Minimum Sample Size for Developing a Multivariable Prediction Model using Multinomial Logistic Regression

作     者：Pate, Alexander Riley, Richard D. Collins, Gary S. van Smeden, Maarten Van Calster, Ben Ensor, Joie Martin, Glen P. 

作者机构：Division of Informatics Imaging and Data Science Faculty of Biology Medicine and Health University of Manchester Manchester Academic Health Science Centre Manchester United Kingdom Centre for Prognosis Research School of Medicine Keele University Staffordshire United Kingdom Centre for Statistics in Medicine Nuffield Department of Orthopaedics Rheumatology and Musculoskeletal Sciences University of Oxford Oxford United Kingdom NIHR Oxford Biomedical Research Centre John Radcliffe Hospital Oxford United Kingdom Julius Center for Health Sciences University Medical Center Utrecht Utrecht University Utrecht Netherlands Department of Clinical Epidemiology Leiden University Medical Center Leiden Netherlands Department of Development and Regeneration KU Leuven Leuven Belgium Department of Biomedical Data Sciences Leiden University Medical Centre Netherlands EPI-center KU Leuven Leuven Belgium 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Forecasting 

摘      要：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 (n) is appropriate relative to the number of events (Ek) and the number of predictor parameters (pk) 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 criteria aims to minimise the model overfitting. The second aims to minimise the difference between the observed and adjusted R2 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 R2 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 R2 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) are natural extensions from previously proposed criteria for binary outcomes. We illustrate 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. © 2022, CC BY.