Estimating a distribution function of the tumor size at metastasis

In studying the relationship between the size of primary cancers and the oc currence of metastases, two quantities are of prime importance. The first i s the distribution of tumor size at the point of metastatic transition, whi le the second is the probability that detectable metastases are present whe n 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 i dentifiable model is introduced by making the hazard function for detecting a metastatic cancer a constant. The new model includes Kimmel and Flehinge r's (1991) second limiting model as a special case. An estimator of the tum or size distribution at metastases is proposed. The result is applied to a set of colorectal cancer data.