ADDRESSING BETWEEN-STUDY HETEROGENEITY AND INCONSISTENCY IN MIXED TREATMENT COMPARISONS

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. 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. A B C

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 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 models: • Different regression coefficient for each treatment • Exchangeable regression coefficient • Common regression (slope) coefficient

5. EXAMPLE NETWORK 2 A B 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 7 2 4 1 10 C D Covariate = publication date (proxy for factors relating to change in clinical practice over time)

6. MTC random effects model 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 logodds ratio of treatment k relative to treatment b;dbk= pooled log odds ratios; σ2= between study variance

7. 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

8. MODEL 2: Exchangeable regression coefficient

9. MODEL 3: Common regression (slope) coefficient Note: Relative treatment effects only vary with the covariate when comparing active treatments to placebo.

10. FULL 17 TRT NETWORK 17 treatments 25 trials 60 data points

11. 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

12. 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