1. Simon Thompson University of Cambridge
Richard Nixon at the MRC Biostatistics Unit, Cambridge ( ) Nasty bivariate distributions for cost-effectiveness analyses
Simon Thompson
University of Cambridge
PSI Conference,
London, May 2017

2. Richard Nixon Simon Thompson
: PhD at MRC BSU on public health intervention studies
: Post-doctoral research at MRC BSU
: Research at Novartis, Basel
2016: PSI/RSS Award for Statistical Excellence
Simon Thompson
Imperial College
MRC BSU, Cambridge
University of Cambridge

3. My introduction to cost data (late 1990s)
Health service costs in RCT of women with menorrhagia

4. Statistical analysis of cost data (BMJ, 2000)
Despite usual skewness in cost distributions, the arithmetic mean is the most informative measure
Analysis based on transforming cost data or comparing medians may provide misleading conclusions

5. Analysis of cost data (early 2000s)
Focus on population mean
Sample mean is unbiased but potentially inefficient
Parametric modelling might be better
Application to cost-effectiveness analysis
Bivariate problem
Use of covariates

6. Parametric modelling of cost data
Stat Med 2004
Health Econ 2005
Med Dec Making 2005

7. Parametric modelling of cost data
Correct choice of distribution increases efficiency
Incorrect choice of distribution can lead to major bias and incorrect variance
Inferences about the population mean are sensitive to model choice, even amongst models that fit the data equally well

8. RN R
BUGS
WinBUGS ST
Computational
expertise
Time

10. UK700 trial
RCT of case-management for psychotic patients: Intensive (case-load patients) vs. Standard (case-load patients) 708 patients randomised Outcome: Days in hospital over 2 years Costs: Costs from resource use (social, hospital, community) x unit costs

11. UK700 trial:
effectiveness data
Days in hospital over 2 years
Control
Intervention

12. UK700 trial:
cost data
Costs over 2 years
Control
Intervention

13. Overall cost-effectiveness
For person j in trial arm i = 1,2 Eij = effectiveness outcome Cij = cost  = mean,  = SD, of some chosen distribution
Distributions: Normal, Gamma, log-Normal …

14. Model without covariates
CE-plane: plot of incremental costs vs. incremental effects
CEAC: plot of probability that the intervention is cost-effective against willingness-to-pay value
Estimation using MCMC

15. Overall cost-effectiveness
CE-plane (5% & 80% contours)
CEAC
Gamma model fits data much better

16. Covariate adjustment xij = baseline continuous covariate (centred)
Example: xij = number of days in hospital in 2 years
prior to randomisation
Gamma distributions used for costs and effects

17. Covariate adjustment
CE-plane (5% & 80% contours)
CEAC
Including covariate improves fit of model

18. Differences between subgroups (interactions)
xij = baseline covariate (centred)
Ii = 0 (control) or 1 (intervention)
Example: xij = 0 (borderline intelligence)
= 1 (normal intelligence)
Gamma distributions used for costs and effects

19. Subgroup differences
CE-plane (5% & 80% contours)
CEAC
Interaction test: change in deviance 2 (2 df): P=0.02

20. Differences between centres
4 centres in the UK700 trial
(Es ,Cs ), s = 1,…,4 are centre interaction parameters:
Modelled as fixed effects
Modelled as random effects (bivariate normal distribution)
Gamma distributions used for costs and effects

21. Differences between centres
CE-plane (5% & 80% contours)
Fixed effects:
Random effects:

22. Differences between centres
CEAC
Fixed effects:
Random effects:

23. Random effects in cost-effectiveness analysis
J Health Econ 2006
Health Econ 2007
Med Dec Making 2010

24. Googling “Richard Nixon BSU”
BSU = Bridgewater State University