Saddlepoint approximations for rank-invariant permutation tests and confidence intervals with interval-censoring

Abstract

Interval-censored data occur when subjects are assessed by using regular follow-up. In such instances, we consider rank-invariant permutation tests to test the significance of a treatment versus a control. For a wide class of such tests, which includes the Peto & Peto class, we present saddlepoint approximations for the exact permutation mid-P-values which achieve extremely small relative errors. The speed and stability of these saddlepoint computations make them practicable for inverting the permutation tests and we compute nominal 100(1-α)% confidence intervals for the treatment effect. Such confidence intervals are of substantial clinical importance since, more than simply stating the level of statistical significance, they quantify the significant benefit of the treatment by providing a confidence interval for the percentage increase in mean (or median) treatment survival time as compared to control. Our methodology makes heavy use of nonparametric MLEs (NPMLEs) for survival functions and some limitations of existing algorithms, such as the hybrid ICM algorithm, are noted and accommodated. The Canadian Journal of Statistics 42: 308-324; 2014 © 2014 Statistical Society of Canada.