Real-world clinical decision making is a complex process that involves balancing the risks and benefits of treatments. Quality-adjusted lifetime is a composite outcome that combines patient quantity and quality of life, making it an attractive outcome in clinical research. We propose methods for constructing optimal treatment length strategies to maximize this outcome. Existing methods for estimating optimal treatment strategies for survival outcomes cannot be applied to a quality-adjusted lifetime due to induced informative censoring. We propose a weighted estimating equation that adjusts for both confounding and informative censoring. We also propose a nonparametric estimator of the mean counterfactual quality-adjusted lifetime survival curve under a given treatment length strategy, where the weights are estimated using an undersmoothed sieve-based estimator. We show that the estimator is asymptotically linear and provide a data-dependent undersmoothing criterion. We apply our method to obtain the optimal time for percutaneous endoscopic gastrostomy insertion in patients with amyotrophic lateral sclerosis.

A subject being followed over time may experience several types of events related, for example, to disease morbidity and mortality. For example, in a Phase III trial of concomitant versus sequential chemotherapy and thoracic radiotherapy for patients with inoperable non-small cell lung cancer (NSCLC) conducted by the Radiation Therapy Oncology Group (RTOG), patients were followed up to 5 years, the occurrence of either disease progression or death being of particular interest. Such "competing risks" data are commonly encountered in cancer and other biomedical followup studies, in addition to the potential complication of right-censoring on the event time(s) of interest. Two quantities are often used when analyzing competing risks data: the cause-specific hazard function (CSH) and the cumulative incidence function (CIF). For a given event, the former describes the instantaneous risk of this event at time t, given that no events have yet occurred; the latter describes the probability of occurrence, or absolute risk, of that event across time and can be derived directly from the subdistribution hazard function (Fine and Gray, 1999).