In many longitudinal studies, it is often of interest to investigate how the {\it geometric functional features} (such as the curvature, location and height of a peak), of a marker's measurement process is associated with the time to event being studied. We propose a joint model for certain geometric functional features of a longitudinal process and a time to event, making use of B-splines to smoothly approximate the infinite dimensional functional data. The proposed approach allows for prediction of survival probabilities for future subjects based on their available longitudinal measurements. We illustrate the performance of our proposed model on a prospective pregnancy study, namely Stress and Time to Pregnancy, a component of Oxford Conception Study, where hormonal measurements of luteinizing hormone (LH) and estrogen indicate timing of ovulation, and whether ovulation is going to occur, in a menstrual cycle. A joint modeling approach was used to assess whether the functional features of the hormonal measurements, such as the peak of the hormonal profile and its curvature, are associated with time to pregnancy. Our simulation studies indicate reasonable performance of the proposed approach.

翻译：在许多纵向研究中,人们往往有兴趣调查标记的测量过程的何何等几何功能特征(如峰值的曲度、位置和高度)如何与正在研究的事件的时间相关。我们提出了一个关于长度过程的某些几何功能特征和发生时间的联合模型,利用B-splines来顺利地接近无限的维度功能数据。拟议方法允许根据现有纵向测量结果预测未来对象的生存概率。我们介绍了我们提议的关于未来怀孕研究模型的绩效,即对怀孕的压力和时间,这是牛津概念研究的一部分,其中对润滑激素(LH)和雌激素的激素测量表明排卵的时机,以及排卵是否将在月经周期中发生。使用联合模型方法评估荷尔蒙测量的功能特征,如荷尔蒙剖面顶峰及其曲线,是否与怀孕时间相关。我们的模拟研究显示拟议方法的合理性能。