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.

中文翻译：

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不活动时间的特定原因的分位数回归

在事件分析中，传统的汇总度量是基于危害函数，生存函数，分位数事件时间，受限平均事件时间和剩余寿命。此外，在竞争风险下，典型的简易措施是针对特定原因的危害函数和累积发生率函数。最近，闲暇时间重新引起了文献的关注，被认为是生命的丧失。在本文中，我们将其进一步解释为生活质量下降和过渡到药物后的时间段，并提出了分位数回归模型，以将不活动时间与竞争风险下的潜在预测因素相关联。我们为在随访期内经历相同类型事件的受试者中的每种特定事件类型，定义了不活动时间分布的适当累积分布函数。建立了得分函数类型的估计方程，并通过假设竞争事件在特定原因的危害分析中被审查，从而推断出回归系数估计量的渐近性质。当所有类型的竞争事件都分解为同一类型时，所提出的方法减少了对不活动时间的规则分位数回归，而没有竞争风险。由于难以估算特定原因的不活动分布的不适当概率密度函数来评估分位数的方差，采用计算有效的摄动方法来推断回归系数。仿真结果表明，我们提出的方法在假定的有限样本设置下效果很好。乳腺癌研究的真实数据集说明了所提出的方法。