1 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
Jan 11, 2016
1
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
2
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.
3
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 explain it nor ensure inconsistency is addressed
• Incorporation of study-level covariates can reduce both heterogeneity and inconsistency by allowing systematic variability between trials to be explained
4
OBJECTIVE• To extend the MTC framework to allow for the
incorporation of study-level covariates
• 3 potential models:
i) Independent treatment x covariate interactions for each treatment compared to placebo
ii) Exchangeable treatment x covariate interactions for each treatment compared to placebo
iii) Common treatment x covariate interactions for each treatment compared to placebo
5
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)
2
1
10
42
7
MTC RANDOM EFFECTS MODEL
6
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
7
MODEL 1: Independent 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
8
MODEL 2: Exchangeable regression coefficient
),(~
),)((~2
Ak
2
B
jAbAkAbAkjbk
BNormal
XddNormal
9
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
•For example, Model 1 (Independent ‘betas’) would require estimation of:
25 baselines
16 treatment means + random effects
16 regression coefficients
1 between-study variance
12
FULL 17 TRT NETWORK: Options• Assume treatment x covariate interactions exchangeable or common within treatment classes
For example,
Anti-coagulants, Anti-platelets, Both
Placebo / No treatment
Alternate Day Low Dose
Aspirin
Fixed Low Dose Warfarin & Low Dose
Aspirin
Adjusted Standard Dose
Warfarin
Adjusted Low Dose Warfarin
Aspirin
Diff Doses
Ximelagatran Indobufen
Fixed Low Dose Warfarin
Medium Dose Aspirin
High Dose Aspirin
Dipyridamole & Low Dose
Aspirin
Dipyridamole
Clopidogrel & Low Dose Aspirin
Fixed Low Dose Warfarin
& Medium Dose Aspirin
2
2
1
21
1
1
1
1
1
1
1
1
431
4
4
32
1
11
2
2 1
white = Anti-coagulant, dark grey = Anti-platelet, black = Mixed (Anti-coagulant + Anti-platelet), light grey = Placebo/no treatment
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FULL 17 TRT NETWORK: Options• Assume treatment x covariate interactions exchangeable or common within treatment classes
o For example,
Anti-coagulants, Anti-platelets, Both
• Simplify treatment network through covariate modellingo For example,
i) model different doses of same drug using covariates
ii) assume effect of combinations of drugs additive (on scale of analysis)
Alternate Day Low Dose
Aspirin
Fixed Low Dose Warfarin & Low Dose
Aspirin
Adjusted Standard Dose
Warfarin
Adjusted Low Dose Warfarin
Aspirin
Diff Doses
Ximelagatran Indobufen
Fixed Low Dose Warfarin
Placebo / No treatment
Medium Dose Aspirin
High Dose Aspirin
Dipyridamole & Low Dose
Aspirin
Dipyridamole
Clopidogrel & Low Dose Aspirin
Fixed Low Dose Warfarin
& Medium Dose Aspirin
2
2
1
21
1
1
1
1
1
1
1
1
431
4
4
32
1
11
2
2 1
Assume a dose-response relationship across aspirin regimens
Fixed Low Dose Warfarin & Low Dose
Aspirin
Adjusted Standard Dose
Warfarin
Adjusted Low Dose Warfarin
Aspirin (Doses)
Ximelagatran Indobufen
Fixed Low Dose Warfarin
Placebo / No treatment
Dipyridamole & Low Dose
Aspirin
Dipyridamole
Clopidogrel & Low Dose Aspirin
Fixed Low Dose Warfarin
& Medium Dose Aspirin
2
2
1
21
1
1
1
1
1
9
4
7
2
1
1
1
2
2 1
2
Assume a dose-response relationship across aspirin regimens
Fixed Low Dose Warfarin & Low Dose
Aspirin
Adjusted Standard Dose
Warfarin
Adjusted Low Dose Warfarin
Aspirin (Doses)
Ximelagatran Indobufen
Fixed Low Dose Warfarin
Placebo / No treatment
Dipyridamole & Low Dose
Aspirin
Dipyridamole
Clopidogrel & Low Dose Aspirin
Fixed Low Dose Warfarin
& Medium Dose Aspirin
2
2
1
21
1
1
1
1
1
9
4
7
2
1
1
1
2
2 1
2
Assume effect of aspirin is additive when given in combination
Adjusted Standard Dose
Warfarin
Adjusted Low Dose Warfarin
Aspirin (Doses)
Ximelagatran Indobufen
Placebo / No treatment
Dipyridamole & possible
Aspirin (Doses)
Clopidogrel & Low Dose Aspirin
Fixed Low Dose Warfarin
& possible Aspirin (Doses)
2
1
21 2
9
4
7
2
4
2 1
2
1
2
1
Assume effect of aspirin is additive when given in combination
• Reduced 16 treatments to 9 groupings• Strong assumptions made that need exploring• Work in progress
2
19
FULL 17 TRT NETWORK: Options• Treatment x covariate interactions exchangeable or common within treatment classes
o For example,
Anti-coagulants, Anti-platelets, Both
• Simplify treatment network through covariate modellingo For example,
i) model different doses of same drug using covariates
ii) assume effect of combinations of drugs additive (on scale of analysis)
• Combination of the above. Lots of possibilities!
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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