The complexity of X-chromosome inactivation arouses the X-linked genetic association being overlooked in most of the genetic studies, especially for genetic association analysis on time to event outcomes. To fill this gap, we propose novel methods to analyze the X-linked genetic association for competing risk failure time data based on a subdistribution hazard function. Specifically, we consider two mechanisms for a single genetic variant on X-chromosome: (1) all the subjects in a population undergo the same inactivation process; (2) the subjects randomly undergo different inactivation processes. According to the assumptions, one of the proposed methods can be used to infer the unknown biological process under scenario (1), while another method can be used to estimate the proportion of a certain biological process in the population under scenario (2). Both of the two methods can infer the direction of skewness for skewed X-chromosome inactivation and derive asymptotically unbiased estimates of the model parameters. The asymptotic distributions for the parameter estimates and constructed score tests with nuisance parameters only presented under the alternative hypothesis are illustrated under both assumptions. Finite sample performance of these novel methods is examined via extensive simulation studies. An application is illustrated with implementation on a cancer genetic study with competing risk outcomes.

中文翻译：

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X染色体遗传关联的竞争风险建模和测试

X 染色体失活的复杂性引起了在大多数遗传研究中被忽视的 X 连锁遗传关联，特别是对于事件结果时间的遗传关联分析。为了填补这一空白，我们提出了基于子分布风险函数分析竞争风险失败时间数据的 X 连锁遗传关联的新方法。具体而言，我们考虑了 X 染色体上单个遗传变异的两种机制：（1）群体中的所有受试者都经历相同的失活过程；(2)受试者随机经历不同的灭活过程。根据假设，可以使用所提出的方法之一来推断场景（1）下的未知生物过程，而另一种方法可以用来估计场景（2）下某个生物过程在种群中的比例。这两种方法都可以推断偏斜 X 染色体失活的偏斜方向，并推导出模型参数的渐近无偏估计。在两个假设下都说明了参数估计的渐近分布和仅在备择假设下呈现的带有滋扰参数的构造得分测试。这些新方法的有限样本性能通过广泛的模拟研究进行了检查。举例说明了在具有竞争风险结果的癌症遗传研究中实施的应用。这两种方法都可以推断偏斜 X 染色体失活的偏斜方向，并推导出模型参数的渐近无偏估计。在两个假设下都说明了参数估计的渐近分布和仅在备择假设下呈现的带有滋扰参数的构造得分测试。这些新方法的有限样本性能通过广泛的模拟研究进行了检查。举例说明了在具有竞争风险结果的癌症遗传研究中实施的应用。这两种方法都可以推断偏斜 X 染色体失活的偏斜方向，并推导出模型参数的渐近无偏估计。在两个假设下都说明了参数估计的渐近分布和仅在备择假设下呈现的带有滋扰参数的构造得分测试。这些新方法的有限样本性能通过广泛的模拟研究进行了检查。举例说明了在具有竞争风险结果的癌症遗传研究中实施的应用。这些新方法的有限样本性能通过广泛的模拟研究进行了检查。举例说明了在具有竞争风险结果的癌症遗传研究中实施的应用。这些新方法的有限样本性能通过广泛的模拟研究进行了检查。举例说明了在具有竞争风险结果的癌症遗传研究中实施的应用。