Department of Biostatistics, Johns Hopkins University, 615 N. Wolfe St., Baltimore, MD 21205, U.S.A.
Stat Med. 2012 Nov 20;31(26):3223-40. doi: 10.1002/sim.5439. Epub 2012 Aug 1.
We propose nonparametric inference methods on the mean difference between two correlated functional processes. We compare methods that (1) incorporate different levels of smoothing of the mean and covariance; (2) preserve the sampling design; and (3) use parametric and nonparametric estimation of the mean functions. We apply our method to estimating the mean difference between average normalized δ power of sleep electroencephalograms for 51 subjects with severe sleep apnea and 51 matched controls in the first 4 h after sleep onset. We obtain data from the Sleep Heart Health Study, the largest community cohort study of sleep. Although methods are applied to a single case study, they can be applied to a large number of studies that have correlated functional data.
我们提出了两种相关功能过程均值差的非参数推断方法。我们比较了以下几种方法：（1）对均值和协方差进行不同程度的平滑处理；（2）保留采样设计；（3）使用参数和非参数方法估计均值函数。我们将该方法应用于估计 51 例严重睡眠呼吸暂停患者和 51 例匹配对照者在睡眠起始后 4 小时内睡眠脑电图平均归一化 δ 功率的均值差。我们从睡眠心脏健康研究中获取数据，该研究是睡眠领域最大的社区队列研究。尽管该方法应用于单个案例研究，但也可以应用于具有相关功能数据的大量研究。
