Transfer Entropy for Linear QT Correction Under Stationary and Gaussian Assumptions of the QT/RR Probability Distribution

Massimo W Rivolta
Dipartimento di Informatica, Università degli Studi di Milano


Recently, Transfer Entropy (TE) was proposed as a new approach to correct the QT interval by setting TE(RR->QT) equal to 0.

In the first part of the study, we provided a closed-form solution for the coefficient of a linear correction formula according to TE=0, when the random process QT/RR is stationary and normally distributed. When the QT/RR history is neglected, the obtained coefficient is equivalent to the slope of the QT/RR relationship obtained by minimum mean square error (MMSE). When the history is instead considered, the optimal coefficient takes a different expression. Also, we found that TE=0 cannot always be set. Therefore, we introduced a new QT correction paradigm according to minimum transfer entropy (MTE).

In the second part of the study, we computed the correction formulas according to both MMSE and MTE, from QT/RR series extracted from 25 Holter ECG recordings available on Physionet. The MTE approach considered individual Pearson's correlation coefficients between previous QT interval and RR value, which was found statistically different than 0, i.e., 0.70 +/- 0.31 (p<0.01).

The individual coefficients obtained with both approaches were: MMSE=0.143 +/- 0.061 vs MTE=0.101 +/- 0.052 (p<0.05), with the latter resulting in an average reduction of about 27%.

The study suggested that the use of QT/RR history significantly changes the value of the optimal coefficient.