Blizzard L, Hosmer D W
Menzies Research Institute, University of Tasmania, Hobart, Australia.
Biom J. 2006 Feb;48(1):5-22. doi: 10.1002/bimj.200410165.
An estimate of the risk, adjusted for confounders, can be obtained from a fitted logistic regression model, but it substantially over-estimates when the outcome is not rare. The log binomial model, binomial errors and log link, is increasingly being used for this purpose. However this model's performance, goodness of fit tests and case-wise diagnostics have not been studied. Extensive simulations are used to compare the performance of the log binomial, a logistic regression based method proposed by Schouten et al. (1993) and a Poisson regression approach proposed by Zou (2004) and Carter, Lipsitz, and Tilley (2005). Log binomial regression resulted in "failure" rates (non-convergence, out-of-bounds predicted probabilities) as high as 59%. Estimates by the method of Schouten et al. (1993) produced fitted log binomial probabilities greater than unity in up to 19% of samples to which a log binomial model had been successfully fit and in up to 78% of samples when the log binomial model fit failed. Similar percentages were observed for the Poisson regression approach. Coefficient and standard error estimates from the three models were similar. Rejection rates for goodness of fit tests for log binomial fit were around 5%. Power of goodness of fit tests was modest when an incorrect logistic regression model was fit. Examples demonstrate the use of the methods. Uncritical use of the log binomial regression model is not recommended.
经混杂因素调整后的风险估计值可从拟合的逻辑回归模型中获得，但当结局并非罕见时，该估计值会大幅高估。对数二项模型（具有二项误差和对数链接）正越来越多地用于此目的。然而，尚未对该模型的性能、拟合优度检验和逐例诊断进行研究。本文使用广泛的模拟来比较对数二项模型、Schouten等人（1993年）提出的基于逻辑回归的方法以及Zou（2004年）和Carter、Lipsitz与Tilley（2005年）提出的泊松回归方法的性能。对数二项回归导致高达59%的“失败”率（不收敛、预测概率超出范围）。Schouten等人（1993年）的方法所得估计值在高达19%已成功拟合对数二项模型的样本中以及高达78%对数二项模型拟合失败的样本中产生大于1的拟合对数二项概率。泊松回归方法也观察到类似的百分比。三种模型的系数和标准误差估计值相似。对数二项拟合的拟合优度检验的拒绝率约为5%。当拟合错误的逻辑回归模型时，拟合优度检验的功效适中。文中通过示例展示了这些方法的使用。不建议盲目使用对数二项回归模型。
