The current paper is motivated by longitudinal progress tests given to medical students in the United Kingdom, which are used to assess students' applied medical knowledge during their learning programme. The main analytic interest is the maximum competency each student achieves on the assessment and the point in the programme at which each student attains this competency. Direct estimates of maximum competency and the time at which students realised this competency are useful for optimising allocation of classroom and hands-on experiences, as well as to inform curriculum development. Models have been developed for estimating the timing of a threshold or cut-off common across people or for estimating different rates of change that occur for different phases of time. However, less attention has been paid to models interested in the timing of a value that can change across people—such as maximum competency—and where growth is flat in some phases of time. In this paper, we build a model that borrows pieces from various existing methods such as reparameterisations of polynomial models, splines for ceiling effects, time-to-criterion models, dynamic measurement and non-linear mixed-effect models to allow the motivating questions to be addressed from these data.

中文翻译：

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在医学生进步测试中模拟达到最大能力的时间

当前论文的动机是对英国医学生进行的纵向进度测试，该测试用于评估学生在学习计划中的应用医学知识。主要的分析兴趣是每个学生在评估中达到的最大能力，以及每个学生在课程中获得这种能力的时间点。直接估计最大能力和学生意识到这种能力的时间有助于优化课堂和实践经验的分配，并为课程开发提供信息。已经开发了模型来估计人们共同的阈值或截止时间，或者估计不同时间阶段发生的不同变化率。然而，很少有人关注模型，这些模型关注的是可以在人与人之间发生变化的价值的时间——例如最大能力——以及在某些时间阶段增长持平的模型。在本文中，我们构建了一个模型，该模型借鉴了各种现有方法，例如多项式模型的重新参数化、天花板效应样条、时间标准模型、动态测量和非线性混合效应模型，以允许激发问题从这些数据中得到解决。