This document discusses statistics used in meta-analyses. It explains that meta-analyses statistically combine results from multiple studies on a topic. Effect measures are calculated for individual studies and then combined to find an overall effect. For dichotomous outcomes, common effect measures are risk ratio, odds ratio, and absolute risk reduction. Random effects models account for heterogeneity between studies, while fixed effect models assume one true effect. Forest plots visually display individual study results and the overall effect, allowing readers to assess consistency and precision.

1. Statistics in Meta-analysis and
the forest plot
Dr. Imran Rizvi
Assistant professor, Neurology
KGMU

2. Outline
• Statistics in meta-analysis
• Visual display of the results: Forest plot
• How to do the analysis: RevMan

3. Introduction

4. Meta-analysis
• Type of secondary research.
• The statistical combination of results from two or
more separate studies.

5. Effect/ Treatment Effect

6. Meta-analysis answers the following
questions
• What is the direction of effect?
• What is the size of effect?
• Is the effect consistent across studies?

7. Statistics in meta-analysis
Meta-analysis is a 2 stage process.
1. Calculate an effect estimate (summary statistics) for
each study (RR, OR, HR etc for each study)
2. Calculate the overall treatment effect (usually as a
weighted average of these summary statistics).

8. Calculating effect measure of individual
studies
• Calculation of effect measure depends upon the type of
outcome data.
• Outcome data can be of following 4 types.
Dichotomous (Binary data)
Continuous data
Ordinal data
Time to event (survival rate)

9. Types of outcome Definition and example
Dichotomous (Binary) When the outcome for every participant
falls in one of two possibilities.
Example: Dead/Living
Clinical Improvement/No clinical
improvement.
Continuous Data that can take any value in a specified
range.
Example: BP reduction following T/t
Blood sugar reduction following T/t
Ordinal Ordinal outcome data arise when each
participant is classified in a category and
when the categories have a natural order.
Mild/moderate/severe
Pain scales/ disability scales
Time to event Time elapsed before an event is
experienced.
Time to death after cancer/MI

10. Effect measures used according to the type of outcome
Type of Outcome Effect measure (Summary)
commonly used
Dichotomous (Binary) Risk Ratio= Relative Risk= RR
Odds ratio
Risk difference (ARR)
NNT
Continuous The mean difference and the
standardized mean difference.
Ordinal Proportional Odds ratio
Longer ordinal scales: continuous data
Shorter ordinal scales: can be clubbed
into 2 categories to be analysed as
dichotomous data
Time to event Hazard ratio

11. Risk Ratio/ Relative Risk
• Most commonly used measure when the outcome is
dichotomous.
• Ratio of risk of event in the experimental group to Risk of
event in the control group.
• RR= Risk in exposed/ Risk in non exposed

13. RR= A/A+B
C/C+D
Treatment Event No event Total
Intervention arm A B A+B
Control arm C D C+D

14. Example
• 545 TBM patients were randomly assigned to receive
dexamethasone (N=274) Or placebo (N=271).
• The primary outcome measure was death.
• 87 deaths occurred in the dexamethasone arm, 112
deaths occurred in the placebo arm.
• What is the RR ?

15. RR calculation
Treatm
ent
Death Alive Total
Dexa 87 187 274
Placebo 112 159 271
545
• Risk of event in
exposed=
87/274=31.75%
• Risk of event in
control=112/271=41.33
%
• RR=31.75/41.33=0.77

16. Interpretation
• RR=1: Risk of event in the exposed is equal to the risk of
event in the non exposed (No association).
• RR<1: Risk of event in exposed is less than risk of event
in the non exposed.
• RR>1: Risk of event in exposed is more than risk of event
in the non exposed.

17. Odds ratio
• Ratio of the odds of an event in the Treatment group to
the odds of an event in the control group.
• The odds of an event is the number of events divided by
the number of non-events.
• Odds ratios are most commonly used in case-control
studies.

18. OR calculation
Treatm
ent
Event No
event
Total
Interve
ntion
arm
A B A+B
Control
arm
C D C+D
• Odds of event in
intervention arm= A/B
• Odds of event in
control arm= C/D
• OR= odds of event in
intervention/odd of
event in control
• A/B÷C/D=AD/BC

19. Interpretation
• OR=1 Exposure does not affect odds of outcome.
• OR>1 Exposure associated with higher odds of outcome.
• OR<1 Exposure associated with lower odds of outcome.

20. Absolute Risk Reduction
• ARR is also called as Risk difference
• The difference between the risk of an event in the control
group and the risk of an event in the treated group.

21. ARR
Treatm
ent
Event No
event
Total
Interven
tion arm
A B A+B
Control
arm
C D C+D
• Risk of event in
controls: C/C+D
• Risk of event in
intervention: A/A+B
• ARR= C/C+D – A/A+B

22. Treatm
ent
Death Alive Total
Dexa 87 187 274
Placebo 112 159 271
545
• Risk of death in
controls=112/271=
41.33%
• Risk of death in
intervention=87/274=
31.75
• ARR=41.33-
31.75=9.58%
If 100 TBM cases are given dexa
about 10 will be prevented from
dying

23. Number needed to treat
• The NNT is the average number of patients who need to
be treated to prevent one additional bad outcome.
• NNT is the reciprocal of the absolute risk reduction (i.e.,
1/absolute risk reduction).
• The higher the NNT, the less effective is the treatment

24. NNT
Treatm
ent
Event No
event
Total
Interven
tion arm
A B A+B
Control
arm
C D C+D
• Risk of event in
control= C/C+D
• Risk of event in
intervention=A/A+B
• ARR=C/C+D-A/A+B
• NNT=1/ARR

25. NNT
Treatm
ent
Death Alive Total
Dexa 87 187 274
Placebo 112 159 271
545
• Risk of death in
controls=112/271= 41.33%
• Risk of death in
intervention=87/274=
31.75
• ARR=41.33-31.75=9.58%
• NNT=100/9.58=10.45
About 10 TBM cases needs
to be given dexa to
prevent 1 death.

26. Effect estimate Definition Formula Advantage
Odds ratio Ratio of odds of event
in intervention group
to odds of event in the
control group.
A/B÷C/D=AD/BC Most useful measure
for case-control study.
Risk ratio Ratio of risk of event
in intervention group
to risk of event in the
control group.
A/A+B÷C/C+D Useful in clinical
trials.
Absolute risk reduction Difference between
risk of event in control
and risk of event in
intervention group.
C/C+D-A/A+B Useful in clinical
trials.
Number needed to treat Average number of
patients that needs to
be treated to prevent
one additional poor
outcome
1/ARR Useful for clinical
trials and to convey
information to the
patient

27. Confidence interval
• The results of any experiment are an estimate of the truth.
• The true effect of treatment may actually be greater or
less than what we observed.
• CI Is the range of values that is likely to include the true
population value .
• CIs give us an idea of how confident we are about a
studies estimate of treatment effect.
• The narrower the range, the more precise the study’s
estimates.
• 95% CI represents the range within which we can be 95
%certain that the true answer lies.

28. Helps to decide significance?

30. Step 2: Calculation of overall t/t effect
• Overall effect is calculated by a weighted averaged of
individual studies.
• Weight of individual study= inverse of variance
Two models are commonly used to combine the effects of
individual studies
1. Fixed Effect model
2. Random Effects model

31. Fixed Effect model
• We assume that there is one true effect size that underlies
all the studies in the analysis.
• All the studies are evaluating the same true effect.
• Any difference observed in the effect size is due to
random error.
• Fixed effect= common effect.
• There is only one source of variance i.e sampling error.

33. Random effects model
• We assume that Effect size may differ from study to
study.
• For example effect size may vary according to the age of
participants, dose of drug, timing of outcome assessment.
• Random effects model allows for heterogeneity.
• Consider there are 2 sources of variance
1. Within study variance (sampling error)
2. Between study variance (Age, dose, outcome
assesment)

35. • To calculate the overall mean the weighted average of
individual studies is calculated.
• Weighted average = Sum of(estimate X Weight)/sum of W
• Weight = 1/Variance

36. Weight of studies in the 2 models

37. Assumption Heterogeneity Confidence
interval
Fixed effect model •One true effect
underlies all
studies.
•Differences are
due to chance.
Ignored Narrow
Random effects
mode
•Effect size varies
amongst studies.
•Difference are not
due to chance
Taken into account Wider

38. Which model to use ?
• If significant clinical or statistical heterogeneity is present
use the random effects model. Otherwise use fixed effect
model.
• Clinical heterogeneity: Age, population, dose of
intervention, method of outcome assessment.
• Statistical heterogeneity.

39. DISPLAYING THE RESULTS: FOREST PLOT

40. Forest plot
• The typical graph used for displaying results of a meta-
analysis: forest plot
• Blobbogram
• At one glance we can see the effect of individual studies
as well as the overall effect.

43. • The horizontal axis usually represents the scale of
statistics. (OR, RR, ARR, SMD etc).
• The vertical line is known as the “line of null effect.”
• This line is placed at the value where there is no
association between an exposure and outcome.
• For OR, RR the vertical line passes through 1.
• For ARR, MD the vertical line passes through 0.

46. Study lines

47. • Effect estimates of individual studies are represented by
boxes.
• Size of the box represents the weight of the study.
• The horizontal line represents the 95% confidence
intervals of the study.
• Any study line which crosses the line of null effect does
not illustrate a significant result.

50. The diamond

51. • The diamond represent the overall effect estimate.
• A vertical line through the vertical points of the diamond,
represents the overall effect.
• The horizontal points of the diamond represent the 95%
confidence interval of this combined point estimate.
• If the horizontal tips of the diamond cross the vertical line,
the combined result is not significant.

56. DEMO: HOW TO DO
ANALYSIS IN REVMAN

57. Hypothetical Meta-analysis
• Intensified ATT regimen Vs Standard ATT regimen for
management of TBM.
• P= TBM patients >18 years
• I= intensified ATT (Levofloxacin plus HRZS)
• C= standard ATT (HRZS)
• O= death at 6 months
• Search Literature
• Narrow down the articles
• Data extraction

73. Forest plot

74. THANK YOU