Estimating a distribution function of the tumor size at metastasis

In studying the relationship between the size of primary cancers and the occurrence of metastases, two quantities are of prime importance. The first is the distribution of tumor size at the point of metastatic transition, while the second is the probability that detectable metastases are present when cancer comes to medical attention. Kimmel and Flehinger (1991, Biometrics 47, 987-1004) developed a general nonparametric model and studied its two limiting cases. Because of unidentifiablity of their general model, a new identifiable model is introduced by making the hazard function for detecting a metastatic cancer a constant. The new model includes Kimmel and Flehinger's (1991) second limiting model as a special case. An estimator of the tumor size distribution at metastases is proposed. The result is applied to a set of colorectal cancer data.