1. Modelling Partially & Completely Missing Preference-Based Outcome Measures (PBOMs) Keith Abrams Department of Health Sciences, University of Leicester, UK John Brazier, Tony O’Hagan, Samer Kharroubi Centre for Bayesian Statistics in Health Economics (CHEBS), University of Sheffield, UK Aki Tsuchiya Sheffield Health Economics Group (SHEG), University of Sheffield, UK

2. Outline Missing PBOM Data Modelling Missing PBOM Data Example - IBS Study Other Scenarios & Links with Other Work

3. Why is data missing? Partially Missing –Missing PBOM on some individuals –Missing dimensions of PBOM Completely Missing Data –Only collected on a sub-sample –Not collected at all

4. Why is missing data important? Efficiency Precision Missing at Random (MAR) conditional on covariates & other outcomes, e.g. random sub-sample Informative missing data, e.g. death, produce biased results

5. Solutions to missing data? Collect PBOMs in RCTs evaluating health- care interventions Minimise missing data Complete case analysis – problem if substantial ‘missing data’ Model missing data –Mean value imputation – limited applicability –Multiple Imputation – accounts for uncertainty –Regression imputation – uses relationship between covariates & PBOMs –Bayesian approach …

6. Multivariate Model - 1 Missing data are treated as parameters & imputed/predicted using the posterior predictive distribution

7. Multivariate Model - 2 Product Normal Formulation:

8. Example – IBS Study N=161 patients with Irritable Bowel Syndrome (IBS) PBOMs: SF-6D & EQ-5D NPBOMs: IBS-QoL [34 items] (Overall & 8 sub-scales) Demographic data: age & sex Assessed at Baseline & 3 months follow-up Missing Data –Age & Sex complete –IBS n=13 –EQ-5D n=4 –IBS & EQ-5D n=1

9. Example – IBS Study Using Multivariate Model for EQ-5D & IBS (+ age & sex) implemented in WinBUGS using ‘vague’ priors Overall (n=161) –EQ-5D: 64.21 (2.039) & 95% CrI: 60.15 to 68.18 Assume 81 patients do not have EQ-5D Complete Case Analysis (n=80) –EQ-5D: 60.44 (3.117) & 95% CrI: 54.11 to 66.38 Predictive Analysis (n=80+81) –EQ-5D: 60.58 (2.789) & 95% CrI: 54.93 to 65.88

10. IBS Study – Extension & Further Work 1 Distributional assumptions (both model & prior distributions), e.g. IBS study EQ-5D: -7.7 to +100 Sensitivity to prior distributions, especially on variance parameters Use of other studies which may have considered both EQ-5D & IBS-QoL – prior distributions, possibly down weighted according to patient population considered Modelling of 8 sub-scales of IBS-QoL & relationship with EQ-5D

11. IBS Study – Extension & Further Work 2 Additional baseline demographics, e.g. employment Consideration of whether certain individuals (defined by demographics & IBS-QoL scores) are ‘poorly’ predicted – Conditional Predictive Ordinates (CPOs) Assessment of predictive performance – cross-validation

12. Applications to Other Scenarios Studies which have not used a PBOM at all BUT where there are other studies which have, i.e. ‘Borrowing Strength’ Assumptions – Exchangeable, i.e. the relationship between PBOM & NPBOM is the same across studies ‘Bank of Reference Studies’ for common conditions/diseases, BUT … –Should not be seen as a replacement for well designed studies which use PBOMs –Limited use when there is a treatment-baseline interaction, which might be different for PBOMs & NPBOMs

13. Links with Other Work Regression-based approaches (‘mapping’) (Tsuchiya et al, 2003) Cross-Calibration (Parmigiani et al, 2003) – categorical data Modelling missing cost data (Lambert et al, 2003) Missing data due to death (informative missing data) –`Quality Adjusted Survival’ techniques (including multi-state modelling) –Joint modelling of both PBOM/NPBOMs & Missing/Death Process (Billingham, 2002)

14. References Akehurst RL et al. Health-Related Quality of Life and Cost Impact of Irritable Bowel Syndrome in a UK Primary Care Setting. Pharmacoeconomics 2002;20(7):455-462. Billingham LJ, Abrams KR. A Bayesian method for synthesizing evidence. The Confidence Profile Method. SMMR 1990;6(1):31-55. Lambert PC et al. Glasziou P & Irwig L. An evidence-based approach to individualising treatment. BMJ 1995;311:1356-1359. Prevost TC et al. Hierarchical models in generalised synthesis of evidence: an example based on studies of breast cancer. Stat Med 2000;19:3359-76. Sutton AJ & Abrams KR. Bayesian methods in meta-analysis and evidence synthesis. SMMR 2001;10(4):277-303. Spiegelhalter DJ, Abrams KR, Myles JP. Bayesian Approaches to Clinical Trials & Health-care Evaluation. London: Wiley, 2003.