Interpreting the concordance statistic of a logistic regression model: relation to the variance and odds ratio of a continuous explanatory variable.
Interpreting the concordance statistic of a logistic regression model: relation to the variance and odds ratio of a continuous explanatory variable.
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DOI：
10.1186/1471-2288-12-82
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发表时间：
2012-06-20
影响因子：
4
通讯作者：
Steyerberg EW
中科院分区：
文献类型：
--
作者：
Austin PC;Steyerberg EW
当结果是二元的时，c统计量（相当于受试者工作特征曲线下的面积）是逻辑回归模型预测准确性的标准度量。在假设连续解释变量服从正态分布的条件下，推导出了一个解析表达式。然后，我们进行了一系列广泛的Monte Carlo模拟，以检查在双正态假设下导出的表达式是否允许在解释变量遵循正态分布的情况下准确预测经验c-统计量。我们还研究了预测的c-统计量的准确性时，解释变量遵循伽马，对数正态分布或均匀分布的组合样本的条件和不条件。在方差相等的二正态性假设下，c统计量遵循标准正态累积分布函数，依赖于正态分量的标准差（反映更大的异质性）和对数比值比（反映更大的效应）的乘积。在方差不等的二正态性假设下，c统计量遵循标准正态累积分布函数，依赖于有条件和无条件的解释变量的标准化差异。在我们的蒙特卡罗模拟中，我们发现，当解释变量的分布在有和没有该条件的整个样本中呈正态分布、伽玛分布、对数正态分布和均匀分布时，这些表达式可以合理准确地预测经验c统计量。一个连续解释变量的区分能力不能仅仅通过其比值比来判断，而总是需要考虑与总体异质性的关系。
When outcomes are binary, the c-statistic (equivalent to the area under the Receiver Operating Characteristic curve) is a standard measure of the predictive accuracy of a logistic regression model. An analytical expression was derived under the assumption that a continuous explanatory variable follows a normal distribution in those with and without the condition. We then conducted an extensive set of Monte Carlo simulations to examine whether the expressions derived under the assumption of binormality allowed for accurate prediction of the empirical c-statistic when the explanatory variable followed a normal distribution in the combined sample of those with and without the condition. We also examine the accuracy of the predicted c-statistic when the explanatory variable followed a gamma, log-normal or uniform distribution in combined sample of those with and without the condition. Under the assumption of binormality with equality of variances, the c-statistic follows a standard normal cumulative distribution function with dependence on the product of the standard deviation of the normal components (reflecting more heterogeneity) and the log-odds ratio (reflecting larger effects). Under the assumption of binormality with unequal variances, the c-statistic follows a standard normal cumulative distribution function with dependence on the standardized difference of the explanatory variable in those with and without the condition. In our Monte Carlo simulations, we found that these expressions allowed for reasonably accurate prediction of the empirical c-statistic when the distribution of the explanatory variable was normal, gamma, log-normal, and uniform in the entire sample of those with and without the condition. The discriminative ability of a continuous explanatory variable cannot be judged by its odds ratio alone, but always needs to be considered in relation to the heterogeneity of the population.
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影响因子：
5
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