Study design and regulatory information
CADENCE-Adults was a cross-sectional, laboratory-based study registered with Clinicaltrials.gov (NCT02650258). The University of Massachusetts Amherst Institutional Review Board Data approved the study protocol. Data collection for 21–60-year-old adults was conducted at the University of Massachusetts Amherst from January 2016 to October 2017. Each participant provided signed informed consent. The complete methodology, procedures, and inclusion/exclusion criteria have been described in a previous report  and are briefly described herein.
To ensure a sex- and age-balanced sample, minimize sources of bias and improve the generalizability of the findings, 160 ambulatory adults were recruited, representing 10 men and 10 women for each 5-year age-group between 21 and 60 years (i.e., 21–25, 26–30, 31–35 years of age, etc.). Exclusion criteria included: current tobacco use, pregnancy, hospitalization for mental illness in the past 5 years, body mass index (BMI) < 18.5 kg/m2 or > 40 kg/m2, stroke or cardiovascular disease, Stage 2 hypertension (systolic blood pressure ≥ 160 mmHg or diastolic blood pressure ≥ 100 mmHg), use of medication and/or diagnosis of a condition that could alter HR response to exercise, and implantation of a pacemaker or similar implanted medical device. Details regarding sample size calculation, risk stratification process, and clinical safety testing procedures have been previously published .
Treadmill testing procedures
Participants (fasted at least 4 h) were fitted with T31 Coded Transmitter chest strap (Polar Kempele, Finland). Resting HR was assessed after 5 min of sitting quietly. Participants then performed up to twelve 5-min treadmill walking bouts separated by 2-min standing rest periods on a Cybex 751 T (Cybex International Inc., MA, USA). Treadmill grade was maintained at 0% for the duration of the protocol and speed (regularly verified using a tachometer) increased from 0.5 mph (13.4 m/min) to a maximum of 6.0 mph (160.9 m/min) in 0.5 mph (13.4 m/min) increments. HR was monitored for the duration of the treadmill test, and participants were asked to self-report RPE during the last minute of each bout using the 6 to 20 Borg scale . The test was terminated when the participant either: 1) transitioned to running; 2) achieved > 75% of age-predicted HRmax [0.75 * (220-age)]; 3) reported ≥14 RPE. However, participants finished their respective bouts in which they exceeded these termination criteria unless a safety concern arose. Additionally, either the participant or the research staff could terminate the protocol for any other reason, including fatigue, instability, or other safety concerns.
Measures and related data treatment
Participant characteristics and anthropometric variables
Sex, age, and race/ethnicity were self-reported for descriptive purposes. Standing height, leg length, and weight were collected using a standardized protocol as detailed previously . Briefly, standing height was measured using a wall-mounted stadiometer (ShorrBoard® Infant/Child/Adult Portable Height-Length Measuring Board; Weigh and Measure LLC, Olney, Maryland, USA). Leg length was calculated by subtracting the seated height, measured by a stadiometer, from standing height. Weight was assessed using a scale (DC-430 U; Tanita Corporation, Tokyo, Japan). For each of these three parameters, up to three measurements were taken if the first two measurements differed by > 0.3 cm, in the case of standing height or leg length, or by > 0.5 kg, in the case of weight. The two closest measurements for each parameter were averaged. Body mass index (BMI) was calculated by dividing body weight by standing height squared (kg/m2) .
Steps were directly observed and counted via hand-tally during each treadmill bout. A video camera recording of the participants’ feet served as a back-up verification source. Total tallied steps per bout were divided by 5 (bout duration) to obtain a measurement of cadence in steps/min.
Relative intensity variables
To approximate steady-state HR, the HR data were averaged over minutes 2:45–3:45 and 3:45–4:45 of each 5-min bout. HRmax was estimated using the standard equation of 220 - age . HRresting was based on the lowest observed HR during seated rest before the treadmill protocol. HRR was calculated using HRmax - HRresting. RPE was queried in the last minute of each treadmill bout. Relative intensity was interpreted using the ACSM Guidelines for Exercise Testing and Prescription . Thus, the relatively-defined moderate intensity indicators were defined as ≥64%HRmax [100 * (HR/HRmax)], ≥ 40%HRR [100 * (HR - HRresting) / (HRmax - HRresting)], and ≥ 12 RPE. Relatively-defined vigorous intensity was defined as ≥77%HRmax, ≥ 60%HRR, and ≥ 14 RPE.
Data from four participants were not included due to equipment malfunction. Therefore, the final analytic data set included 156 adults (40.4 ± 11.5 years; 50.6% men) representing 1214 treadmill walking bouts, regardless of whether the participant reached the relatively-defined moderate or vigorous intensity thresholds. Running is a biomechanically distinct ambulatory pattern  and therefore the running and walking cadence-intensity relationships differ. Since the purpose of this analysis was to evaluate the relationship between walking cadence and relatively-defined moderate and vigorous intensity, the limited number of running bouts (n = 27 in total, 2.2% of all bouts) were deliberately excluded, leaving 1214 walking bouts for this specific analysis. The final analytical dataset and corresponding data dictionary are provided in Additional files 1 and 2, respectively, formatted in accordance with those previously published in earlier reports from the CADENCE-Adults study [20, 21].
Sample characteristics are presented as means and standard deviations or percentages, as appropriate. A non-linear relationship was observed between cadence and each of the relatively-defined intensity indicators. Specifically, the data displayed two distinct linear trends before and after a breakpoint. Therefore, consistent with previous analyses [20, 21], a segmented regression model was used to quantify the cadence-intensity relationship separately for four different age groups (Group 1: participants 21–30 years; Group 2: participants 31–40 years; Group 3: participants 41–50 years; Group 4: participants 51–60 years). The breakpoint was identified using an iterative process to determine that which minimized the mean square error of the model. Also, since each participant provided multiple data points (i.e., they provided repeated measures of variables across treadmill bouts), thus violating the assumption of data independence, the segmented regression model was fitted with fixed and random coefficients. This approach incorporated random intercepts to account for participant effects. Marginal R2 values, which represent the proportion of variance in relatively-defined intensity explained by a model’s fixed effects, were used to assess model fit. Based on previous studies also addressing the relationship between cadence and relatively-defined intensity , sex, leg length, and BMI were included as additional variables in separate and individual segmented regression models to control for their potential moderating effects. Marginal R2 values for each of these analyses were interpreted to determine whether these additional variables improved the overall prediction of the model.
Consistent with previous analyses [20, 21], we used the segmented regression equation along with the 95% prediction intervals (PIs) to solve for incremental cadence thresholds corresponding to each relatively-defined moderate and vigorous intensity indicator. Classification accuracy of walking bouts was determined respective to each intensity indicator’s identified optimal cadence threshold. As a single example, walking bouts that were ≥ 40%HRR and also ≥ the identified optimal cadence threshold were classified as true positives (TP). If they were < 40%HRR and also < the identified optimal cadence threshold they were classified as true negatives (TN). Accordingly, false positives (FP) and false negatives (FN) were classified if walking bouts were mismatched between the criterion intensity indicator and the identified optimal cadence threshold. Each optimal cadence threshold was then evaluated in terms of sensitivity (the probability of a cadence threshold accurately identifying walking at greater than or equal to a specific relative intensity threshold), specificity (the probability of a cadence threshold accurately identifying walking below a specific relative intensity threshold), positive predictive value [PPV = TP / (TP + FP); the probability of an individual walking at a given cadence achieving a specified relative intensity level], negative predictive value [NPV = TN / (TN + FN); the probability of an individual walking below a given cadence not achieving a specified relative intensity level], and overall accuracy [(TP + TN)/(TP + TN + FP + FN)].
A Receiver Operating Characteristic (ROC) curve analysis, which evaluates classifiers by displaying the performance of a binary classification method with continuous or discrete ordinal output, was also performed . For relatively-defined moderate intensity, twelve ROC curves were estimated corresponding to cadence-based classifications of reaching ≥64%HRmax, ≥ 40%HRR, or ≥ 12 RPE for each of the four age groups. For vigorous intensity, another twelve ROC curves were estimated corresponding to cadence-based classifications of reaching ≥77%HRmax, ≥ 60%HRR, or ≥ 14 RPE. Also, an optimal threshold was then identified for each ROC curve analysis by selecting the cadence that maximized Youden’s index (a measure of the overall rate of correct classification, i.e., a sum of sensitivity and specificity) [29, 30]. Sensitivity, specificity, PPV, NPV, overall accuracy, and area under the curve (AUC) were also reported. AUC values were interpreted as poor (< 0.70), fair (0.70–0.79), good (0.80–0.89), and excellent (≥ 0.90) . The bootstrap method with 20,000 replicates was used to identify 99% CIs for optimal cadence thresholds and AUC values .
The two analytical methods (regression and ROC analysis) were each used to derive two optimal thresholds, one for a particular age group and intensity. Heuristic cadence thresholds (i.e., rounded multiples of 5 steps/min) were set based on optimal thresholds associated with relatively-defined intensity indicators and identified from the segmented regression and ROC analyses. Guided by our previous work [20, 21], we settled upon heuristic values using an a priori systematic reconciliation process that considered the trade-offs in terms of sensitivity, specificity, PPV, NPV, and overall accuracy between the two analytical approaches. The final selected heuristic cadence thresholds purposely reflected a favored tolerance for FN versus FP classifications.