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ADDRESSING BETWEEN-STUDY HETEROGENEITY AND INCONSISTENCY IN
MIXED TREATMENT COMPARISONS
Application to stroke prevention treatments for Atrial Fibrillation patients.
Nicola Cooper, Alex Sutton, Danielle Morris,
Tony Ades, Nicky Welton
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MIXED TREATMENT COMPARISON
• MTC - extends meta-analysis methods to enable comparisons between all relevant comparators in the clinical area of interest.
A B
C
Option 1: Two pairwise M-A analyses (A v C, B v C)
Option 2: MTC (A v B v C) provides probability each treatment is the ‘best’ of all treatments considered for treating condition x.
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HETEROGENIETY & INCONSISTENCY
• As with M-A need to explore potential sources of variability:
i) Heterogeneity - variation in treatment effects between trials within pairwise contrasts, and
ii) Inconsistency - variation in treatment effects between pairwise contrasts
• Random effect - allows for heterogeneity but does NOT ensure inconsistency is addressed
• Incorporation of study-level covariates can reduce both heterogeneity and inconsistency by allowing systematic variability between trials to be explained
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OBJECTIVE
• To extend the MTC framework to allow for the incorporation of study-level covariates
• 3 models:
i) Different regression coefficient for each treatment
ii) Exchangeable regression coefficient
iii) Common regression (slope) coefficient
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EXAMPLE NETWORK
A B
C D
Stroke prevention treatments for Atrial Fibrillation patients (18 trials)
A = Placebo
B = Low dose anti-coagulant
C = Standard dose anti-coagulant
D = Standard dose aspirin
Covariate = publication date (proxy for factors relating to change in clinical practice over time)
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1
10
42
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MTC RANDOM EFFECTS MODEL
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0 :Note
),(~),(~
)(logit
treatment, for trial),(~
22
AA
AbAkbkjbk
jkbjb
jbjk
jkjkjk
d
ddNormaldNormal
bk
bkp
kjnpBinomialr
rjk = observed number of individuals experiencing an event out of njk;
pjk = probability of an event; jb = log odds of an event in trial j on
‘baseline’ treatment b; jbk = trial-specific log odds ratio of treatment k
relative to treatment b; dbk = pooled log odds ratios; σ2 = between
study variance
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MODEL 1: Different regression coefficient for each treatment
NOTE: Relative treatment effects for the active treatment versus placebo are allowed to vary independently with covariate; thus, ranking of effectiveness of treatments allowed to vary for different covariate values
),)((~ 2 jAbAkAbAkjbk XddNormal
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MODEL 2: Exchangeable regression coefficient
),(~
),)((~2
Ak
2
B
jAbAkAbAkjbk
BNormal
XddNormal
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MODEL 3: Common regression (slope) coefficient
Note: Relative treatment effects only vary with the covariate when comparing active treatments to placebo.
AbddNormal
AbXddNormal
AbAk
jAAAkjbk
if ),(
if),(~
2
2
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FULL 17 TRT NETWORK
AD A
Low A-C + Low A
Std A-C
Low A-C
Low A
X I
Fixed A-C
Placebo
Med A
High A
D + Low A
D
C + Low A
Low A-C + Med A
2 2
1
21
1
1
1
1
1
1
1
1
3
44
2
46
1
1
11
2
1 1
T
Std A-C + T
11
1
17 treatments25 trials60 data points
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FULL 17 TRT NETWORK: ISSUES• Model becomes over-specified as number of parameters to be estimated approaches or exceeds the number of data points available
e.g. Model 1 - requires estimation of 25 baselines, 16 treatment means, 16 regression coefficients, & between-study variance (+ random effects).
• May be sensible to consider treatments within classes
e.g. Anti-coagulant, Anti-platelet, Both
• Best fitting model “exchangeable treatment x covariate effects by class”
Reference: Cooper NJ, Sutton AJ, Morris D, Ades AE, Welton NJ. Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: Application to stroke prevention treatments in individuals with non-rheumatic Atrial Fibrillation. Submitted to Statistics in Medicine
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DISCUSSION• Number of different candidate models - especially for large treatment networks often with limited data
• Need to be aware of limitations posed by available data & importance of ensuring model interpretability and relevance to clinicians
• Uncertainty in the regression coefficients and the treatment differences not represented on graphs (which can be considerable)
• Results from MTC increasingly used to inform economic decision models. Incorporation of covariates may allow separate decisions to be made for individuals with different characteristics