Clustered survival data often arise in biomedical research. When the outcome
depends on the size of the cluster, the cluster size is said to be informative. The
assumption of non informative cluster size is commonly used even though it may be
not true in some situations.We propose a test for the assumption of Informative Cluster
Size (ICS) in clustered survival data with right censoring. Standard martingale
results are used to obtain the asymptotic distribution of the test statistic. Simulation
studies show that the proposed test works well under various scenario. To illustrate
the proposed approach, we consider several applications: periodontal data, a multicentric
study of patients with liver disease and a recent data set of patients with
metastatic cancer treated by immunotherapy.

KEYWORDS:
Clustered data, Hypothesis testing, Informative cluster size, Survival analysis