Semiparametric inference in observational duration-response studies, with duration possibly right-censored

Once treatment is found to be effective in clinical studies, attention often focuses on optimum or efficacious treatment delivery. In treatment duration-response studies, the optimum treatment delivery refers to the treatment length that optimises the mean response. In many studies, the treatment length is often left to the discretion of an attending investigator or physician but may be abruptly terminated because of treatment-terminating events. Thus, a recommended treatment length often delineates a 'treatment duration policy' which prescribes that treatment be given for a specified length of time or until a treatment-terminating event occurs, whichever comes first. Estimating a functional relationship between the response and a treatment duration policy, continuously in time, is the focus of this paper.