A modified risk detection approach of biomarkers by frailty effect on multiple time to event data

Multiple indications of disease progression found in a cancer patient by loco-regional relapse, distant metastasis and death. Early identification of these indications is necessary to change the treatment strategy. Biomarkers play an essential role in this aspect. The survival chance of a patient is dependent on the biomarker, and the treatment strategy also differs accordingly, e.g., the survival prediction of breast cancer patients diagnosed with HER2 positive status is different from the same with HER2 negative status. This results in a different treatment strategy. So, the heterogeneity of the biomarker statuses or levels should be taken into consideration while modelling the survival outcome. This heterogeneity factor which is often unobserved, is called frailty. When multiple indications are present simultaneously, the scenario becomes more complex as only one of them can occur, which will censor the occurrence of other events. Incorporating independent frailties of each biomarker status for every cause of indications will not depict the complete picture of heterogeneity. The events indicating cancer progression are likely to be inter-related. So, the correlation should be incorporated through the frailties of different events. In our study, we considered a multiple events or risks model with a heterogeneity component. Based on the estimated variance of the frailty, the threshold levels of a biomarker are utilised as early detection tool of the disease progression or death. Additive-gamma frailty model is considered to account the correlation between different frailty components and estimation of parameters are performed using Expectation-Maximization Algorithm. With the extensive algorithm in R, we have obtained the threshold levels of activity of a biomarker in a multiple events scenario.