Minimum sample size for developing a multivariable prediction model using multinomial logistic regression.
Minimum sample size for developing a multivariable prediction model using multinomial logistic regression.
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DOI：
10.1177/09622802231151220
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发表时间：
2023-03
影响因子：
2.3
通讯作者：
Martin, Glen P.
中科院分区：
文献类型：
--
作者：
Pate, Alexander;Riley, Richard D.;Collins, Gary S.;van Smeden, Maarten;Van Calster, Ben;Ensor, Joie;Martin, Glen P.
多项Logistic回归模型使人们能够预测具有2个类别的分类结果的风险。在开发这样的模型时，研究人员应该确保参与者的数量()相对于每个类别k的事件数量()和预测参数的数量()是合适的。我们根据现有的为二元结果开发的标准提出了三个标准来确定所需的最小n。第一个标准旨在最大限度地减少模型的过度拟合。第二个目标是将观测到的Nagelkerke和调整后的Nagelkerke之间的差异降至最小。第三个标准旨在确保准确估计总体风险。对于准则(I)，我们表明样本量必须基于与多项Logistic回归的子模型相对应的不同的一对一Logistic回归模型的预期Cox-Snell，而不是基于多项Logistic回归的总体Cox-Snell。我们通过模拟研究测试了所提出的标准(I)的性能，发现它导致了期望的过拟合度。标准(二)和(三)是先前提出的二元结果标准的自然延伸，不需要通过模拟进行评估。我们通过一个实际例子说明了如何实施样本大小标准，考虑到当卵巢肿块出现时，肿瘤类型的多项式风险预测模型的发展。给出了仿真和实例代码。我们将把我们提出的标准嵌入到pmsampsize R库和Stata模块中。
Multinomial logistic regression models allow one to predict the risk of a categorical outcome with > 2 categories. When developing such a model, researchers should ensure the number of participants () is appropriate relative to the number of events () and the number of predictor parameters () for each category k. We propose three criteria to determine the minimum n required in light of existing criteria developed for binary outcomes. The first criterion aims to minimise the model overfitting. The second aims to minimise the difference between the observed and adjusted Nagelkerke. The third criterion aims to ensure the overall risk is estimated precisely. For criterion (i), we show the sample size must be based on the anticipated Cox-snell of distinct ‘one-to-one’ logistic regression models corresponding to the sub-models of the multinomial logistic regression, rather than on the overall Cox-snell of the multinomial logistic regression. We tested the performance of the proposed criteria (i) through a simulation study and found that it resulted in the desired level of overfitting. Criterion (ii) and (iii) were natural extensions from previously proposed criteria for binary outcomes and did not require evaluation through simulation. We illustrated how to implement the sample size criteria through a worked example considering the development of a multinomial risk prediction model for tumour type when presented with an ovarian mass. Code is provided for the simulation and worked example. We will embed our proposed criteria within the pmsampsize R library and Stata modules.
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影响因子：
1.3
作者：
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通讯作者：
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