Variance and sample size calculations in quality-of-life-adjusted survival analysis (Q-TWiST)

The Quality-Adjusted Time Without Symptoms or Toxicity (Q-TWiST) statistic previously introduced by Glasziou, Simes and Gelber (1990, Statistics In Medicine 9, 1259-1776) combines toxicity, disease-free survival, and overall survival information in assessing the impact of treatments on the lives of patients. This methodology has received positive reviews from clinicians as intuitive and useful, but to date, the variance of this statistic has remained unspecified. We review aspects of the Q-TWiST method for analyzing clinical trial data, extend the method to accommodate multiple treatment arms, and provide closed-form asymptotic variance formulas. We also provide a framework for designing Q-TWiST clinical trials with sample sizes determined using the derived asymptotic variance formulas. Trials currently collecting quality of life data did not have the benefit of these sample size calculation techniques in designing their studies.