Assessing accuracy of Weibull shape parameter estimate from historical studies for subsequent sample size calculation in clinical trials with time-to-event outcome

Abstract

Background: Recent developments in literature on sample size calculations for time-to-event outcomes involve assumption of Weibull distributed times. These methods require a point estimate of the Weibull shape parameter obtained from historical studies. However, very limited guidance exists in published literature to assess how reliable this point estimate is when it is obtained from published results of a historical study. Methods: We conduct simulations to assess how accurate and reliable the point estimate of the Weibull shape parameter is when it is estimated from published results of median survival time and/or corresponding interquartile range. Accuracy of this estimate is assessed using the criteria of average relative bias, root mean square error, and coefficient of variation for various combinations of sample sizes and censoring rates. Sensitivity of these calculations is assessed first, by increasing the number of survival quantiles used to calculate accuracy, and second, by using the full Kaplan Meier (KM) curve from the historical study. Results: Our simulations suggest that point estimate of the shape parameter is reasonably accurate when estimated from historical studies with sample size ≥ 50 with censoring rate approximately 20%. Knowledge of the median and inter-quartile range seems to be adequate for this purpose. For historical studies with small sample sizes or higher censoring rates, more information needs to be abstracted from the published KM curves to improve accuracy. Conclusions: We conclude that assessing the accuracy of Weibull shape parameter estimate is important before it can be used to conduct sample size calculations for a subsequent trial. Keywords: Censoring, Historical data, KM curves, Sample size, Shape parameter, Weibull