Analysing secondary outcomes is a common practice for case-control studies. Traditional secondary analysis employs either completely parametric models or conditional mean regression models to link the secondary outcome to covariates. In many situations, quantile regression models complement mean-based analyses and provide alternative new insights on the associations of interest. For example, biomedical outcomes are often highly asymmetric, and median regression is more useful in describing the 'central' behaviour than mean regressions. There are also cases where the research interest is to study the high or low quantiles of a population, as they are more likely to be at risk. We approach the secondary quantile regression problem from a semiparametric perspective, allowing the covariate distribution to be completely unspecified. We derive a class of consistent semiparametric estimators and identify the efficient member. The asymptotic properties of the resulting estimators are established. Simulation results and a real data analysis are provided to demonstrate the superior performance of our approach with a comparison with the only existing approach so far in the literature.

中文翻译：

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二次分析分位数回归中的半参数有效估计。

分析次要结果是病例对照研究的常见做法。传统的二次分析采用完全参数化模型或条件均值回归模型将二次结果与协变量联系起来。在许多情况下，分位数回归模型补充了基于均值的分析，并提供了有关感兴趣关联的替代新见解。例如，生物医学结果通常是高度不对称的，中值回归在描述“中心”行为方面比均值回归更有用。在某些情况下，研究兴趣是研究人群的高分位数或低分位数，因为他们更有可能面临风险。我们从半参数的角度处理二次分位数回归问题，允许协变量分布完全不确定。我们推导出一类一致的半参数估计量并确定有效成员。建立了所得估计量的渐近性质。提供模拟结果和真实数据分析，通过与文献中迄今为止唯一现有的方法进行比较来证明我们的方法的优越性能。