Analysis of experiments with high frequency time series responses and the implications for power and sample size

Given more accessible non-invasive measuring devices, experimental response can now be observed as high-dimensional and high-frequency time series. Amidst the complex dependence structure in the data analysis, sample size determination and power analysis remain to be the key thematic focus of statistical inference. The issue is confounded with the complexity of time lag structure and phase shift usually observed in a non-uniform but normal process typically present in medical imaging data. To address these issues in case-control studies, responses can be analyzed to obtain evidence of group differences through time series clustering based on dynamic time warping. The warping of multiple time series provides a flexible distance measure robust to time point concurrence. Time series clustering partitions experimental units into groups, enabling the computation of distances to measure effect size through sum of squares of pairwise distances in warped time series.Time series clustering provides an alternative to analysis of variance when experimental responses are high-frequency time series data. Kernel regression is formulated to link sample size, effect size, power of the test, and level of significance accounting for the structure of the data generating process of the time series responses. This provides a strategy for clinicians to optimize the power of the test that can be achieved with a minimal sample size for this experimental setup. Time series clustering method is able to differentiate case and control groups in the simulated data and in the ADHD-200 fMRI dataset. The distance measured between two or more groups of time series can be used to determine sample size for a target power.