Blizzard L, Hosmer D W
Menzies Research Institute, University of Tasmania, Private Bag 23, Hobart, TAS 7001, Australia.
Biom J. 2007 Dec;49(6):889-902. doi: 10.1002/bimj.200610377.
An estimate of the risk or prevalence ratio, adjusted for confounders, can be obtained from a log binomial model (binomial errors, log link) fitted to binary outcome data. We propose a modification of the log binomial model to obtain relative risk estimates for nominal outcomes with more than two attributes (the "log multinomial model"). Extensive data simulations were undertaken to compare the performance of the log multinomial model with that of an expanded data multinomial logistic regression method based on the approach proposed by Schouten et al. (1993) for binary data, and with that of separate fits of a Poisson regression model based on the approach proposed by Zou (2004) and Carter, Lipsitz and Tilley (2005) for binary data. Log multinomial regression resulted in "inadmissable" solutions (out-of-bounds probabilities) exceeding 50% in some data settings. Coefficient estimates by the alternative methods produced out-of-bounds probabilities for the log multinomial model in up to 27% of samples to which a log multinomial model had been successfully fitted. The log multinomial coefficient estimates generally had lesser relative bias and mean squared error than the alternative methods. The practical utility of the log multinomial regression model was demonstrated with a real data example. The log multinomial model offers a practical solution to the problem of obtaining adjusted estimates of the risk ratio in the multinomial setting, but must be used with some care and attention to detail.
对混杂因素进行调整后的风险或患病率比估计值，可通过拟合二分类结局数据的对数二项式模型（二项式误差，对数链接）获得。我们提出对对数二项式模型进行修改，以获得具有两个以上属性的名义结局的相对风险估计值（“对数多项式模型”）。我们进行了广泛的数据模拟，以比较对数多项式模型与基于Schouten等人（1993年）针对二分类数据提出的方法的扩展数据多项逻辑回归方法，以及基于Zou（2004年）和Carter、Lipsitz与Tilley（2005年）针对二分类数据提出的方法的泊松回归模型单独拟合的性能。在某些数据设置中，对数多项回归产生的“不可接受”解（概率超出范围）超过50%。替代方法的系数估计在高达27%已成功拟合对数多项式模型的样本中，产生了对数多项式模型概率超出范围的情况。对数多项式系数估计通常比替代方法具有更小的相对偏差和均方误差。通过一个实际数据示例展示了对数多项回归模型的实际效用。对数多项式模型为在多项设置中获得风险比的调整估计值问题提供了一个实际解决方案，但必须谨慎使用并关注细节。
