk (C) RR
14/133 0.105
128/148 0.865
0.105/0.865 0.121
13
Discrete - Risk Difference (Absolute Risk
Reduction)
Event No event Experimental a b ne Control c d n
c
Pea/ne
Pcc/nc
number of patients experiencing event number of
patients
Risk Risk Difference (Risk in experimental
group) (Risk in Control Group)
RD Pe- Pc a/(ab) c/(cd)
14
Risk Difference ARR (1)
13/46 0.283
Risk (E) Risk (C) RD
7/38 0.184
0.283 - 0.184 0.099
15
Risk Difference ARR (2)
Risk (E) Risk (C) RD
14/133 0.105
128/148 0.865
0.105 - 0.865 -0.76
16
NNT (Number Needed to Treat)

• NNT the number of people we need to treat to
  prevent one extra person from having the event
• NNT is the inverse of the risk difference
• NNT 1 / risk difference
• NNTs are specific to the particular length of
  follow up

17
Number Needed to Treat (1)
OR 1.743 RR 1.538 RD 0.099 NNT
1/0.099 10.1
18
Number Needed to Treat (2)
OR 0.018 RR 0.121 RD -0.76 NNT
1/0.76 1.316
19
When to use OR / RR / RD
Association OR RR RD (0,?) (0,?) (-
1,1) Decreased lt1 lt1 lt0 None 1 1 0 Increased
gt1 gt1 gt0
OR vs RR Odds Ratio Relative Risk if event
occurs infrequently (i.e. a and c
small relative to b and d) RR a(cd)/(ab)c
ad/bc OR Odds Ratio gt Relative Risk if event
occurs frequently RD vs RR When interpretation in
terms of absolute difference is better than in
relative terms (eg. Interest in absolute
reduction in adverse events)
20
Three Principal Issues
Consider when choosing a summary statistic

• Communication, i.e. a straightforward and
  clinically useful interpretation
• Consistency of the statistic across different
  studies
• Reasonable mathematical properties.

21
Risk ratio and odds ratio are better for
meta-analysis than the risk difference. Risk
ratios are easier to understand than odds ratios.
22

• Absolute measures can be more informative than
  relative measures because they reflect the
  baseline risk as well as the change in risk with
  the intervention.
• obtaining confidence intervals for absolute
  measures are problematic.

23

• Remember that NNT is useful for presenting
  results, but not for analysis purposes. The other
  three statistics (OR, RR, RD) can be used for
  either.

24
Outcome
Discrete (event)
Continuous (measured)
Mean Standardized Difference Mean
Difference (MD) (SMD)
Odds Relative Risk Ratio Risk Difference (OR) (
RR) (RD)
(Basic Data)
(Basic Data)
Overall Estimate
Overall Estimate
25
Continuous Data-Mean Difference (MD)
Number Mean Standard Deviation Experimental ne
se Control nc sc
26
Continuous Data Standardized Mean Difference
(SMD)
Number Mean Standard Deviation Experimental ne
se Control nc sc
27
When to use MD / SMD

• Mean Difference
• When studies have comparable outcome measures
  (ie. Same scale, probably same length of
  follow-up)
• A meta-analysis using MDs is known as a weighted
  mean difference (WMD)
• Standardized Mean Difference
• When studies use different outcome measurements
  which address the same clinical outcome (eg
  different scales)
• Converts scale to a common scale number of
  standard deviations

28
Heterogeneity
A variety of varieties

• Clinical diversity
• Methodological diversity
• Statistical heterogeneity

29
Clinical diversity

• Study location and setting
• Age, sex, diagnosis and disease severity of
  participants
• Treatments people may be receiving at the start
  of a study
• Dose or intensity of the intervention
• Definitions of outcomes.

30
Methodological diversity

• Sampling error may vary among studies (sample
  size)
• Study quality (for example, the extent to which
  allocation to interventions was concealed, or
  whether outcomes were assessed blind to treatment
  allocation)
• Analysis (for example, performing an
  intention-to-treat analysis compared with an as
  treated analysis)

31
Statistical heterogeneity

• The individual estimates of treatment effect will
  vary by chance, because of randomization.
• We need to know whether there is more variation
  than wed expect by chance alone.

32
Heterogeneity
How to Identify it

• Common sense
• are the patients, interventions and outcomes in
  each of the included studies sufficiently similar
• Statistical tests

33
Things You Can Do
With diversity and heterogeneity

• Using a different statistical model for combining
  studies, called a random effects meta-analysis.
• Investigate heterogeneity by splitting the
  studies into subgroups and looking at the forest
  plot.
• Investigating heterogeneity using
  meta-regression.

34
Statistical Models
For Calculating overall effects

• Fixed effects model (FEM)
• Random effects model (REM)

35
Fixed Effects Model

• Require from each study
• effect estimate and
• standard error of effect estimate
• Combine these using a weighted average
• pooled estimate
• where weight 1 / variance of estimate
• Assumes a common underlying effect behind every
  trial

sum of (estimate ? weight) sum of weights
36
Fixed-Effects Model
x
37
Random-Effects Model

• Assume true effect estimates really vary across
  studies
• Two sources of variation
• within studies (between patients)
• between studies (heterogeneity)
• What the software does
• Revise weights to take into account both
  components of variation
• Weight
• When heterogeneity exists we get
• a different pooled estimate (but not necessarily)
  with a different interpretation
• a wider confidence interval
• a larger p-value

1 Variance heterogeneity
38
Random-Effects Model
x
39
Effect of model choice on study weights
Larger studies receive proportionally less weight
in RE model than in FE model
40

• Thus,
• Random-effect model is more susceptible to
  publication bias.

41
Generic Inferential Framework

• Methodologic choices in dealing with
  heterogeneous data

42
Features in Graphic Display

• For each trial
• estimate (square)
• 95 confidence interval (CI) (line)
• size (square) indicates weight allocated
• Solid vertical line of no effect
• if CI crosses line then effect not significant
  (pgt0.05)
• Horizontal axis
• arithmetic RD, MD, SMD
• logarithmic OR, RR
• Diamond represents combined estimate and 95 CI
• Dashed line plotted vertically through combined
  estimate

43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
(No Transcript)
47
(No Transcript)
48
Fixed vs Random Effects Discrete Data

Fixed Effects
Random Effects
49
(No Transcript)
50
Cochrane Systematic Review
Steps

• Well formulated question
• Comprehensive data search
• Unbiased selection and extraction process
• Critical appraisal of data
• Synthesis of data
• Perform sensitivity and subgroup analyses if
  appropriate and possible
• Prepare a structured report

51
Heterogeneity Exploring it

• Subgroup analyses
• subsets of trials
• subsets of patients
• subgroups should be pre-specified to avoid bias
• Meta-regression
• relate size of effect to characteristics of the
  trials

52
Exploring Heterogeneity
subgroup analysis
53

• Perform a narrative, qualitative summary when
  data are too sparse, of too low quality or too
  heterogeneous to proceed with a meta-analysis

54
Funnel Plot Publication Bias
55
Possible sources of asymmetry in funnel plots

• Selection biases
• Publication bias
• Location biases
• Language bias
• Citation bias
• Multiple publication bias
• Poor methodological quality of smaller studies
• Poor methodological design
• Inadequate analysis
• Fraud
• True heterogeneity
• Size of effect according to study size (for
  example, due to differences in the intensity of
  interventions or differences in underlying risk
  between studies of different sizes)
• Artefactual
• chance

56
Funnel Plot

• Scatter plot of effect estimates against sample
  size
• Used to detect publication bias
• If no bias, expect symmetric, inverted funnel
• If bias, expect asymmetric or skewed shape

x x x x
x x x x x x x x
x x x
x x x x x x x
Suggestion of missing small studies
57
Symmetrical plot in the absence of bias.
In the absence of bias. smaller studies without
statistically significant effects are shown as
open circles in the figure.
58
Asymmetrical Plot
In the presence of reporting bias
59
Asymmetrical plot
In the presence of bias due to low methodological
quality of smaller studies.
60

• Any Question?!