Sample sizes for the SF-6D preference based measure of health from the SF-36: a practical guide

Background Health Related Quality of Life (HRQoL) measures are becoming more frequently used in clinical trials and health services research, both as primary and secondary endpoints. Investigators are now asking statisticians for advice on how to plan and analyse studies using HRQoL measures, which includes questions on sample size. Sample size requirements are critically dependent on the aims of the study, the outcome measure and its summary measure, the effect size and the method of calculating the test statistic. The SF-6D is a new single summary preference-based measure of health derived from the SF-36 suitable for use clinical trials and in the economic evaluation of health technologies. Objectives To describe and compare two methods of calculating sample sizes when using the SF-6D in comparative clinical trials and to give pragmatic guidance to researchers on what method to use. Methods We describe two main methods of sample size estimation. The parametric (t-test) method assumes the SF-6D data is continuous and normally distributed and that the effect size is the difference between two means. The non-parametric (Mann-Whitney MW) method assumes the data are continuous and not normally distributed and the effect size is defined in terms of the probability that an observation drawn at random from population Y would exceed an observation drawn at random from population X. We used bootstrap computer simulation to compare the power of the two methods for detecting a shift in location. Results This paper describes the SF-6D and retrospectively calculated parametric and nonparametric effect sizes for the SF-6D from a variety of studies that had previously used the SF-36. Computer simulation suggested that if the distribution of the SF-6D is reasonably symmetric then the t-test appears to be more powerful than the MW test at detecting differences in means. Therefore if the distribution of the SF-6D is symmetric or expected to be reasonably symmetric then parametric methods should be used for sample size calculations and analysis. If the distribution of the SF-6D is skewed then the MW test appears to be more powerful at detecting a location shift (difference in means) than the t-test. However, the differences in power (between the t and MW tests) are small and decrease as the sample size increases. Conclusions We have provided a clear description of the distribution of the SF-6D and believe that the mean is an appropriate summary measure for the SF-6D when it is to be used in clinical trials and the economic evaluation of new health technologies. Therefore pragmatically we would recommend that parametric methods be used for sample size calculation and analysis when using the SF-6D.