#### 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

#### Abstract

Transfer Entropy (TE) measures the amount of information which flows from a random process to another one. Recently, TE was used to assess the inter-relationship between the RR and QT intervals, conditioned on different numbers of past values. As a result, a new approach for correcting the QT interval was proposed by setting TE(RR->QT)=0 (no information flows from the RR to the corrected QT).

In this study, we provided three closed-form solutions for the coefficient of a linear QT correction formula obtained when setting TE=0 and, the bivariate random process (RR/QT) is stationary and normally distributed. The three solutions arise from different assumptions on the underlying random process. We proved that setting TE=0 is equivalent to the correction obtained by minimum mean square error (MMSE), i.e., the slope of the QT/RR relationship when assuming no correlation between RR and the previous QT interval. In case such correlation instead exists, the optimal solution takes a different expression which we also derived. Finally, we showed that the condition TE=0 cannot always be theoretically reached, suggesting the introduction of a new QT correction paradigm, according to minimum transfer entropy (MTE) principle.

The correction formulas, according to both MMSE and MTE, were tested on QT/RR series extracted from 25 Holter recordings available on Physionet. We verified if the Pearson's correlation between previous QT interval and RR value was statistically significant, thus motivating the use of the new MTE-based coefficient. The correlation found was 0.69+/-0.28 (p<0.01). The individual coefficients computed according to the two approaches were MMSE: 0.133+/-0.069 vs MTE: 0.093+/-0.052 (p<0.01), with an average reduction of approximately 30%.

In conclusion, the study paves the ground for a better understanding of the newly introduced QT correction scheme and may open up interesting investigations in scenarios such as drug safety testing and cardiac risk assessment.