Among scaling analysis methods based on the root-mean-square deviation from the estimated trend, it has been demonstrated that centered detrending moving average (DMA) analysis with a simple moving average has good performance when characterizing long-range correlation or fractal scaling behavior. Furthermore, higher-order DMA has also been proposed; it is shown to have better detrending capabilities, removing higher-order polynomial trends than original DMA. However, a straightforward implementation of higher-order DMA requires a very high computational cost, which would prevent practical use of this method. To solve this issue, in this study, we introduce a fast algorithm for higher-order DMA, which consists of two techniques: (1) parallel translation of moving averaging windows by a fixed interval; (2) recurrence formulas for the calculation of summations. Our algorithm can significantly reduce computational cost. Monte Carlo experiments show that the computational time of our algorithm is approximately proportional to the data length, although that of the conventional algorithm is proportional to the square of the data length. The efficiency of our algorithm is also shown by a systematic study of the performance of higher-order DMA, such as the range of detectable scaling exponents and detrending capability for removing polynomial trends. In addition, through the analysis of heart-rate variability time series, we discuss possible applications of higher-order DMA.

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For the assessment of autonomic nervous system activity based on heart rate variability (HRV) analysis, characteristics of high-frequency (HF; 0.15 to 0.4 Hz) and low-frequency (LF; 0.04 to 0.15 Hz) components have been widely employed. HF and LF band powers quantified by power spectral analysis have most commonly been used in the conventional studies; the physiological significance of these measures has also been extensively studied. However, nonlinear characteristics of HF and LF components have not been well established. In this paper, we investigated nonlinear properties of HF and LF components in 122 healthy subjects and 108 patients with congestive heart failure (CHF). By analyzing bandpass-filtered time series of HRV corresponding to HF and LF components, it is shown that amplitude variability of HF and LF components displays long-range correlation, which cannot be explained by linear HRV properties. Compared with the age-matched healthy control group, the CHF patients showed significantly decreased long range correlation of HF component amplitude variability. These findings suggest that nonlinear properties of HF and LF components provides some complementary information on HRV dynamics.

Objectives:Studies of palliative care are often performed using single-arm pre–post study designs that lack causal inference. Thus, in this study, we propose a novel data analysis approach that incorporates risk factors from single-arm studies instead of using paired t-tests to assess intervention effects.Methods:Physical, psychological and social evaluations of eligible cancer inpatients were conducted by a hospital-based palliative care team. Quality of life was assessed at baseline and after 7 days of symptomatic treatment using the European Organization for Research and Treatment of Cancer QLQ-C15-PAL. Among 35 patients, 9 were discharged within 1 week and 26 were included in analyses. Structural equation models with observed measurements were applied to estimate direct and indirect intervention effects and simultaneously consider risk factors.Results:Parameters were estimated using full models that included associations among covariates and reduced models that excluded covariates with small effects. The total effect was calculated as the sum of intervention and covariate effects and was equal to the mean of the difference (0.513) between pre- and post-intervention quality of life (reduced model intervention effect, 14.749; 95% confidence intervals, −4.407 and 33.905; p = 0.131; covariate effect, −14.236; 95% confidence interval, −33.708 and 5.236; p = 0.152).Conclusion:Using the present analytical method for single-arm pre–post study designs, factors that modulate effects of interventions were modelled, and intervention and covariate effects were distinguished based on structural equation model.