Xu J L, Prorok P C
Department of Mathematics, University of Houston, Texas 77204-3476, USA.
Biometrics. 1998 Sep;54(3):859-64.
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.
在研究原发性癌症大小与转移发生之间的关系时，有两个量至关重要。第一个是转移转变点处肿瘤大小的分布，第二个是癌症就医时存在可检测到的转移的概率。金梅尔和弗莱兴格（1991年，《生物统计学》47卷，987 - 1004页）开发了一个通用的非参数模型，并研究了其两种极限情况。由于其通用模型的不可识别性，通过使检测转移性癌症的风险函数为常数引入了一个新的可识别模型。新模型将金梅尔和弗莱兴格（1991年）的第二个极限模型作为特殊情况包含在内。提出了转移时肿瘤大小分布的估计量。该结果应用于一组结直肠癌数据。
