A longitudinal study was undertaken recently in the USA to investigate the perceptual efficacy of a supplement tablet. Efficacy was assessed using an 11-attribute 5-point Rating Scale (RS). The RS diary time-intensity data were analyzed using functional data analysis (FDA). The mean RS functional curves and their 1st and 2nd derivative curves are produced. Attribute intensities (symptom relief) are compared to baseline measures. Two indices of efficacy were used to measure reduction in symptom severity. Results show symptoms decreased over the 12-week study with use of the tablet. The focus of this paper is on applied use of FDA and the new index A.RS which shows advantages by providing examination of the full range of longitudinal data (0–84 days) and a percentage efficacy index versus a traditional efficacy index that is based on the difference between just two time points (day 0 and day 84). The analytic methods in this paper have relevancy for sensory and consumer time-intensity research and longitudinal study.

中文翻译：

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使用功能数据分析 (FDA) 进行感知功效的时间强度 (TI) 评估，以补充片剂纵向研究为例

美国最近进行了一项纵向研究，以调查补充剂片剂的感知功效。使用 11 属性 5 点评分量表 (RS) 评估疗效。使用功能数据分析 (FDA) 分析 RS 日记时间强度数据。生成平均 RS 功能曲线及其一阶和二阶导数曲线。将属性强度（症状缓解）与基线测量进行比较。使用两个功效指数来衡量症状严重程度的减轻。结果显示，在为期 12 周的研究中，使用该药片后症状有所减轻。本文的重点是 FDA 和新指数 A.RS 的应用使用，通过对全方位纵向数据（0-84 天）和百分比功效指数的检查显示出优势，而传统功效指数基于仅两个时间点（第 0 天和第 84 天）之间的差异。本文的分析方法与感官和消费者时间强度研究和纵向研究具有相关性。