In 2019 we published a pair of articles in Statistics in Medicine that describe how to calculate the minimum sample size for developing a multivariable prediction model with a continuous outcome, or with a binary or time‐to‐event outcome. As for any sample size calculation, the approach requires the user to specify anticipated values for key parameters. In particular, for a prediction model with a binary outcome, the outcome proportion and a conservative estimate for the overall fit of the developed model as measured by the Cox‐Snell R² (proportion of variance explained) must be specified. This proposal raises the question of how to identify a plausible value for R² in advance of model development. Our articles suggest researchers should identify R² from closely related models already published in their field. In this letter, we present details on how to derive R² using the reported C statistic (AUROC) for such existing prediction models with a binary outcome. The C statistic is commonly reported, and so our approach allows researchers to obtain R² for subsequent sample size calculations for new models. Stata and R code is provided, and a small simulation study.

中文翻译：

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关于根据报告的C统计量（AUROC）估算Cox-Snell R2的说明，以告知样本量计算以开发具有二元结果的预测模型

在2019年，我们在《医学统计学》上发表了两篇文章，描述了如何计算最小样本量，以开发具有连续结果，二进制结果或事件发生时间结果的多变量预测模型。对于任何样本量计算，该方法都要求用户指定关键参数的预期值。特别是，对于具有二元结果的预测模型，必须指定结果比例和由Cox-Snell R ²（解释的方差比例）测量的已开发模型整体拟合的保守估计。该建议提出了一个问题，即如何确定R ²的合理值。在模型开发之前。我们的文章建议研究人员应从其领域中已经发布的密切相关的模型中识别R ²。在这封信中，我们介绍了如何使用已报告的C统计量（AUROC）来为此类现有的具有二进制结果的预测模型导出R ^2的详细信息。该Ç统计数字是常见的，所以我们的方法，使研究人员获得[R ²为后续的计算样本量的新车型。提供了Stata和R代码，并进行了小型仿真研究。