Employing Area Under the Curve (AUC) to Reduce Many Repeated Measures into Single Variables for Analysis: A Simulation Study

Background: The proliferation of fitness apps and wearable technology provides researchers interested in health and fitness with vast opportunities to test hypotheses involving a continuous stream of data collected on individual research participants in real-world settings. Although there are a variety of methods available to analyze such repeated measures data, one method that may benefit researchers in these endeavors is Area Under the Curve (AUC). To our knowledge, AUC has yet to be assessed for efficacy with many repeated measures collected from fitness apps. As such, the purpose of this study was to assess the efficacy of AUC with larger numbers of repeated measures typical of a fitness app using simulated data. Methods: We generated two samples of 21 hypothetical cyclists with 30 and 100 repeated measures of performance data (speed, time, and power) based on a Strava app segment, and calculated AUC using the trapezoidal rule and definite integrals with the best-fitting line. We then assessed the relations between time, speed, and power with all three calculations using bivariate correlations, multiple regression analysis, and a mediation analysis whereby power was hypothesized to predict a reduction in time indirectly through speed. We repeated these analyses with data assuming a normal and a lognormal distribution, and with equal versus unequal timepoints between consecutive repeated measures in the normal distribution. Results: There was little difference in relative performance comparing the two AUC calculation methods in the two samples (30 versus 100 repeated measures). However, there was a difference in the proportion mediated in the mediation results when comparing the two samples based on the number of repeated measures and spacing between consecutive repeated measures. Conclusions: The results of this study suggest that Area Under the Curve may be a viable method for assessing cumulative level of a behavior when dealing with datasets including many repeated measures such as those acquired from wearable technology and fitness apps. However, there may be differences in results when dealing with different numbers of repeated measures and variability in time between events. As such, future studies should assess AUC with larger numbers of repeated measures using non-simulated data in diverse performance scenarios.