  The inactivity time, or lost lifespan specifically for mortality data,
concerns time from occurrence of an event of interest to the current time point
and has recently emerged as a new summary measure for cumulative information
inherent in time-to-event data. This summary measure provides several benefits
over the traditional methods, including more straightforward interpretation yet
less sensitivity to heavy censoring. However, there exists no systematic
modeling approach to inferring the quantile inactivity time in the literature.
In this paper, we propose a regression method for the quantiles of the
inactivity time distribution under right censoring. The consistency and
asymptotic normality of the regression parameters are established. To avoid
estimation of the probability density function of the inactivity time
distribution under censoring, we propose a computationally efficient method for
estimating the variance-covariance matrix of the regression coefficient
estimates. Simulation results are presented to validate the finite sample
properties of the proposed estimators and test statistics. The proposed method
is illustrated with a real dataset from a clinical trial on breast cancer.
