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Biometrics. 2017 Mar;73(1):260-270. doi: 10.1111/biom.12559. Epub 2016 Jul 11.

Tumor dormancy and frailty models: A novel approach.

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University Centre for Statistics in the Biomedical Sciences (CUSSB), Vita-Salute San Raffaele University, Milan, Italy.
Department of Biostatistics, Oslo Center for Biostatistics and Epidemiology, Institute of Basic Medical Sciences, University of Oslo, Norway.
Scientific Directorate Fondazione IRCCS Istituto Nazionale Tumori, Milan, Italy.
Unit of Medical Statistics, Biometry and Bioinformatics "Giulio A. Maccacaro" Campus Cascina Rosa, Fondazione IRCCS Istituto Nazionale Tumori, Milan, Italy.
Department of Clinical Sciences and Community Health, University of Milan, Milan, Italy.


Frailty models are here proposed in the tumor dormancy framework, in order to account for possible unobservable dependence mechanisms in cancer studies where a non-negligible proportion of cancer patients relapses years or decades after surgical removal of the primary tumor. Relapses do not seem to follow a memory-less process, since their timing distribution leads to multimodal hazards. From a biomedical perspective, this behavior may be explained by tumor dormancy, i.e., for some patients microscopic tumor foci may remain asymptomatic for a prolonged time interval and, when they escape from dormancy, micrometastatic growth results in a clinical disease appearance. The activation of the growth phase at different metastatic states would explain the occurrence of metastatic recurrences and mortality at different times (multimodal hazard). We propose a new frailty model which includes in the risk function a random source of heterogeneity (frailty variable) affecting the components of the hazard function. Thus, the individual hazard rate results as the product of a random frailty variable and the sum of basic hazard rates. In tumor dormancy, the basic hazard rates correspond to micrometastatic developments starting from different initial states. The frailty variable represents the heterogeneity among patients with respect to relapse, which might be related to unknown mechanisms that regulate tumor dormancy. We use our model to estimate the overall survival in a large breast cancer dataset, showing how this improves the understanding of the underlying biological process.


Compound Poisson; Frailty models; Gamma distribution; Tumor dormancy; Unobservable heterogeneity

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