Power considerations for the application of detrended fluctuation analysis in gait variability studies

The assessment of gait variability using stochastic signal processing techniques such as detrended fluctuation analysis (DFA) has been shown to be a sensitive tool for evaluation of gait alterations due to aging and neuromuscular disease. However, previous studies have suggested that the application of DFA requires relatively long recordings (600 strides), which is difficult when working with clinical populations or older adults. In this paper we propose a model for predicting DFA variance in experimental data and conduct a Monte Carlo simulation to estimate the sample size and number of trials required to detect a change in DFA scaling exponent. We illustrate the model in a simulation to detect a difference of 0.1 (medium effect) between two groups of subjects when using short gait time series (100 to 200 strides) in the context of between- and within-subject designs. We assumed that the variance of DFA scaling exponent arises due to individual differences, time series length, and experimental error. Results showed that sample sizes required to achieve acceptable power of 80% are practically feasible, especially when using within-subject designs. For example, to detect a group difference in the DFA scaling exponent of 0.1, it would require either 25 subjects and 2 trials per subject or 12 subjects and 4 trials per subject using a within-subject design. We then compared plausibility of such power predictions to the empirically observed power from a study that required subjects to synchronize with a persistent fractal metronome. The results showed that the model adequately predicted the empirical pattern of results. Our power simulations could be used in conjunction with previous design guidelines in the literature when planning new gait variability experiments.