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Multiple indications of disease progression found in a cancer patient byloco-regional relapse, distant metastasis and death. Early identification ofthese indications is necessary to change the treatment strategy. Biomarkersplay an essential role in this aspect. The survival chance of a patient isdependent on the biomarker, and the treatment strategy also differsaccordingly, e.g., the survival prediction of breast cancer patients diagnosedwith HER2 positive status is different from the same with HER2 negative status.This results in a different treatment strategy. So, the heterogeneity of thebiomarker statuses or levels should be taken into consideration while modellingthe survival outcome. This heterogeneity factor which is often unobserved, iscalled frailty. When multiple indications are present simultaneously, thescenario becomes more complex as only one of them can occur, which will censorthe occurrence of other events. Incorporating independent frailties of eachbiomarker status for every cause of indications will not depict the completepicture of heterogeneity. The events indicating cancer progression are likelyto be inter-related. So, the correlation should be incorporated through thefrailties of different events. In our study, we considered a multiple events orrisks model with a heterogeneity component. Based on the estimated variance ofthe frailty, the threshold levels of a biomarker are utilised as earlydetection tool of the disease progression or death. Additive-gamma frailtymodel is considered to account the correlation between different frailtycomponents and estimation of parameters are performed usingExpectation-Maximization Algorithm. With the extensive algorithm in R, we haveobtained the threshold levels of activity of a biomarker in a multiple eventsscenario.

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