Robust segmented regression: application to oxygen uptake plateau identification

Abstract

Recently, segmented regression has been utilized as a "working" model for a bootstrap test to detect true oxygen uptake plateau. This approach employs an iterative procedure based on least squares to fit the model. However, it is widely acknowledged that least squares is highly sensitive to outliers, often yielding inefficient estimates. This paper proposes an alternative iterative method by substituting the least squares step with a M-estimator step. Leveraging the robust features of M-estimators, the proposed method is expected to exhibit resilience against outliers. To empirically investigate the performance of the proposed method, a Monte Carlo simulation study is conducted. For comparison purposes, the classical iterative method is also considered. The results indicate that, in uncontaminated scenarios, both methods exhibit similar behavior, with the classical method presenting a slightly superior performance. However, in contaminated cases, the classical method is highly deteriorated, with significant bias and root mean squared error, while the proposed method demonstrates much better performance. Both methods are employed to fit the "working" 3-segment regression model and perform a plateau test on apparently contaminated oxygen uptake data. The results reveal that, due to the presence of outliers, the classical method produces inflated estimates for the error variance and larger standard errors for all parameters, in comparison to the proposed method. Moreover, the plateau test conducted using the classical (robust) method leads to the rejection (confirmation) of a plateau of oxygen uptake for the same data. Overall, these findings highlight the superiority of the proposed method in handling outliers.