We study the efficiency of covariate-specific estimates of pure risk (one minus the survival function) when some covariates are only available for case-control samples nested in a cohort. We focus on the semiparametric additive hazards model in which the hazard function equals a baseline hazard plus a linear combination of covariates with either time-varying or time-invariant coefficients. A published approach uses the design-based inclusion probabilities to reweight the nested case-control data. We obtain more efficient estimates of pure risks by calibrating the design weights to data available in the entire cohort, for both time-varying and time-invariant covariate coefficients. We develop explicit variance formulas for the weight-calibrated estimates based on influence functions. Simulations show the improvement in precision by using weight calibration and confirm the consistency of variance estimators and the validity of inference based on asymptotic normality. Examples are provided using data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial Study (PLCO).

中文翻译：

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权重校准以提高使用嵌套案例控制设计从加性风险模型估计纯风险的效率

当某些协变量仅可用于嵌套在队列中的病例对照样本时，我们研究了纯风险（减去生存函数）的协变量特定估计的效率。我们专注于半参数加性风险模型，其中风险函数等于基线风险加上具有时变或时不变系数的协变量的线性组合。已发布的方法使用基于设计的包含概率来重新加权嵌套的病例对照数据。我们通过将设计权重校准到整个队列中可用的数据来获得更有效的纯风险估计，包括时变和非时变协变量系数。我们为基于影响函数的权重校准估计开发了显式方差公式。仿真表明通过使用权重校准提高了精度，并确认了方差估计量的一致性和基于渐近正态性的推理的有效性。使用来自前列腺癌、肺癌、结肠直肠癌和卵巢癌筛查试验研究 (PLCO) 的数据提供了示例。