  Effectiveness of immune-oncology chemotherapies has been presented in recent
clinical trials. The Kaplan-Meier estimates of the survival functions of the
immune therapy and the control often suggested the presence of the lag-time
until the immune therapy began to act. It implies the use of hazard ratio under
the proportional hazards assumption would not be appealing, and many
alternatives have been investigated such as the restricted mean survival time.
In addition to such overall summary of the treatment contrast, the lag-time is
also an important feature of the treatment effect. Identical survival functions
up to the lag-time implies patients who are likely to die before the lag-time
would not benefit the treatment and identifying such patients would be very
important. We propose the semiparametric piecewise accelerated failure time
model and its inference procedure based on the semiparametric maximum
likelihood method. It provides not only an overall treatment summary, but also
a framework to identify patients who have less benefit from the immune-therapy
in a unified way. Numerical experiments confirm that each parameter can be
estimated with minimal bias. Through a real data analysis, we illustrate the
evaluation of the effect of immune-oncology therapy and the characterization of
covariates in which patients are unlikely to receive the benefit of treatment.
