The Saddlepoint Correction in Conditional Logistic Likelihood Analysis
本文详细研究了Barndorfi-Nielsen和Cox提出的双鞍点近似在多元逻辑回归模型中的应用，展示了鞍点修正如何简化非中心超几何随机变量均值的近似计算，并推广了McCullagh的算法，用于从多个四格表近似计算条件最大似然估计。
Barndorfi-Nielsen & Cox (1979) introduced the double saddlepoint approximation to the conditional likelihood function for a structural parameter vector given a sufficient statistic for a nuisance parameter vector. This approximation is considered in some detail for the case of multiple logistic regression models with polytomous outcome states. It is shown that the profile score with saddlepoint correction yields a simple derivation of an approximation to the mean of a noncentral hypergeometric random variable, discussed by Levin (1984) and Gart (1987), while providing analogous formulae in more general cases; and extends, to the general case, an algorithm of McCullagh (1984) for the approximate calculation of conditional maximum likelihood estimates of log odds ratio regression coefficients from several fourfold tables.