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首页> 外文期刊>The American statistician >A Fresh Look at the Discriminant Function Approach for Estimating Crude or Adjusted Odds Ratios
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A Fresh Look at the Discriminant Function Approach for Estimating Crude or Adjusted Odds Ratios

机译：重新看待判别函数法来估计粗略或调整的赔率

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摘要

Assuming a binary outcome, logistic regression is the most common approach to estimating a crude or adjusted odds ratio corresponding to a continuous predictor. We revisit a method termed the discriminant function approach, which leads to closed-form estimators and corresponding standard errors. In its most appealing application, we show that the approach suggests a multiple linear regression of the continuous predictor of interest on the outcome and other covariates, in place of the traditional logistic regression model. If standard diagnostics support the assumptions (including normality of errors) accompanying this linear regression model, the resulting estimator has demonstrable advantages over the usual maximum likelihood estimator via logistic regression. These include improvements in terms of bias and efficiency based on a minimum variance unbiased estimator of the log odds ratio, as well as the availability of an estimate when logistic regression fails to converge due to a separation of data points. Use of the discriminant function approach as described here for multivariable analysis requires less stringent assumptions than those for which it was historically criticized, and is worth considering when the adjusted odds ratio associated with a particular continuous predictor is of primary interest. Simulation and case studies illustrate these points.
机译：假设结果是二进制，逻辑回归是估算对应于连续预测变量的原始或调整后的优势比的最常用方法。我们重新审视一种称为判别函数法的方法，该方法会导致闭合形式的估计量和相应的标准误差。在其最吸引人的应用中，我们证明了该方法建议了对结果和其他协变量感兴趣的连续预测变量的多元线性回归，以代替传统的逻辑回归模型。如果标准诊断方法支持此线性回归模型附带的假设（包括误差的正态性），那么通过逻辑回归，所得估计量将比通常的最大似然估计量具有明显优势。这些包括基于对数优势比的最小方差无偏估计量的偏倚和效率方面的改进，以及由于数据点分离而导致逻辑回归无法收敛时估计的可用性。此处描述的判别函数方法用于多变量分析的要求比历史上受到批评的假设要宽松的假设少，因此当与特定连续预测变量相关的调整后的优势比成为主要关注对象时，值得考虑。仿真和案例研究说明了这些观点。

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