ANALYSIS OF REPEATED MEASURES COST DATA WITH ZERO OBSERVATIONS: An Application To The Costs Associated With Inflammatory Polyarthritis Nicola J Cooper, Paul C Lambert, Keith R Abrams, Alex J Sutton Department of Epidemiology and Public Health, University of Leicester

INTRODUCTION Modelling cost data often problematic due to: Strongly right skewed data distribution; & Significant percentage of zero-cost observations. This analysis demonstrates how repeated measures cost data may be modelled using Bayesian MCMC simulation methods.

MOTIVATING DATASET Patient-specific secondary healthcare & second line drug costs of 433 individuals with inflammatory polyarthritis (of which rheumatoid arthritis (RA) is a subset) Covariates: RA classification, Year since onset (1 to 5)

LOGISTIC REGRESSION probability(Cost) LINEAR REGRESSION ln(Cost)  RA Random effects (Intercept) Covariates Prob. cost  Year [1,2,3,4,5] Cost prediction Individuals Years Fixed effects Random effects (Intercept & slope) Fixed effects

TWO-STAGE MODEL RESULTS

CONCLUSIONS Use of MCMC Bayesian methods permits great flexibility in model specification, allowing non-standard models, such as the two-stage model, to be fitted in a straightforward manner. Advantages over the equivalent Classical approach include: Incorporation of greater parameter uncertainty in the results; Use of all data to estimate and cross-validate the model while only fitting the model a single time; Ability to incorporate expert opinion either directly or regarding the relative credibility of different data sources.

ANALYSIS OF REPEATED MEASURES COST DATA WITH ZERO OBSERVATIONS: AN APPLICATION TO THE COSTS ASSOCIATED WITH INFLAMMATORY POLYARTHRITIS Nicola J Cooper, Paul C Lambert, Keith R Abrams, Alex J Sutton. Department of Epidemiology and Public Health, University of Leicester, England INTRODUCTION: MOTIVATING DATASET: ADVANTAGES OF THIS APPROACH: ACKNOWLEDGEMENTS: Many thanks to the NOAR team for all their help REFERENCES: Cooper, N. J.; Sutton, A. J.; Mugford, M., and Abrams, K. R. Use of Bayesian Markov Chain Monte Carlo methods to model cost-of- illness data. Medical Decision Making. 2003; TWO-STAGE MODEL RESULTS: CONTACT DETAILS: For more information please The modelling of cost data is often problematic due to the distribution of such data. Commonly observed problems include: 1) a strongly right skewed data distribution; and 2) a significant percentage of zero-cost observations. In this analysis we illustrate how repeated measures cost data may be modelled using Bayesian MCMC simulation methods. Patient-specific secondary healthcare and second line drugs resource- use data from a prospective longitudinal study & the Norfolk Arthritis Register (NOAR) for 433 individuals with early inflammatory polyarthritis (figures 1&2). The NOAR database also includes information on various patient level covariates: RA classification – categorical (yes, no) Year since onset – continuous (years) The use of MCMC Bayesian methods permits great flexibility in model specification, allowing non-standard models, such as the two-stage model considered here, to be fitted in a straightforward manner. The advantages such an approach has over the equivalent Classical approach include: Incorporation of greater parameter uncertainty in the results; Use of all data to estimate and cross-validate the model while only fitting the model a single time; Ability to incorporate expert opinion either directly or regarding the relative credibility of different data sources. where For i = 1 to M year of observation, j = 1 to N individuals  ’s~Normal(0,10 10 ),  ’s~Normal(0,10 10 ),  ’s~Normal(0,  2 )  2 ~InverseGamma(0.001,0.001) GENERAL METHODOLOGY: TWO-STAGE MODEL: Two-stage (hurdle) model with random effects fitted to repeated measures (annual) data and evaluated within a Bayesian framework using WinBUGS software. Assumes linear relationship between cost and time LOGISTIC MODEL probability(Cost) LINEAR MODEL ln(Cost)