Introduction: Joint models are increasingly used in clinical trials. An important part of model building is to properly assess the descriptive and predictive ability of these models. Normalised prediction discrepancies (npd) and normalised prediction distribution errors (npde) have been developed to evaluate graphically and statistically non-linear mixed effect models for continuous responses. In this work, we propose to use a combined test to evaluate joint models. Methods: Prediction discrepancies (pd) are defined as the quantile of the observation within its predictive distribution and obtained by Monte-Carlo simulations. The pd for unobserved (censored) event times are imputed in a uniform distribution based on the model prediction of the probability of censoring, using a similar method as the one developed to handle data under the lower quantification limit (LOQ). We propose to combine the p-values of the tests on longitudinal data and on time-to-event (TTE) data, adjusted with a Bonferroni correction. We performed simulation studies based on a joint model characterising the relationship between prostate specific antigen biomarker (PSA) and survival in prostate cancer patients to evaluate the type I error and power of npd/npde to detect different types of model misspecifications. Results: For all types of misspecifications, the type I error of the combined test was found to be close to the expected 5%. The power of the combined test to detect model misspecifications increased with the difference from the true model and as expected, with sample size. Graphically the power increase can be related to larger differences in the shape of the survival function or PSA evolution. Conclusions: npd can be readily extended for event data by imputing the pd for censored event under the model. The test showed an adequate type I error, and was quite sensitive to alternative models tested.

翻译：引言：联合模型在临床试验中应用日益广泛。模型构建的重要环节是正确评估其描述与预测能力。标准化预测偏差（npd）及标准化预测分布误差（npde）已被开发用于连续型响应数据非线性混合效应模型的图形与统计评估。本研究提出采用联合检验方法评估联合模型。方法：预测偏差（pd）定义为观测值在其预测分布中的分位数，通过蒙特卡洛模拟获得。针对未观测（删失）事件时间的pd值，基于模型预测的删失概率，采用与处理低定量限（LOQ）数据类似的方法，通过均匀分布进行插补。我们提出结合纵向数据与时间-事件数据的检验p值，并使用Bonferroni校正进行调整。基于描述前列腺癌患者前列腺特异性抗原生物标志物（PSA）与生存关系的联合模型开展模拟研究，评估npd/npde在检测不同类型模型误设时的第一类错误率和检验效能。结果：对于所有误设类型，联合检验的第一类错误率均接近预期的5%。联合检验检测模型误设的效能随与真实模型差异增大而提升，且与样本量呈正相关。图形显示，效能提升与生存函数或PSA演变曲线的形状差异增大相关。结论：通过模型框架下对删失事件pd进行插补，可将npd直接扩展应用于事件数据。该检验具有恰当的第一类错误率，且对备择模型检验表现出较高灵敏度。