Scott Alastair John, Lee Alan J, Wild C J
Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand.
Lifetime Data Anal. 2007 Dec;13(4):545-63. doi: 10.1007/s10985-007-9054-0. Epub 2007 Sep 9.
Breslow and Holubkov (J Roy Stat Soc B 59:447-461 1997a) developed semiparametric maximum likelihood estimation for two-phase studies with a case-control first phase under a logistic regression model and noted that, apart for the overall intercept term, it was the same as the semiparametric estimator for two-phase studies with a prospective first phase developed in Scott and Wild (Biometrica 84:57-71 1997). In this paper we extend the Breslow-Holubkov result to general binary regression models and show that it has a very simple relationship with its prospective first-phase counterpart. We also explore why the design of the first phase only affects the intercept of a logistic model, simplify the calculation of standard errors, establish the semiparametric efficiency of the Breslow-Holubkov estimator and derive its asymptotic distribution in the general case.
布雷斯洛和霍卢布科夫（《皇家统计学会学报B辑》59:447 - 461，1997a）在逻辑回归模型下，针对具有病例对照第一阶段的两阶段研究，开发了半参数最大似然估计，并指出，除了总体截距项外，它与斯科特和怀尔德（《生物统计学》84:57 - 71，1997）所开发的具有前瞻性第一阶段的两阶段研究的半参数估计量相同。在本文中，我们将布雷斯洛 - 霍卢布科夫的结果扩展到一般二元回归模型，并表明它与其前瞻性第一阶段的对应物具有非常简单的关系。我们还探究了为何第一阶段的设计仅影响逻辑模型的截距，简化了标准误差的计算，确立了布雷斯洛 - 霍卢布科夫估计量的半参数效率，并推导了其在一般情况下的渐近分布。
