Saddlepoint inference for rank tests based on clustered competing risks with random cluster sizes

In multicenter clinical trials and clustered data studies, the assumption of independent observations is frequently violated when conducting linear rank tests for competing risks. This paper introduces a very powerful testing framework for competing risks with random cluster sizes and correlated failure times. The test statistic is designed as a doubly stochastic sum to incorporate the variability in cluster number and cluster size. A shared frailty model is used to model intra-cluster dependence, and the exact cumulant generating function under the null hypothesis is obtained for saddlepoint approximation. This method results in accurate p-values without the need for assuming large-sample normality and leads to correct inference in small samples and sparse-event settings. The results of the simulation studies show that the proposed saddlepoint method is effective with respect to maintaining the nominal type I error rates and have competitive statistical power under different types of dependence. Its practical applicability is demonstrated using examples of datasets related to lung cancer, diabetic retinopathy and lymphoma.