Abstract：
Semiparametric probabilistic index models allow for the comparison of two groups of observations, whilst adjusting for covariates, thereby fitting nicely within the framework of generalized pairwise comparisons (GPC). As with most regression approaches in this setting, the limited amount of data results in invalid inference as the asymptotic normality assumption is not met. In addition, separation issues might arise when considering small samples. In this article, we show that the parameters of the probabilistic index model can be estimated using generalized estimating equations, for which adjustments exist that lead to estimators of the sandwich variance-covariance matrix with improved finite sample properties and that can deal with bias due to separation. In this way, appropriate inference can be performed as is shown through extensive simulation studies. The known relationships between the probabilistic index and other GPC statistics allow to also provide valid inference for example, the net treatment benefit or the success odds.
摘要：
半参数概率指数模型允许比较两组观测值，在调整协变量的同时，从而在广义成对比较(GPC)的框架内很好地拟合。与此设置中的大多数回归方法一样，由于不满足渐近正态假设，有限的数据量导致无效的推断。此外,当考虑小样本时，可能会出现分离问题。在这篇文章中,我们证明了概率指数模型的参数可以使用广义估计方程来估计，对于存在的调整，导致三明治方差-协方差矩阵的估计器具有改进的有限样本属性，并且可以处理由于分离引起的偏差。这样,通过广泛的模拟研究表明，可以进行适当的推断。概率指数和其他GPC统计数据之间的已知关系也可以提供有效的推断，例如，净治疗效益或成功几率。
