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 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)

2

1

10

42

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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: 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

10

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