Exploring Factors Related to Metastasis Free Survival in Breast Cancer Patients Using Bayesian Cure Models

Abstract

<b>Background:</b> Breast cancer is a fatal disease and the most frequently diagnosed cancer in women with anincreasing pattern worldwide. The burden is mostly attributed to metastatic cancers that occur in one-third ofpatients and the treatments are palliative. It is of great interest to determine factors affecting time from cancerdiagnosis to secondary metastasis. Materials and <br/><b>Methods</b>: Cure rate models assume a Poisson distribution for thenumber of unobservable metastatic-component cells that are completely deleted from the non-metastasis patientbody but some may remain and result in metastasis. Time to metastasis is defined as a function of the numberof these cells and the time for each cell to develop a detectable sign of metastasis. Covariates are introduced tothe model via the rate of metastatic-component cells. We used non-mixture cure rate models with Weibull andlog-logistic distributions in a Bayesian setting to assess the relationship between metastasis free survival andcovariates. <br/><b>Results</b>: The median of metastasis free survival was 76.9 months. Various models showed that fromcovariates in the study, lymph node involvement ratio and being progesterone receptor positive were significant,with an adverse and a beneficial effect on metastasis free survival, respectively. The estimated fraction of patientscured from metastasis was almost 48%. The Weibull model had a slightly better performance than log-logistic.<br/><b>Conclusions</b>: Cure rate models are popular in survival studies and outperform other models under certainconditions. We explored the prognostic factors of metastatic breast cancer from a different viewpoint. In thisstudy, metastasis sites were analyzed all together. Conducting similar studies in a larger sample of cancer patientsas well as evaluating the prognostic value of covariates in metastasis to each site separately are recommended.