Trial sequential analysis of cumulative metaanalysis

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Trial sequential analysis of cumulative
meta-analysis
Jørn Wetterslev MD, Ph.D Copenhagen Trial
Unit Centre for Clinical Intervention
Research Rigshospitalet
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Group sequential boundaries in a single trial
Zk
Reject H0
Z2
Z?
-1.96 (plt0.025)
Accept H0
IF2
IF1
IF3
IF4
100
(Number of patients randomised)
IFk Ik / IMax
3
Group sequential boundaries same group size
Z 1.96
Z - 1.96
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Lan-DeMets discrete sequential boundaries

• Offers an opportunity for analysis
• at any time during a randomised trial without an
  increase in the final risk of a type 1 error
• Offers an opportunity to avoid unnecessary
  inclusion of participants in a trial when
  sufficient evidence has been reached before the
  calculated fixed sample size

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Discrete sequential boundaryin a randomised
clinical trial
Z-value
Discrete sequential boundary
Z-curve
Z 1.96
P 0.05
ni / N
N/N1.0
Information fraction
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Test when you want!

• Offers an opportunity to transfer group
  sequential boundaries from a single randomised
  trial to
• trial squential monitoring boundaries in
  cumulative meta-analyses as trials size vary a
  lot and cannot be changed retrospectively

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Meta-analysis

• Advantages
• Increase strenght and precision
• Makes it possible to analyse for bias
• Cautiousness
• Repetitive updating increase risk of type I
  error
• When is the information size sufficiently large
  ?
• Avoid Garbage in - garbage out

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• But what about
• cumulative meta-analysis ?
• There seems to be a substantial risk of increased
  random error in cumulative meta-analysis
• They are also undergoing repetitive testing on
  accumulating data !

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Trial sequential analysis

• Estimate required information size
• Trial sequential monitoring boundaries
• Adjust for repetitive testing
• Re-evaluate the evidence in a cumulative
  meta-analysis

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How much information do we need to make a
decision?

• How do we protect the error risk levels when
  cumulative meta-analysis are
• updated repeatedly with new trials and analysed
  multiple times ?

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The required information size in meta-analysis

• should be at least as large as the sample size
  in a single well-powered randomised trial

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Sample size in a randomised clinical trials

• The number of participants to be included in
  the trial to detect or reject an anticipated
  intervention effect µ with the chosen error risks
• Type 1 error ?
• Type 2 error ? (power 1- ?)

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The sample size in a randomized clinical trial
with equal group sizes

• SS 4 (Z?/2 Z?)2 ? / ?2
• ? PC - PE intervention effect
• ? P (1- P) the variance P (PCPE) / 2
• PC and PE
• event rates in control and intervention group

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Information size in meta-analysis

• Also the information size in a cumulative
  meta-analysis should be increased with multiple
  up-dating when testing are repeated adding
  information from new trials

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The information size in a meta-analysis with
equal group sizes and a binary outcome

• IS ? SS 4 (Z?/2 Z?)2 ? / ?2
• ? PC - PE intervention effect
• ? P (1- P) the variance
• P (PCPE) / 2
• PC and PE
• event proportions in control and intervention
  group

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Information size in acumulative meta-analysis of
randomised trials

• Should account
• For heterogeneity between trials
• Repetitive testing on accumulating data when the
  meta-analysis is up-dated

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An a priori heterogeneity- adjusted information
size (APHIS)

• Calculated setting µ and ? to a clinically
  relevant value possibly found in evidence based
  on other interventions in that area

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Low-bias heterogeneity-adjusted information size
(LBHIS)

• Calculated based on the meta-analytic estimate
  of µ and ? for k trials with low risk of bias in
  the meta-analysis

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Sum upinformation size in a cumulative
meta-analysis

• Should be increased with the heterogeneity
  between the trials estimates of the
  intervention-effects
• Should be increased in multiple up-dating adding
  new information from new trials

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Trial sequential monitoring boundary
Zk
Reject H0
C1
C2
C3
Z?
1.96 (plt0.025)
IF2
IF1
IF3
IF4
100
(N IS)
(Number of randomised patients)
IFk Ik / IMax
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Trial sequential monitoring boundary
Zk
Reject H0
Z2
Z?
1.96 (plt0.025)
IF2
IF1
IF3
IF4
100
(Number of randomised patients)
IFk Ik / IMax
22
Trial sequential monitoring boundary
Zk
Reject H0
Z2
Z?
1.96 (plt0.025)
Accept H0
IF2
IF1
IF3
IF4
100
(Number of randomised patients)
IFk Ik / IMax
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Trial sequential analysis (TSA)
Zk
3.71 (P 0.0001)
Z 1.96
P 0.05
Number of randomised patients
N IS
Discrete sequential boundary
Cumulative Z-score
Nominal P-value
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• An example from perioperative medicine
• Perioperative beta-blockade
• in
• non-cardiac surgery
• Bangalore S et al
• Lancet 2008

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Non-fatal myocardial infarction perioperative
ß-blockade
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Non-fatal myocardial infarction perioperative
ß-blockade
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Non-fatal stroke perioperative ß-blockade
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All-cause mortality with perioperative ß-blockade
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All-cause mortality with perioperative ß-blockade
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Atrial fibrillation off vs. on pump CABG
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Atrial fibrillation off vs. on pump CABG
APHIS 5,021
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72
I2 47.3
Interventionseffekt RRR 20
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AT III for critically ill patients No
significant interaction between risk of bias and
intervention effect I2 0 probably due to
lack of effect of AT III on mortality
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Trial sequential analysis of AT III effect on
mortality in 3,458 patients
APHIS 3,263 RRR 10 (49 to 44)
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Trial sequential analysis of AT III effect on
mortality in 3,458 patients
LBHIS 25,303 RRR 5
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Thank you !