A COMPARISON OF STATISTICAL METHODS FOR COST-EFFECTIVENESS ANALYSES THAT USE DATA FROM CLUSTER RANDOMIZED TRIALS

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1 A COMPARISON OF STATISTICAL METHODS FOR COST-EFFECTIVENESS ANALYS THAT U DATA FROM CLUSTER RANDOMIZED TRIALS M Gomes, E Ng, R Grieve, R Nixon, J Carpenter and S Thompson Health Economists Study Group meeting York, January 2011

2 Overview CEA can be undertaken alongside CRTs Unit of randomisation is the cluster, not the patient Previous review found that most of CEA of CRTs ignore clustering Methods are available but it is unclear which performs best Aim is to evaluate relative performance of alternative methods We use simulations and a case study

3 Methods for analyses Seemingly Unrelated Regressions System of regression equations allowing error terms to be correlated Implemented with and without Generalised Estimating Equations Independent estimating equations with. Two-Stage Bootstrap Non-parametric. Involves resampling clusters as well as individuals Unless many clusters, it can overestimate the variance. Implemented using a estimator (Davison & Hinkley 1997). Multilevel Models Bivariate normal. Variance, correlation constant across clusters and arms

4 DGP is general and flexible Data Generating Process Cost-effectiveness data simulated in 2 stages, clusters then individuals Can mimic a wide range of potential scenarios varying parameters (e.g. No. of clusters, cluster size dist, ICCs, correlation) allow various distributions of the data at cluster and individual level Fair to all methods Performance measures - Bias - Root mean square error (rm) - Confidence interval (CI) coverage and width 2000 simulations throughout

5 Varying parameters for base case and SA Parameter Rationale for consideration Base case Range for SA N GEE, SUR, TSB rely on asymptotics 20 3 to 30 CoV GEE, SUR, TSB not tested for imbalance 0 0 to 1 ICC cost See if methods can handle higher ICCs to 0.3 ICC QALY As above to 0.3 η GEE,SUR,MLM assume normal errors to 3 - True incremental cost = True incremental QALY = True INB = 1000 (NICE threshold = /QALY) - True ICER =

6 Mean () bias Results for base case (Parameter of interest INB) out (2.45) SUR GEE 2SB MLM (2.45) (2.45) out (2.45) (2.45) ML* (2.45) rm CI coverage Mean CI width Lower tail coverage Upper tail coverage * MLM estimated by MCMC in WinBUGS produced similar results

7 Results for one-way SA CI coverage SUR GEE 2SB MLM out ML Base case Few clusters per arm (M=3) Few individuals per cluster (n m =10) Highly imbalanced cluster size (cv imb =1) High ICC for costs (ICCc=0.3) High ICC for outcomes (ICCe=0.3) Highly skewed gamma costs (cv cost =3)

8 CI coverage Multi-way SA CI coverage From moderate to few clusters (10, 5, 3 clusters per arm) From moderate to high cluster size imbalance (CoV=0.5 and 1) moderate imbalance (CoV=0.5) high imbalance (CoV=1) No. of clusters per arm No. of clusters per arm MLM GEE TSB_shrink SUR

9 rm Multi-way SA - rm From moderate to few clusters (10, 5, 3 clusters per arm) From moderate to high cluster size imbalance (CoV=0.5 and 1) moderate imbalance (CoV=0.5) high imbalance (CoV=1) No. of clusters per arm No. of clusters per arm GEE MLM TSB_shrink SUR

10 Multi-way SA CI coverage SUR GEE 2SB MLM out out ML Mean () Bias 6.63 (4.40) 6.63 (4.41) 6.63 (4.40) 7.10 (4.38) 9.08 (4.42) 7.95 (4.33) rm CI coverage Mean CI width Lower tail coverage Upper tail coverage

11 Case study - Outreach Case study with a data structure that reflects our DGP. 40 clusters; balanced clusters; skewed costs (CoV=1.6) out Robust SUR GEE 2SB MLM Robust Robust out ML Incremental cost () (15.84) (19.49) (19.47) (24.67) (18.94) (19.27) Incremental outcome () (0.020) (0.046) (0.046) (0.051) (0.045) (0.046) INB () (403.2) (934.7) (933.9) (1031.4) (908.7) (917.8) Methods perform similarly. TSB without shows much larger CIs

12 Summary - Methods that ignore clustering give poor performance - MLMs performs well throughout - GEE and SUR: Perform badly when clusters<20 Worsen with high cluster size imbalance - 2SB performs well once corrected Except when cluster size is highly unbalanced (poor precision)