Simon Thompson University of Cambridge Richard Nixon at the MRC Biostatistics Unit, Cambridge (2001-2007) Nasty bivariate distributions for cost-effectiveness analyses Simon Thompson University of Cambridge PSI Conference, London, May 2017

Richard Nixon Simon Thompson 1997-2000: PhD at MRC BSU on public health intervention studies 2001-07: Post-doctoral research at MRC BSU 2007-16: Research at Novartis, Basel 2016: PSI/RSS Award for Statistical Excellence Simon Thompson 1996-99 Imperial College 2000-11 MRC BSU, Cambridge 2011- University of Cambridge

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

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

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

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

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

RN R BUGS WinBUGS ST Computational expertise Time

UK700 trial RCT of case-management for psychotic patients: Intensive (case-load 10-15 patients) vs. Standard (case-load 30-35 patients) 708 patients randomised Outcome: Days in hospital over 2 years Costs: Costs from resource use (social, hospital, community) x unit costs

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

UK700 trial: cost data Costs over 2 years Control Intervention

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 …

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

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

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

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

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

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

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

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

Differences between centres CEAC Fixed effects: Random effects:

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

Googling “Richard Nixon BSU” BSU = Bridgewater State University