The use of bootstrap methods for estimating sample size and analysing health-related quality of life outcomes

Health-related quality of life (HRQoL) measures are increasingly used in trials as primary outcome measures. Investigators are now asking statisticians for advice on how to plan and analyse studies using such outcomes. HRQoL outcomes, like the SF-36, are usual measured on an ordinal scale, although most investigators assume that there exists an underlying continuous latent variable and that the actual measured outcomes (the ordered categories) reflect contiguous intervals along this continuum. The ordinal scaling of HRQoL measures means they tend to generate data that have discrete, bounded and skewed distributions. Thus, standard methods of analysis that assume Normality and constant variance may not be appropriate. For this reason, conventional statistical advice would suggest non-parametric methods be used to analyse HRQoL data. The bootstrap is one such computer intensive non-parametric method for estimating sample sizes and analysing data. We describe three methods of estimating sample sizes for two-group cross-sectional comparisons of HRQoL outcomes. We then compared the power of the three methods for a two-group cross-sectional study design using bootstrap simulation. The results showed that under the location shift alternative hypothesis, conventional methods of sample size estimation performed well, particularly Whitehead's method. Whitehead's method is recommended if the HRQoL outcome has a limited number of discrete values (<7) and/or the expected proportion of cases at either of the bounds is high. If a pilot data set is readily available then bootstrap simulation will provide a more accurate and reliable estimate, than conventional methods.Finally, we used the bootstrap for hypothesis testing and the estimation of standard errors and confidence intervals for parameters, in an example data set. We then compared and contrasted the bootstrap with standard methods of analysing HRQoL outcomes. In the data set studied, with the SF-36 outcome, the use of the bootstrap for estimating sample sizes and analysing HRQoL data produces results similar to conventional statistical methods. These results suggest that bootstrap methods are not more appropriate for analysing HRQoL outcome data than standard methods.