Calibration is a vital aspect of the performance of risk prediction models, but research in the context of ordinal outcomes is scarce. This study compared calibration measures for risk models predicting a discrete ordinal outcome, and investigated the impact of the proportional odds assumption on calibration and overfitting. We studied the multinomial, cumulative, adjacent category, continuation ratio, and stereotype logit/logistic models. To assess calibration, we investigated calibration intercepts and slopes, calibration plots, and the estimated calibration index. Using large sample simulations, we studied the performance of models for risk estimation under various conditions, assuming that the true model has either a multinomial logistic form or a cumulative logit proportional odds form. Small sample simulations were used to compare the tendency for overfitting between models. As a case study, we developed models to diagnose the degree of coronary artery disease (five categories) in symptomatic patients. When the true model was multinomial logistic, proportional odds models often yielded poor risk estimates, with calibration slopes deviating considerably from unity even on large model development datasets. The stereotype logistic model improved the calibration slope, but still provided biased risk estimates for individual patients. When the true model had a cumulative logit proportional odds form, multinomial logistic regression provided biased risk estimates, although these biases were modest. Non-proportional odds models require more parameters to be estimated from the data, and hence suffered more from overfitting. Despite larger sample size requirements, we generally recommend multinomial logistic regression for risk prediction modeling of discrete ordinal outcomes.
翻译:校准是风险预测模型性能的一个重要方面,但是,在ordinal结果背景下的研究却很少。这项研究比较了风险模型的校准措施,预测离散的正统结果,并调查了对校准和校准过大比例概率假设的影响。我们研究了多数值、累积、相邻类别、持续比率和定型逻辑/逻辑模型。为了评估校准,我们调查了校准拦截和斜坡、校准图和估计校准指数。我们利用大量抽样模拟,研究了不同条件下的风险估算模型的性能,假设真实模型具有多数值的多数值后勤格式或累积日志比例概率表,并调查了模型对校准和校正比例的成比例性假设。我们开发模型的校准率比重比重比重大得多,但校准率比重比重比重比重比重比重比重比重比重也大,但对大型模型的师型发展模型进行了校准,但准确的校准率模型比重比重比重也比重了比重。 校正的校准模型要求的校准的校准比比比比比比比比值是更精确的校正的校定,比比比比比值比比比比比比比比比比,比比比比比比比比比比比比比比比比比比比比比比重,比比比比比比比比了更的,比比比比比比比比比比比比比比比比比比比比比比比比比比比比比比比比比,比比比比比比比比比比比比比比比比比比,比比比比比比比比比比比比比比比比比比比比比比比比比比比,比比比比比比比比比比比比比比比比比比比比比比比比比比的比的比比比比比比比比比比比比比比,比比比比比比比比比比比比比比比比比比比比比比比比比比的比比比比比比比比比比比比比比比比比比比比比比比比比比比比比比比比比比比的比的比比比比比