Analysis of cost data in randomized trials: an application of the non-parametric bootstrap

Health economic evaluations are now more commonly being included in pragmatic randomized trials. However a variety of methods are being used for the presentation and analysis of the resulting cost data, and in many cases the approaches taken are inappropriate. In order to inform health care policy decisions, analysis needs to focus on arithmetic mean costs, since these will reflect the total cost of treating all patients with the disease. Thus, despite the often highly skewed distribution of cost data, standard non-parametric methods or use of normalizing transformations are not appropriate. Although standard parametric methods of comparing arithmetic means may be robust to non-normality for some data sets, this is not guaranteed. While the randomization test can be used to overcome assumptions of normality, its use for comparing means is still restricted by the need for similarly shaped distributions in the two groups. In this paper we show how the non-parametric bootstrap provides a more flexible alternative for comparing arithmetic mean costs between randomized groups, avoiding the assumptions which limit other methods. Details of several bootstrap methods for hypothesis tests and confidence intervals are described and applied to cost data from two randomized trials. The preferred bootstrap approaches are the bootstrap-t or variance stabilized bootstrap-t and the bias corrected and accelerated percentile methods. We conclude that such bootstrap techniques can be recommended either as a check on the robustness of standard parametric methods, or to provide the primary statistical analysis when making inferences about arithmetic means for moderately sized samples of highly skewed data such as costs.