Estimation of the QT-RR relation: trade-off between goodness-of-fit and extrapolation accuracy

Correction of the QT interval in the ECG for changes in heart rate (RR interval) is needed to compare groups of patients and assess the risk of sudden cardiac death. The QTc represents the QT interval at 60 bpm, although most patients typically have a faster heart rate, thus requiring extrapolation of the QT-RR relationship. Objective: This paper investigates the ability of QT-RR models with increasing number of parameters to fit beat-to-beat variations in the QT interval and provide a reliable estimate of the QTc. Approach: One-, two- and three-parameter functions generalising the Bazett and Fridericia formulas were used in combination with hysteresis reduction (memory) obtained by time-averaging the history of RR intervals with exponentially-decaying weights. In normal men and women datasets of Holter recordings in normal subjects (24 h monitoring), two measures were computed for each model: the root mean square error (RMSE) of fitting and the difference between the estimated QTc and a reference QTc obtained by collecting data points around RR = 1000 ms. Main results: The two-and three-parameter functions all gave similar low RMSE with uncorrelated residues. An optimal memory parameter was found that still minimized the RMSE and could be used for all functions and subjects. This reduction in RMSE resulted from changes in the parameters linked to the increased steepness of the QT-RR relation after hysteresis reduction. At optimal memory, the two and three-parameter models provided poorer prediction of the QTc as compared to the Fridericia's model in subjects with fast heart rates, since accurate representation of the steeper QT-RR relation worsened the extrapolation that was then needed to determine the QTc. Significance: As a result, among all models investigated, the Fridericia formulation offered the best trade-off for QTc prediction robust to memory and fast heart rates.