1. Modelling health care costs: practical examples and applications Andrew Briggs Philip Clarke University of Oxford & Daniel Polsky Henry Glick University of Pennsylvania

2. Modelling health care costs: Presentation overview Statement of problem Examples of cost distributions –Overall –By treatment group Testing cost differences –Raw scale –Transformations –Back transformation Multivariate analysis –Raw scale –Transformation Summary/future directions

3. Modelling health care costs: Statement of problem Common to collect cost data in clinical trials Cost data almost always skewed and may exhibit substantial kurtosis Nevertheless, arithmetic means are the concern of decision makers –Only the mean can be used to estimate total cost of care –Only total cost of care will lead to balanced budgets Cost models have a role beyond the simple estimation of within trial analysis –May be used to generalise to broader populations –May be used for sub-group analysis

4. Modelling health care costs: Examples of cost distributions

7. Modelling health care costs: Cost distributions by treatment

13. Approaches for testing cost differences Parametric T-test or nonparametric bootstrap on untransformed cost –Both unbiased –Inefficient? (Log) transformation of cost –Straight retransformation biased –Use –Or non-parametric smearing Generalised linear models – lognormal: –Expectation modelled directly so no retransformation problem –Wide variety of possible link function/distributions

14. Zhou’s test based on log normality Special case of homogeneity of log variances – test of geometric means is equivalent to test of arithmetic means By symmetry: for special case of homogeneity of log means – test of equality of log variances is equivalent to test of arithmetic means? Zhou’s proposed test combines the two

15. P-values and confidence intervals for back-transformed cost differences

17. Approaches to model selection Examine fit using standard regression diagnostics –R 2, normal probability plots etc. –Summarises fit to observed data Test the predictive ability of the models directly –Ability to predict observations not used in model fitting

18. Predictive ability of the models A simulation experiment 1.Sample was split into two equal parts Part i designated ‘training sub-sample’ Part ii designated ‘test sub-sample’ 2.Each model fitted using the training sub-sample and costs predicted for the test sub-sample 3.Mean square error calculated for each model Process repeated in 10,000 trials

19. Results of a simulation exercise

20. P-values and confidence intervals for back-transformed cost differences

22. Modelling health care costs: Summary Different approaches to modelling health care cost can lead to quite different estimates Difficult to tell which is most appropriate Transforming cost data can be more efficient –GLM intuitive in modelling expectations –But modelling log cost better for heavy tails? Covariate adjustment can help precision and should be used whenever possible –Will be used to extrapolate beyond the data –Creates sub-group effects with transformed models –Creates challenges for summarising incremental cost across different covariate patterns

23. Modelling health care costs: Log cost distributions by treatment