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

Disease progression in a cancer patient are identified by a number of indications in the form of loco-regional relapse, distant metastasis etc. Biomarkers play an essential role in early identification of these indications. The biomarkers can influence how a particular cancer behaves and how it may respond to a specific treatment, e.g., the survival probability of breast cancer patients diagnosed with HER2 positive status is different from the same with HER2 negative status. Researches have shown that the genetic mutations are often inconsistent across tumours and this is depicted in the form of bimodal and multi-modal expression values. 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. In the presence of competing events, 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 portray 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. The process can be performed for a single biomarker using a competing risk model with correlated frailty and estimates are obtained using Expectation-Maximization algorithm. 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. For multiple biomarkers, we have employed a sequential proportional hazard model using p-value combination method which will incorporate the correlations between the biomarkers. With the extensive algorithm in R, we have obtained the threshold levels of activity of multiple biomarkers in a competing risk scenario.