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. AB 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 AB CD 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)

MTC RANDOM EFFECTS MODEL 6 r jk = observed number of individuals experiencing an event out of n jk ; p jk = 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; d bk = pooled log odds ratios; σ 2 = 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

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 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 white = Anti-coagulant, dark grey = Anti-platelet, black = Mixed (Anti-coagulant + Anti-platelet), light grey = Placebo/no treatment

14 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 modelling o 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 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 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 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) 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 modelling o 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!

20 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