Nonparametric inference on quantile lost lifespan

Quantile regression on inactivity time

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 semi-parametric 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.

Cause-specific quantile regression on inactivity time

In time-to-event analysis, the traditional summary measures have been based on the hazard function, survival function, quantile event time, restricted mean event time, and residual lifetime. Under competing risks, furthermore, typical summary measures have been the cause-specific hazard function and cumulative incidence function. Recently inactivity time has recaptured attention in the literature, being interpreted as life lost. In this paper, we further interpret it as quality of life reduced and time period after transition to a drug, and propose a quantile regression model to associate the inactivity time with potential predictors under competing risks. We define the proper cumulative distribution function of the inactivity time distribution for each specific event type among those subjects who experience the same type of events during a follow-up period. A score function-type estimating equation is developed and asymptotic properties of the regression coefficient estimators are derived by assuming that competing events are censored at their occurrence times as in the cause-specific hazard analysis. The proposed approach reduces to a regular quantile regression on the inactivity time without competing risks when all types of competing events are collapsed into the same type. Due to difficulty in estimating the improper probability density function of the cause-specific inactivity distribution to evaluate the variance of the quantiles, a computationally efficient perturbation method is adopted to infer the regression coefficients. Simulation results show that our proposed method works well under the assumed finite sample settings. The proposed method is illustrated with a real dataset from a breast cancer study.