A Nonparametric Approach to QT Interval Correction for Heart Rate

Abstract

We propose to use generalized additive models to fit the relationship between QT interval and RR (RR = 60/heart rate), and develop two new methods for correcting the QT for heart rate: the linear additive model and log-transformed linear additive model. The proposed methods are compared with six commonly used parametric models that were used in four clinical trial data sets and a simulated data set. The results show that the linear additive models provide the best fit for the vast majority of individual QT–RR profiles. Moreover, the QT correction formula derived from the linear additive model outperforms other correction methods.

Key Words:

• Clinical trial
• Generalized additive model
• Nonparametric regression model
• QTc
• QT interval correction

Notes

M1 = Model 1: Linear model QT = β + αRR.

M2 = Model 2: Hyperbolic model QT = β + α/RR.

M3 = Model 3: Parabolic model QT = βRR^α.

M4 = Model 4: Logarithmic model QT = β + αln(RR).

M5 = Model 5: Shifted logarithmic model QT = ln(β + αRR).

M6 = Model 6: Exponential model QT = β + αe ^−RR.

M7 = Model 7: Linear additive model QT = β + S(RR).

M8 = Model 8: Log-transformed linear additive model QT = exp(β + S(RR)).

M1 = Model 1: Linear model QT = β + αRR.

M2 = Model 2: Hyperbolic model QT = β + α/RR.

M3 = Model 3: Parabolic model QT = βRR^α.

M4 = Model 4: Logarithmic model QT = β + αln(RR).

M5 = Model 5: Shifted logarithmic model QT = ln(β + αRR).

M6 = Model 6: Exponential model QT = β + αe ^−RR.

M7 = Model 7: Linear additive model QT = β + S(RR).

M8 = Model 8: Log-transformed linear additive model QT = exp(β + S(RR)).

∗The number in parentheses is the number of cases for which M1 and M7 1have identical zero correlation coefficients to the 16th decimal places.

M1 = Model 1: Linear model QT = β + αRR.

M2 = Model 2: Hyperbolic model QT = β + α/RR.

M3 = Model 3: Parabolic model QT = βRR^α.

M4 = Model 4: Logarithmic model QT = β + αln(RR).

M5 = Model 5: Shifted logarithmic model QT = ln(β + αRR).

M6 = Model 6: Exponential model QT = β + αe ^−RR.

M7 = Model 7: Linear additive model QT = β + S(RR).

M8 = Model 8: Log-transformed linear additive model QT = exp(β + S(RR)).

∗The number in parentheses is the number of cases for which M1 and M7 have identical zero correlation coefficients to the 16th decimal places.