## Abstract

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 R^{2}(proportion of variance explained) must be specified. This proposal raises the question of how to identify a plausible value for R^{2}in advance of model development. Our articles suggest researchers should identify R^{2}from closely related models already published in their field. In this letter, we present details on how to derive R^{2}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 R^{2}for subsequent sample size calculations for new models. Stata and R code is provided, and a small simulation study.Original language | English |
---|---|

Pages (from-to) | 859-864 |

Number of pages | 6 |

Journal | Statistics in Medicine |

Volume | 40 |

Issue number | 4 |

Early online date | 7 Dec 2020 |

DOIs | |

Publication status | Published - 20 Feb 2021 |

## Keywords

- clinical prediction model
- C statistic (AUROC)
- R squared
- sample size

## Fingerprint

Dive into the research topics of 'A note on estimating the Cox-Snell R_{2}from a reported C statistic (AUROC) to inform sample size calculations for developing a prediction model with a binary outcome'. Together they form a unique fingerprint.