Using parametric models, a procedure for projecting survival estimates beyond the follow-up limits of a clinical trial is developed. The methodology consists of fitting an appropriate parametric model to the tail of a survival curve and using the estimated model in conjunction with the Kaplan-Meier product-limit estimate to produce a composite survival-function estimator. This estimator is especially useful whenever a parametric model is more easily fit to the tail rather than to the entire survival curve. Probability plots are used to evaluate different parametric models as well as to determine appropriate values for the cut points that define the survival-function tail. The bootstrap method provides estimates of variation in the projected survival curve. The resulting projected survival estimates allow one to make inferences on long-term treatment effects in clinical trials. As a motivating application, we project survival curves to estimate long-term treatment effects on quality-of-life-adjusted survival. This represents an extension of a statistical procedure called Q-TWiST (Quality-adjusted Time Without Symptoms of disease and Toxicity of treatment), which evaluates treatments in terms of both quantity and quality of life. In a standard Q-TWiST analysis, the average time spent in each of a number of health states, which differ in quality of life, is estimated from clinical trial data. The health states are weighted according to the quality of life experienced, and the results are combined to produce an estimate of quality-adjusted survival. Such estimates, however, are restricted to the follow-up limit of the data. The way in which the extrapolation methodology provides longer range estimates of Q-TWiST is described. To illustrate the techniques, we apply the methodology to data from the International Breast Cancer Study Group Trial V, which compares long-duration adjuvant chemotherapy versus short-duration chemotherapy in the treatment of node-positive breast cancer. Five-year median follow-up data are used to predict 10-year results in terms of mean survival and mean Q-TWiST. The results indicate that patients continue to benefit greatly from the long-duration chemotherapy between 5 and 10 years following treatment.
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