Grant: Discovery Grants Program - Individual

In this project I plan to address two important issues in survival analysis. The first is estimation of the proportion, or testing for presence, of immune individuals (long-term survivors) in a sample where we observe some time-to-event data for each individual (for instance, time to pain-relief following a drug administration, or time to relapse following a remission; the individuals who do not exhibit relief or relapse are termed 'immune'). I propose to study the problem under different types of 'censoring' where instead of the exact time we can often only observe whether the latter is bigger or smaller than some censoring time (for instance, under 'Case-1 interval censoring' we only have the inspection times and whether or not the event in question ocurred before it (the 'current status')). Interestingly, even if we do not have the actual number of immune individuals, censoring information such as above often helps us draw valid inferences. The problem precisely is to figure out how to calculate the required proportion and its sampling variation approximately. The second issue is inference about the 'hazard' function which gives the 'risk' of occurrence of the event in question in the immediate future given that it has not occurred so far, i.e., describes an individual's 'aging' pattern. I am interested in hazard functions with non-monotonic shapes, such as 'bathtub' (which implies an initial decrease followed by gradual increase in risk, as for instance in machine parts following repair) or 'unimodal' (which is inverted bathtub, i.e., initial increase followed by gradual decrease in risk, as for instance in some cancer patients following treatment). My goal here is to estimate the function when it has such shapes, or test whether it does, under different types of censoring mentioned above. Both the issues arise often in biostatistical studies but so far have been dealt with using parametric models mostly. Thus it is important to develop systematic nonparametric methodology that are flexible but difficult.