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Analysis of Repeated Measures Cost Data with Zero Observations: An Application to the Costs Associated with Inflammatory

This analysis demonstrates how Bayesian MCMC simulation methods can be used to model repeated measures cost data with zero-cost observations. The study focuses on the costs associated with inflammatory polyarthritis, specifically rheumatoid arthritis, using patient-specific healthcare and drug cost data. The two-stage model is used to estimate and cross-validate the results, incorporating parameter uncertainty and expert opinion.

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Analysis of Repeated Measures Cost Data with Zero Observations: An Application to the Costs Associated with Inflammatory

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  1. 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

  2. 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.

  3. 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)

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

  5. TWO-STAGE MODEL RESULTS

  6. 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.

  7. 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 TWO-STAGE MODEL: INTRODUCTION: TWO-STAGE MODEL RESULTS: 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. where MOTIVATING DATASET: 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) For i = 1 to M year of observation, j = 1 to N individuals ’s~Normal(0,1010), ’s~Normal(0,1010), ’s~Normal(0,2) 2~InverseGamma(0.001,0.001) ADVANTAGES OF THIS APPROACH: LOGISTIC MODEL probability(Cost) LINEAR MODEL ln(Cost) • 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. 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; 23 38-53. GENERAL METHODOLOGY: • 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 CONTACT DETAILS:For more information please e-mail: njc21@leicester.ac.uk

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