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arXiv 2209.04716stat.ME
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在插补删失协变量时先外推再插补可减少偏倚

Extrapolation before imputation reduces bias when imputing censored covariates

Sarah C. Lotspeich, Tanya P. Garcia

AI总结:

针对严重删失协变量插补中条件均值积分被截断导致高偏倚的问题,提出将半参数生存估计与参数化尾部外推拼接的混合方法,先外推再插补,显著降低偏倚并改善临床试验患者优先级排序。

摘要:

在为一项新的亨廷顿病临床试验识别信息丰富的受试者时,对症状进展进行建模存在问题,因为关键协变量——确诊时间——可能被严重删失。插补是一种有吸引力的策略,即用删失协变量的条件均值替换删失值,但现有方法在严重删失下出现了超过200%的偏倚。要良好地计算这些条件均值,需要先估计删失协变量的生存函数,再从删失值到无穷大对该生存函数进行积分。为了灵活估计生存函数,现有方法使用带Breslow估计量的半参数Cox模型,这使得条件均值的被积函数(即估计的生存函数)在观测数据之外没有定义。于是积分只能估计到最大的观测协变量值,而这种近似可能截断生存函数的尾部并导致严重偏倚,尤其是在严重删失情况下。我们提出一种混合方法,将半参数生存估计量与参数化扩展拼接在一起,从而能够将积分近似到无穷大。在模拟研究中,我们提出的先外推再插补的方法显著降低了现有插补方法所表现出的偏倚,即使参数化扩展被错误指定时也是如此。我们进一步展示了使用修正后的条件均值进行插补如何有助于为未来临床试验对患者进行优先级排序。

英文摘要:

Modeling symptom progression to identify informative subjects for a new Huntington's disease clinical trial is problematic since time to diagnosis, a key covariate, can be heavily censored. Imputation is an appealing strategy where censored covariates are replaced with their conditional means, but existing methods saw over 200% bias under heavy censoring. Calculating these conditional means well requires estimating and then integrating over the survival function of the censored covariate from the censored value to infinity. To estimate the survival function flexibly, existing methods use the semiparametric Cox model with Breslow's estimator, leaving the integrand for the conditional means (the estimated survival function) undefined beyond the observed data. The integral is then estimated up to the largest observed covariate value, and this approximation can cut off the tail of the survival function and lead to severe bias, particularly under heavy censoring. We propose a hybrid approach that splices together the semiparametric survival estimator with a parametric extension, making it possible to approximate the integral up to infinity. In simulation studies, our proposed approach of extrapolation then imputation substantially reduces the bias seen with existing imputation methods, even when the parametric extension was misspecified. We further demonstrate how imputing with corrected conditional means helps to prioritize patients for future clinical trials.

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