将反应建模为高频计数数据的函数：身体活动与脂肪量之间的关联
Modelling a response as a function of high frequency count data: the association between physical activity and fat mass
摘要：
我们提出了一种新的统计建模方法，其中响应是高频计数数据的函数。我们的应用程序是关于调查的健康结果之间的关系，脂肪量和身体活动（PA）测量的加速度计。加速度计将身体活动的强度量化为给定时间段内每个时期的计数。我们使用的数据从雅芳纵向研究的父母和孩子（ALSPAC），其中加速度计数据可作为一个时间序列的加速度计计数每分钟超过7天的一个子集的儿童。为了比较个人之间的加速度计配置文件，并减少高维度的配置文件的功能摘要使用。我们使用直方图作为功能摘要，由于其简单性，适用性和易于解释。我们的模型是广义标量函数回归或信号回归的扩展。它还允许多维函数预测因子和度量协变量的加性非线性预测因子。添加剂多维功能预测允许调查特定的问题，PA的影响是否随其强度，性别，一天中的时间或一周中的一天而变化。该模型的主要特点是，它利用了测量的PA的完整轮廓，而不需要定义轻，中度和剧烈活动的强度水平的临界点。我们发现，PA的影响（不一定是因果关系）不是线性的，也不是恒定的活动强度。此外，几乎没有证据表明PA强度的影响因性别而异，或者它是否发生在工作日或周末。
英文摘要：
We present a new statistical modelling approach where the response is a function of high frequency count data. Our application is about investigating the relationship between the health outcome fat mass and physical activity (PA) measured by accelerometer. The accelerometer quantifies the intensity of physical activity as counts per epoch over a given period of time. We use data from the Avon longitudinal study of parents and children (ALSPAC) where accelerometer data is available as a time series of accelerometer counts per minute over seven days for a subset of children. In order to compare accelerometer profiles between individuals and to reduce the high dimension a functional summary of the profiles is used. We use the histogram as a functional summary due to its simplicity, suitability and ease of interpretation. Our model is an extension of generalised regression of scalars on functions or signal regression. It allows also multi-dimensional functional predictors and additive non-linear predictors for metric covariates. The additive multidimensional functional predictors allow investigating specific questions about whether the effect of PA varies over its intensity, by gender, by time of day or by day of the week. The key feature of the model is that it utilises the full profile of measured PA without requiring cut-points defining intensity levels for light, moderate and vigorous activity. We show that the (not necessarily causal) effect of PA is not linear and not constant over the activity intensity. Also, there is little evidence to suggest that the effect of PA intensity varies by gender or whether it happens on weekdays or on weekends.
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