Fitzmaurice Garrett M, Lipsitz Stuart R, Arriaga Alex, Sinha Debajyoti, Greenberg Caprice, Gawande Atul A
Harvard Medical School, Boston, MA 02115, USA
Brigham and Women's Hospital, Boston, MA 02115, USA.
Biostatistics. 2014 Oct;15(4):745-56. doi: 10.1093/biostatistics/kxu012. Epub 2014 Apr 4.
Relative risks (RRs) are often considered the preferred measures of association in prospective studies, especially when the binary outcome of interest is common. In particular, many researchers regard RRs to be more intuitively interpretable than odds ratios. Although RR regression is a special case of generalized linear models, specifically with a log link function for the binomial (or Bernoulli) outcome, the resulting log-binomial regression does not respect the natural parameter constraints. Because log-binomial regression does not ensure that predicted probabilities are mapped to the [0,1] range, maximum likelihood (ML) estimation is often subject to numerical instability that leads to convergence problems. To circumvent these problems, a number of alternative approaches for estimating RR regression parameters have been proposed. One approach that has been widely studied is the use of Poisson regression estimating equations. The estimating equations for Poisson regression yield consistent, albeit inefficient, estimators of the RR regression parameters. We consider the relative efficiency of the Poisson regression estimator and develop an alternative, almost efficient estimator for the RR regression parameters. The proposed method uses near-optimal weights based on a Maclaurin series (Taylor series expanded around zero) approximation to the true Bernoulli or binomial weight function. This yields an almost efficient estimator while avoiding convergence problems. We examine the asymptotic relative efficiency of the proposed estimator for an increase in the number of terms in the series. Using simulations, we demonstrate the potential for convergence problems with standard ML estimation of the log-binomial regression model and illustrate how this is overcome using the proposed estimator. We apply the proposed estimator to a study of predictors of pre-operative use of beta blockers among patients undergoing colorectal surgery after diagnosis of colon cancer.
相对风险（RRs）通常被认为是前瞻性研究中关联度的首选测量指标，尤其是当感兴趣的二元结局较为常见时。特别地，许多研究人员认为RRs比比值比更直观易懂。尽管RR回归是广义线性模型的一种特殊情况，具体来说是对二项式（或伯努利）结局使用对数链接函数，但由此产生的对数二项式回归并不遵循自然参数约束。由于对数二项式回归不能确保预测概率被映射到[0,1]范围内，最大似然（ML）估计常常会出现数值不稳定，从而导致收敛问题。为了规避这些问题，人们提出了许多估计RR回归参数的替代方法。一种被广泛研究的方法是使用泊松回归估计方程。泊松回归的估计方程能产生RR回归参数的一致估计量，尽管效率不高。我们考虑泊松回归估计量的相对效率，并为RR回归参数开发一种替代的、几乎有效的估计量。所提出的方法基于对真实伯努利或二项式权重函数的麦克劳林级数（围绕零展开的泰勒级数）近似使用近最优权重。这产生了一个几乎有效的估计量，同时避免了收敛问题。我们研究了随着级数项数增加所提出估计量的渐近相对效率。通过模拟，我们展示了对数二项式回归模型的标准ML估计存在收敛问题的可能性，并说明了如何使用所提出的估计量来克服这一问题。我们将所提出的估计量应用于一项关于结肠癌诊断后接受结直肠手术患者术前使用β受体阻滞剂预测因素的研究。
