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

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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 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

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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

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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)

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

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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

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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

•For example, Model 1 (Independent ‘betas’) would require estimation of:

25 baselines

16 treatment means + random effects

16 regression coefficients

1 between-study variance

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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

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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