Effect of stride count on the validity and reliability of autocorrelation-based gait variability variables in older adults requiring long-term care

Abstract

[Purpose] In this study, we aimed to investigate the effects of stride count on the values, validity, and test-retest reliability of autocorrelation-based gait variability variables in older adults requiring long-term care. [Participants and Methods] Thirty participants walked along a 20-meter walkway with a triaxial accelerometer attached to the trunk. The experimental protocol included two walking sessions, each consisting of two consecutive trials. Autocorrelation coefficients were derived from trunk acceleration signals while varying the stride count from 2 to 10 in one-stride increments. We analyzed the influence of stride count on the absolute differences between autocorrelation coefficients and their 10-stride reference values. Additionally, for each stride count, we assessed correlations between autocorrelation coefficients and age-related outcomes, as well as the test-retest reliability of these coefficients. [Results] Absolute differences in autocorrelation coefficients decreased as stride count increased. Variations in stride count influenced age-related outcomes associated with autocorrelation coefficients. Test-retest reliability improved with increasing stride count. [Conclusion] These findings indicate that changes in stride count affect the values, validity, and test-retest reliability of autocorrelation-based gait variability variables in older adults requiring long-term care.

INTRODUCTION

Gait variability is a fundamental physiological phenomenon that reflects adaptive flexibility in response to fluctuating physical and environmental demands. Although locomotion exhibits inherently periodic characteristics, individual stride patterns demonstrate considerable heterogeneity. Notably, even during steady-state ambulation, increased gait variability is associated with impaired postural control¹⁾ and greater locomotor energy expenditure²⁾.

Gait variability is conventionally assessed through the quantification of fluctuations across multiple kinematic parameters, including stride (or step) temporal characteristics³⁾, stride length⁴⁾, step width^{5, 6)}, joint kinematic patterns^{7, 8)}, and trunk acceleration dynamics^{9, 10)}. Among these diverse measures, the autocorrelation coefficient derived from trunk acceleration has emerged as a particularly robust indicator, demonstrating exceptional reliability in older adult populations and gaining increasing recognition as a biomarker for fall history, prospective fall risk, and frailty onset^11,12,13). Contemporary applications have extended their use to therapeutic efficacy evaluation¹⁴⁾, longitudinal change monitoring¹⁵⁾, and disease progression characterization¹⁶⁾.

A critical methodological consideration pertains to the optimal stride count incorporated into analytical procedures. Regarding conventional spatiotemporal parameters, including stride (or step) temporal variability and stride length fluctuations, substantial evidence indicates that insufficient stride sampling systematically compromises test-retest reliability and limits result comparability^{17, 18)}. Furthermore, a minimum threshold of six consecutive strides has been reported for gait variability based on spatiotemporal parameters to ensure adequate measurement precision^{18, 19)}. However, for gait variability analysis based on autocorrelation coefficients derived from trunk acceleration, no minimum stride count has been defined. Therefore, previous studies have used different stride counts, ranging from 3 to over 200^{13, 20, 21)}. This disparity raises fundamental questions about whether, and to what extent, variations in stride count systematically influence the validity and reliability of autocorrelation-based gait variability variables.

Therefore, this study aimed to investigate the effects of stride count on the values, validity, and test-retest reliability of gait variability variables estimated from autocorrelation in older adults requiring long-term care. Based on established findings related to gait variability based on spatiotemporal parameters^{18, 22)}, we hypothesized that the stride count would influence both the validity and test-retest reliability of these analytical variables.

PARTICIPANTS AND METHODS

This study employed a cross-sectional design, approved by the ethics committees of Shinshu University (Approval No. 5566) and Saku Central Hospital (Approval No. R202204-26). This design was chosen because it enables the examination of associations between stride counts and gait variability variables at a single point in time without intervention, which is appropriate for methodological validation studies¹⁸⁾. All participants provided written informed consent before enrollment. This study followed the Strengthening the Reporting of Observational Studies in Epidemiology reporting guidelines²³⁾ and adhered to the principles of the Declaration of Helsinki.

Participants were recruited between July and October 2022 from older adults receiving residential or day-care services at a geriatric health services facility affiliated with Saku Central Hospital. Recruitment was conducted using a consecutive sampling method, which is considered an appropriate approach for controlling sampling bias²⁴⁾. The inclusion criteria were as follows: (1) capacity for independent ambulation over at least 20 m, with or without a single-point cane or ankle-foot orthosis, and (2) age ≥65 years with official certification for long-term care under Japan’s national insurance framework. The exclusion criteria were as follows: (1) cognitive impairment severe enough to compromise task comprehension, (2) dependence on multiple ambulatory aids or walker devices, (3) acute neurological or musculoskeletal pathology, and (4) unresolved severe pain or inflammatory swelling. Comprehensive demographic data, including age, sex, anthropometric measurements (height and weight), and comorbidity profiles, were systematically extracted from electronic medical records. Cognitive function was assessed using the Revised Hasegawa’s Dementia Scale, a culturally validated cognitive screening instrument widely used in Japanese clinical practice (sensitivity: 0.90; specificity: 0.82)²⁵⁾. Additionally, activities of daily living were evaluated using the Barthel Index²⁶⁾.

A triaxial accelerometer (MVP-RF8-HC-2000, MicroStone, Nagano, Japan) was positioned securely at the third lumbar spinous process using an elastic belt, with sensor axes aligned along the vertical, anteroposterior, and mediolateral directions.

Participants ambulated along a standardized 20-m level corridor, unobstructed and demarcated with tape markers, at a comfortable, self-selected walking speed. The experimental protocol included two walking sessions separated by a 10-min rest interval. Each session consisted of two consecutive 20-m ambulatory trials, yielding a total of four trials per participant. All assessments were conducted by a single trained evaluator to ensure consistency. For safety, the evaluator walked behind each participant while avoiding any interference with their natural gait pattern.

Walking time (in seconds) was measured with a stopwatch as the time required to walk the central 15 m of a 20 m walkway. Data acquired in the first and last 2.5 m were removed for acceleration and deceleration assessments. Walking speed was calculated by dividing the walking time by 15.

Acceleration signals were acquired at 200 Hz over the entire 20 m walkway and transmitted wirelessly via Bluetooth for offline processing in MATLAB (R2022a, The MathWorks Inc., Natick, MA, USA). Signal preprocessing applied a zero-lag Butterworth filter (cutoff frequency, 20 Hz) to the acquired acceleration signals. Initial contact events were detected using a peak detection algorithm applied to anteroposterior acceleration waveforms²⁷⁾. One stride was defined as the temporal interval between successive initial contacts of the ipsilateral limb. The stride length was calculated by dividing the 20-m walking distance by the stride count. Cadence was calculated as the stride count divided by 20-m walking time and multiplied by 60. The 20-m walking time was calculated by dividing the total number of acceleration signals measured during the 20-m walk by 200 (sampling frequency). Walking speed, stride count, stride length, and cadence were averaged across two trials for each session.

The initial and final two strides of the acceleration signal were removed to analyze steady-state walking¹⁹⁾. The analysis was performed on the remaining central portion of the data. The variability in gait was estimated using the unbiased autocorrelation procedure⁹⁾. Step-to-step (Ad1) and stride-to-stride (Ad2) autocorrelation coefficients were computed along the vertical (VT), anteroposterior (AP), and mediolateral (ML) axes. The autocorrelation coefficient indicates how similar the original signal is to its time-shifted version. Shifting the signal by one step gives the step-to-step autocorrelation coefficient, and shifting it by one stride gives the stride-to-stride autocorrelation coefficient⁹⁾. Elevated autocorrelation coefficients correspond to reduced gait variability, reflecting enhanced locomotor consistency. The autocorrelation function thus follows the equation:

A=(1 / (N−|m|)) Σ_{i=1}^{N−|m|} (x_i x_{i-m})

where A is the autocorrelation function with a time lag of m, i is the index of each sample, x_i is the i-th data and N represents the sample size.

To evaluate the validity and reliability of each autocorrelation coefficient according to the stride count included in the analysis, autocorrelation coefficients were calculated while varying the stride count from 2 to 10 in one-stride increments^{18, 22)}. Two strides represented the minimum number required to calculate the stride-to-stride autocorrelation coefficients. Ten strides were the maximum number consistently available for analysis across all participants in this study. These autocorrelation-based gait variability variables were averaged across two trials for each session¹¹⁾.

Data distribution characteristics were assessed using the Shapiro–Wilk normality test. Given the inherently bounded nature of autocorrelation coefficients (range: 0–1), Fisher’s z-transformation was applied before parametric statistical procedures to satisfy distributional assumptions. The influence of the stride count on the absolute differences in the autocorrelation coefficients from the 10-stride reference values was examined using one-way repeated-measures analysis of variance (ANOVA), with the stride count as the within-participant factor. Only the data from the first session were analyzed. Averaging the autocorrelation coefficient across participants may cancel random errors with opposite signs, which can obscure variations related to the stride count. Therefore, we used the absolute difference between the autocorrelation coefficient calculated from the 10-stride analysis and that calculated from analyses with fewer strides (2 to 9).

The impact of the stride count on the validity of autocorrelation coefficients was assessed by examining correlations between coefficients calculated using 2 to 10 strides and age-related gait outcomes (age, walking speed, stride length, and cadence)^{5, 21, 28)} previously reported to be associated with these coefficients. Pearson’s correlation coefficient was used for normally distributed variables, whereas Spearman’s rank correlation coefficient was employed for non-normally distributed variables. Pearson’s correlation coefficients were interpreted according to Portney and Watkins: r <0.25 indicated little or no relationship, 0.25 to 0.50 fair, 0.51 to 0.75 moderate-to-good, and >0.75 good-to-excellent²⁹⁾.

The test-retest reliability across stride counts was quantified using intraclass correlation coefficients (ICC[3,1], two-way mixed-effects model, absolute agreement) calculated between sessions.

Statistical significance was set at p<0.05. All statistical analyses were performed using R 4.2.3 (R Foundation for Statistical Computing, Vienna, Austria).

All power analyses were conducted using G*Power 3.1.9.2³⁰⁾. To examine the effect of stride count on the validity of autocorrelation-based gait variability variables, a significance level of 0.05, statistical power of 0.80, and large effect size of 0.50²⁸⁾ were assumed. The power analysis indicated that a minimum sample size of 21 participants was required. For the reliability analysis, the method described by Shoukri et al.³¹⁾ estimated that a sample size of 27 participants was needed to detect an ICC of 0.80, given the same α level and statistical power. Accordingly, a total of 30 participants was deemed sufficient.

RESULTS

A flowchart of participant enrollment in this study is shown in Supplementary Fig. 1. A total of 79 older adults requiring long-term care were screened. Of these, 49 were excluded, primarily due to severe cognitive impairment or walker use. Consequently, 30 participants were included in the final analysis. Of these participants, 76.7% had orthopedic disorders and 63.3% had neurological disorders. Thirteen participants were classified into multiple diagnostic categories. The participant demographic data are presented in Table 1.

Table 1. Participant characteristics.

Variables	Value
Sex (male/female)	22/8
Age (years)	81.9 ± 7.9
Height (m)	1.6 ± 0.1
Weight (kg)	57.3 ± 9.3
Hasegawa Dementia Scale Revised (points)	21.8 ± 4.6
Barthel Index (points)	88.7 ± 10.3
Comorbidity
Orthopedic disorders (%)	76.7% (n=23)
Neurological disorders (%)	63.3% (n=19)

Values are presented as the mean ± standard deviation for continuous variables, and as numbers and percentages for categorical variables.

The participants walked at a mean speed of 0.8 ± 0.2 m/s with a stride length of 0.9 ± 0.2 m and a cadence of 56.4 ± 5.0 strides/min. The overall distribution of stride counts, defined as the number of acceleration peaks in the central section of each signal after excluding the first and last two strides, is presented as a histogram in the Supplementary Material (Supplementary Fig. 2). During the walking test, 56.7% of the participants (n=17) used a single-point cane.

Supplementary Fig. 3 presents a representative example from a single participant, showing how autocorrelation coefficients varied with stride count. All parameters exhibited changes in the measured values as the stride count varied.

Table 2 summarizes the absolute differences in gait variability variables between the 10-stride reference and each shorter analysis window (2 to 9 strides). A one-way repeated-measures ANOVA revealed a significant main effect of stride count on all absolute differences: VT_Ad1 (F_{(7, 203)}=16.2, p<0.001), VT_Ad2 (F_{(7, 203)}=17.4, p<0.001), AP_Ad1 (F_{(7, 203)}=10.6, p<0.001), AP_Ad2 (F_{(7, 203)}=21.7, p<0.001), ML_Ad1 (F_{(7, 203)}=19.3, p<0.001), and ML_Ad2 (F_{(7, 203)}=24.3, p<0.001). For autocorrelation-based gait variability variables, the absolute difference from the 10-stride count reference decreased as the stride count increased from 2 to 9. The largest absolute difference was observed between the 2-stride and 10-stride counts.

Table 2. Absolute differences in autocorrelation coefficients between reduced-stride samples and 10-stride reference values.

Measure	2 strides	3 strides	4 strides	5 strides	6 strides	7 strides	8 strides	9 strides
VT_Ad1	0.060 ± 0.049	0.053 ± 0.047	0.039 ± 0.038	0.025 ± 0.022	0.024 ± 0.020	0.017 ± 0.014	0.013 ± 0.010	0.010 ± 0.007
VT_Ad2	0.105 ± 0.083	0.077 ± 0.070	0.074 ± 0.067	0.056 ± 0.041	0.039 ± 0.030	0.028 ± 0.023	0.024 ± 0.017	0.013 ± 0.011
AP_Ad1	0.067 ± 0.051	0.050 ± 0.048	0.050 ± 0.059	0.036 ± 0.043	0.022 ± 0.019	0.024 ± 0.045	0.012 ± 0.011	0.008 ± 0.007
AP_Ad2	0.094 ± 0.060	0.057 ± 0.049	0.051 ± 0.044	0.048 ± 0.042	0.030 ± 0.020	0.020 ± 0.016	0.020 ± 0.014	0.010 ± 0.008
ML_Ad1	0.080 ± 0.054	0.070 ± 0.044	0.051 ± 0.038	0.040 ± 0.028	0.031 ± 0.025	0.024 ± 0.014	0.021 ± 0.013	0.013 ± 0.010
ML_Ad2	0.134 ± 0.102	0.083 ± 0.066	0.077 ± 0.058	0.054 ± 0.044	0.036 ± 0.039	0.024 ± 0.025	0.023 ± 0.016	0.010 ± 0.010

Values represent the absolute differences between autocorrelation coefficients calculated from the reference 10-strides and those derived from fewer strides, presented as mean ± standard deviation. VT: vertical; AP: anteroposterior; ML: mediolateral; Ad1: step-to-step autocorrelation (step variability); Ad2: stride-to-stride autocorrelation (stride variability).

Table 3 shows the correlations of autocorrelation-based gait variability variables with walking speed and stride length. In addition, Supplementary Table 1 indicates the results of associations of autocorrelation-based gait variability variables with age and cadence. Alterations in stride count changed the relationships with age-related outcomes. Several variables maintained significant correlations despite changes in the stride count. Walking speed for VT_Ad1 consistently demonstrated significant correlations regardless of the stride count (r=0.398 to 0.532, all p<0.05), and stride length for VT_Ad1 also maintained significant correlations (r=0.431 to 0.467, all p<0.05), although the strength of these correlations varied. For other variables, changes in correlation strength resulted in fluctuations in statistical significance. These variables included walking speed for VT_Ad2 (r=0.324 to 0.577, p=0.001 to 0.08, significant from 3 strides onward); stride length for VT_Ad2 (r=0.301 to 0.446, p=0.014 to 0.106; significant from 5 strides onward); stride length for AP_Ad2 (r=0.399 to 0.485, p=0.007 to 0.08; significant except at 8 strides where r=−0.324); and cadence for AP_Ad2 (rho=−0.232 to −0.441; significant only at 4 strides, with rho=−0.441, p=0.015). Additionally, age showed no significant correlation regardless of the stride count (all correlations ranged from r=−0.254 to 0.295; all p>0.05).

Table 3. Correlations of walking speed and stride length with autocorrelation-based gait variability.

Variable	Measure	2 strides	3 strides	4 strides	5 strides	6 strides	7 strides	8 strides	9 strides	10 strides
Walking speed	VT_Ad1	0.532**	0.398*	0.401*	0.436*	0.448*	0.463*	0.467**	0.459*	0.452*
	VT_Ad2	0.324	0.423*	0.377*	0.504**	0.529**	0.565**	0.574**	0.577**	0.574**
	AP_Ad1	0.126	0.078	0.070	0.112	0.128	0.141	0.118	0.127	0.139
	AP_Ad2	0.228	0.184	0.120	0.192	0.255	0.256	0.268	−0.138	0.253
	ML_Ad1	−0.078	−0.050	−0.177	−0.158	−0.140	−0.154	−0.133	−0.138	−0.128
	ML_Ad2	−0.122	−0.006	−0.145	−0.051	−0.018	−0.043	−0.055	−0.055	−0.066
Stride length	VT_Ad1	0.454*	0.466**	0.467**	0.446*	0.452*	0.438*	0.431*	0.434*	0.438*
	VT_Ad2	0.301	0.322	0.359	0.374*	0.401*	0.396*	0.403*	0.418*	0.446*
	AP_Ad1	0.320	0.305	0.324	0.304	0.301	0.313	0.280	0.303	0.319
	AP_Ad2	0.416*	0.485**	0.425*	0.399*	0.449*	0.426*	0.439*	−0.324	0.468**
	ML_Ad1	−0.280	−0.106	−0.266	−0.314	−0.339	−0.359	−0.333	−0.324	−0.297
	ML_Ad2	−0.309	−0.133	−0.204	−0.144	−0.150	−0.176	−0.179	−0.167	−0.152

*p<0.05, **p<0.01. VT: vertical; AP: anteroposterior; ML: mediolateral; Ad1: step-to-step autocorrelation (step variability); Ad2: stride-to-stride autocorrelation (stride variability).

Pearson’s correlation coefficients were calculated for all variables.

The test–retest reliability improved as the stride count increased and reached a plateau at ICC ≥0.8 (Table 4). For AP_Ad1, although the ICC increased with more strides, it remained above 0.80, even when only 2 strides were analyzed. The ICC increased as the stride count increased, exceeding 0.80 when more than 6 strides were analyzed for ML_Ad1, 7 strides for VT_Ad1 and ML_Ad2, 8 strides for AP_Ad2, and 9 strides for VT_Ad2.

Table 4. Intraclass correlation coefficients for test-retest reliability of gait variability measures calculated from varying numbers of strides.

	2 strides	3 strides	4 strides	5 strides	6 strides	7 strides	8 strides	9 strides	10 strides
VT_Ad1	0.586	0.654	0.711	0.770	0.797	0.843*	0.875*	0.887*	0.905*
VT_Ad2	0.637	0.472	0.508	0.634	0.657	0.699	0.785	0.840*	0.859*
AP_Ad1	0.825*	0.904*	0.915*	0.908*	0.923*	0.925*	0.945*	0.958*	0.968*
AP_Ad2	0.790	0.607	0.620	0.726	0.765	0.763	0.814*	0.849*	0.867*
ML_Ad1	0.677	0.654	0.744	0.791	0.846*	0.888*	0.884*	0.902*	0.914*
ML_Ad2	0.416	0.398	0.612	0.744	0.784	0.828*	0.817*	0.879*	0.892*

*ICC ≥0.8. VT: vertical; AP: anteroposterior; ML: mediolateral; Ad1: step-to-step autocorrelation (step variability); Ad2: stride-to-stride autocorrelation (stride variability). Intraclass correlation coefficients (ICC) for gait variability measures across different stride counts.

DISCUSSION

Our findings demonstrate that the absolute differences between autocorrelation coefficients at each stride count and the 10-stride reference progressively decreased as the stride count increased. The changes in the stride count altered the age-related outcomes related to the autocorrelation-based gait variability variables. Furthermore, test-retest reliability measured with the ICC increased with greater stride count. These findings suggest that the stride count influences both the validity and reliability of autocorrelation-based gait variability variables.

Our findings indicate that the stride count directly impacts the accuracy of autocorrelation coefficients derived from trunk accelerometry. Our results are consistent with previous studies on gait variability based on spatiotemporal parameters²²⁾. Measurement accuracy improves as the stride count increases, because random variation between trials and device error—both more pronounced in smaller samples³²⁾—are reduced with larger sample sizes. The autocorrelation coefficient quantifies the similarity among acceleration waveforms; when more strides are analyzed, the coefficients more accurately reflect the true physiological variability of gait rather than chance similarities or discrepancies between individual strides. Additionally, increasing the stride count reduces sampling variance and enhances the signal-to-noise ratio, as additive sensor noise is more effectively averaged and slower inter-stride modulations are better captured. Consequently, analyzing a greater stride count decreases errors in autocorrelation coefficients³³⁾. Therefore, variations in the stride count can alter the measurement values, which may consequently affect validity and test-retest reliability.

The validity of autocorrelation-based gait variability variables is also influenced by the stride count, particularly in relation to their associations with age and spatiotemporal gait parameters. Previous studies have reported significant differences in autocorrelation coefficients between younger and older adults²¹⁾. The lack of a significant correlation with age in the present study may be attributed to the age distribution being skewed toward older participants. Consistent with previous findings, correlations were observed between walking speed, stride length, cadence, and autocorrelation coefficients^{5, 28)}. However, the presence of significant correlations varied depending on the stride count. Notably, for walking speed and stride length, significant correlations with vertical stride-to-stride gait variability emerged as the stride count increased. This finding is supported by our analytical results, showing that the absolute differences in stride-to-stride autocorrelation coefficients decreased with a greater stride count. Therefore, these results suggest that the emergence of significant correlations with increasing stride count may be attributable to improved measurement precision³⁴⁾. Previous studies have reported inconsistent findings regarding autocorrelation coefficient measurements for assessing gait variability. Three studies—Moe-Nilssen and Helbostad⁵⁾, Matsumoto et al.³⁵⁾, and Bogen et al.¹⁵⁾—reported decreased anteroposterior autocorrelation coefficient (increased variability) in older adults with frailty or reduced motor function. These studies collected data over relatively long walking distances: 6 m, 5 m (out of 9 m total), and 6.5 m (out of 10.5 m total). In contrast, Martínez-Ramírez et al.¹³⁾ found no significant differences in anteroposterior step or stride autocorrelation coefficients across frailty levels; however, their effective measurement distance was notably shorter, at only 1 m. The existing literature has not adequately addressed factors affecting gait autocorrelation analysis, particularly the influence of measurement conditions, such as the stride count. Based on our findings, the stride count should be considered a potential factor contributing to discrepant results across studies evaluating gait using autocorrelation coefficients.

The test–retest reliability improved as the stride count increased and reached a plateau at ICC ≥0.8. These results are consistent with previous studies that reported increased reliability of gait variability based on spatiotemporal parameters with a greater stride count¹⁸⁾. When more strides are analyzed, the random fluctuations inherent to each stride are averaged, reducing variability in measurements within the same participant. From a statistical perspective, as error variance decreases, the proportion of true inter-individual differences decreases, resulting in higher ICC values. Because reliability is a prerequisite for clinical interpretation, these results suggest that analyzing a sufficient stride count is essential when applying autocorrelation-based gait assessments.

However, prolonged walking may cause physical or cognitive fatigue in older adults requiring long-term care, which can result in secondary measurement errors³⁶⁾. Therefore, it is important to balance psychometric robustness with feasibility. Previous studies have suggested that at least six strides are needed for stable estimates of gait variability based on spatiotemporal parameters¹⁸⁾. In contrast, our results showed that this stride count did not provide sufficient reliability for autocorrelation-based gait variability variables. This finding highlights the need to standardize the stride count required for reliable analyses using autocorrelation-based gait variability variables.

This study has some limitations. First, the sample size is relatively small; although many participants had comorbidities, disease-specific subgroup analyses could not be performed. Another potential limitation is that the participants in this study were limited to older adults who had been certified as requiring long-term care. Therefore, caution is needed when generalizing the findings to other populations, such as community-dwelling older adults without care certification or those who are hospitalized.

In conclusion, the stride count used in the analysis significantly influences the autocorrelation coefficients and their associated validity and reliability. Specifically, analyses based on a greater stride count reduced the absolute differences from the 10-stride reference in autocorrelation coefficients, altered their correlations with age-related outcomes, and improved test-retest reliability. These results emphasize the need for standardized analytical protocols and adequate stride counts when using the autocorrelation coefficient as a measure of gait variability in older adults who require long-term care. Future research should focus on defining stride thresholds suitable for longitudinal monitoring and clinical applications.

Funding and Conflict of interest

No potential conflicts of interest or sources of funding relevant to this article were reported.