## Open Access Dissertations and Theses

2011

Thesis

#### Degree Name

Master of Science (MSc)

Statistics

Aaron Childs

#### Co-Supervisor

Eleanor Pullenayegum

English

#### Abstract

The money put into health care has been increasing dramatically. Comparison of different programs is important in helping government to make decision as to what health care services to be provided. The cost-effectiveness of different health care programs can be compared based on the improvement of a person's health states and the cost it incurred. To measure the health states of a person, health utility scores can be used. But health utility data exhibit features such as non-normality, heteroscedasticity of variances, and the majority of observations attaining values close to or at the maximum of the measurement scale. This brings challenges to analyzing health utility data. For example, linear regression with the assumption of normality might not be valid since non-normality is present in health utility data. To address these problems, other methods are used. In this study, we investigate the performance of generalized additive models (GAMs) in handling health utility data. In GAMs, the relationship between the response and the predictor variables can be non-linearly defined. So GAM methods give more options in the assumption of the relationship between the response and the predictors. For comparison, we also use ordinary least squares. To evaluate the performance of generalized additive models, simulation is used. Data are generated from the simulation model, and GAMs will be used to fit the simulated data. Bias and coverage probability will be used to assess the performance of the GAM method. A comparison between OLS and GAM will be also be done in the study. And, as an illustration, GAM will be applied to a real data set called Diabetes Hamilton which "vas collected from some diabetic patients who participated in a community program based in Hamilton, Ontario.

When GAM is applied to the real data set, similar results to the OLS method in terms of the estimates of the parameters is observed. Both methods give similar coefficient values for each parameter. From the simulation results, the estimate given by the GAM method is closer to the true value than the OLS method in general. The bias produced by the GAM is smaller than the OLS method. So overall, GAM method seems to be valid in analyzing the data set such as those used in this study and also the general health utility data.

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