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RR curvatures in the design of individual heart rate corrections of the QT interval
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ScienceDirect Journal of Electrocardiology 47 (2014) 385 – 393 www.jecgonline.com
Letters to the Editor Importance of subject-specific QT/RR curvatures in the design of individual heart rate corrections of the QT interval Malik and coauthors [1] investigated whether the curvature in the QT–RR relationship differs from subject to subject and recommend that an individualized correction of QT for RR should take into account individual curvature in order to obtain optimal results. The authors claim to have demonstrated that an individualized correction that takes this curvature into account is more effective than other methods (e.g., a parabolic correction) in removing the heart rate dependency of QTcI. Since the proposed methodology has been generated and tested on the same data set, we do not find the evidence convincing and certainly not conclusive and suggest how an evaluation could be performed. QT and RR are subject to variability of several sources, both technical, such as measurement errors, and biological. The latter include influences from uncontrollable or unobserved factors influencing the subject and therefore potentially the QT–RR relationship. In our view, the question of individual curvature is best addressed in the framework of statistical inference. Instead of a model with a parameter describing curvature, the authors prefer an approach that compares different functional relationships that imply different curvatures [2]. Malik et al. then use the mean squared residuals (MSR) as a criterion for goodness of fit and select the model with the lowest MSR as the best fitting. Each of the 12 models considered is described by two parameters. Therefore, the MSR criterion seems adequate for the comparison of the models and the selection of the best fitting one. The authors show that with the minimum MSR criterion, the QT–RR relationship of different subjects is best described by different models. They conclude that curvature is an important individual parameter in the description of the QT–RR relationship. We however believe that a convincing argument for this conclusion is missing and that the authors have not shown that the new approach is better than, for example, an individualized parabolic correction (referred to as log-linear in their publication). This could be shown, for example, by a statistical test of the null hypothesis that the data follow an individualized parabolic model against the alternative that different subjects follow different models. Such a test could use the MSR as measure of fit. Alternatively, showing that the individualized model is stable over time is an even more convincing argument. Indeed, the structure of the data used by Malik et al. suggests such an approach. Each subject 0022-0736/$ – see front matter © 2014 Elsevier Inc. All rights reserved.
contributed four 14-hour recordings, two in each of two periods. Within each period the recordings were separated by 2 days while there were least 22 days between the two periods. A simple but crude way to show the stability of the individualized correction is to determine the optimal correction models separately for each period and look at the proportion of subjects where the two optimal models coincide. In addition to this crude method, we propose a more quantitative approach that is inspired by the one described by Tornøe et al. [3]. As pointed out by Malik et al., there is a QT correction corresponding to each of the models considered. Indeed, the principal interest in the QT–RR relationship comes from the need for a QTc (i.e., a predicted QT at a fixed RR), which is independent of the actual value of RR. In this context, the QT–RR model is deemed optimal, if it removes the heart rate dependency the best way. Importantly and as a general principle, the quality of the prediction should be evaluated on data distinct from those used for the inference of the relationship. Let QTck designate the corrected QT using model k. Given the structure of the data used by Malik et al. [1], our proposal would be: • For each subject (subject i) use the Holter recordings of one period (learning set) to obtain the 12 models and the corresponding individual correction coefficients αik. • Determine the optimal model ki, opt as described in the article and the optimal correction formula to obtain QTci,opt. • For each subject, use the two Holter recordings of the other period as independent test set. Calculate the individually corrected QTc according to the optimal model (QTci, opt) and according to each of the 12 models (QTck = Ψk(QT, RR, αik) for k = 1,…,12) at all time points available. • For each of the 13 sets of corrected QTc values, obtained from the independent test set calculate the mean squared slopes (MSS) across subjects as suggested in Tornøe et al. [3]. Since focus is on curvature, which may not be properly represented by a slope, it will be prudent to look at the regression residuals as described [1] and determine the mean across subjects of the squared residuals (MSR). If curvature as expressed by the set of the 12 models is a subject-specific trait, the MSS and MSR for the optimal model should be smaller than those for all other
386
Letters to the Editor / Journal of Electrocardiology 47 (2014) 385–393
only one parameter. Wang et al. [5] elaborated on the balance between bias and random error in the different ways of correcting QT for RR, and their observations are likely to apply to an individual correction method based on two parameters instead of only one. We would therefore welcome if Malik et al. showed that their proposed methodology removes heart rate dependency better than others when tested on data not used for its derivation and by this way convincingly show the usefulness of curvature as an additional parameter in individual correction. Georg Ferber, PhD Statistik Georg Ferber GmbH Riehen, Switzerland E-mail address: [email protected] Meijian Zhou M., PhD iCardiac Technologies Rochester, NY, USA Fig. 1. Stability of correction coefficients: parabolic. Stability of individual correction coefficients for a parabolic correction over time. For 60 subjects who participated in a crossover TQT study, correction coefficients were calculated from the baseline days of period 2 (abscissa) and period 3 (ordinate). All beats of the respective 24-hour Holter recordings that passed a semiautomatic quality control procedure were used to derive the correction coefficients. The dashed line represents equal values for both periods. For the majority of the subjects, modest variability between the values obtained in the two periods can be observed, while a few subjects show substantial differences. Figure reproduced from J of Pharmacological & Toxicological Methods (2013). Holzgrefe et al. Preclinical QT safety assessment: crossspecies comparisons and human translation from an industry consortium, http://dx.doi.org/10.1016/j.vascn.2013.05.004.
Borje Darpo, MD, PhD iCardiac Technologies, Rochester NY, USA Karolinska Institutet Division of Cardiovascular Medicine Department of Clinical Sciences Danderyd's Hospital, Stockholm, Sweden http://dx.doi.org/10.1016/j.jelectrocard.2013.12.010 References
models. If this were not the case, we would conclude that the intra-individual variability of the QT–RR relationship is too large to warrant the use of a model with individual curvatures. Batchvarov et al. [4] showed that the inter-individual variability in the QT–RR relationship outweighs the intraindividual one. We agree with the authors that this interindividual variability most likely also extends to curvature. However, the observations of Batchvarov et al. do not preclude the existence of substantial intra-individual variability. Indeed, intra-individual variability can be seen if an individual correction (e.g., a parabolic one) is fitted to 24-hour Holter data obtained in the same subject at different occasions. In a three-period crossover TQT study with 60 subjects, we calculated parabolic QTcI based on 24-hour Holter recordings at baseline of the second and third periods respectively (Fig. 1; reproduced with permission). There is only modest agreement between the exponents of the correction formulae from different periods. There may be situations where an individual correction does not outperform Fridericia's correction if a criterion like the mean squared slope of Tornøe et al. [3] is used. Likewise, even if it can be confirmed that the intersubject variability of curvature outweighs the intraindividual one, this does not automatically imply that an individual correction optimized for both slope and curvature will outperform a simpler one that is based on
[1] Malik M, Hnatkova K, Kowalski D, Keirns JJ, van Gelderen EM. Importance of subject-specific QT/RR curvatures in the design of individual heart rate corrections of the QT interval. J Electrocardiol 2012;45:571–81. [2] Pueyo E, Smetana P, Caminal P, de Luna AB, Malik M, Laguna P. Characterization of QT interval adaptation to RR interval changes and its use as a risk-stratifier of arrhythmic mortality in amiodarone-treated survivors of acute myocardial infarction. IEEE Trans Biomed Eng 2004;51:1511–20. [3] Tornøe CW, Garnett CE, Wang Y, Florian J, Li M, Gobburu JV. Creation of a knowledge management system for QT analyses. J Clin Pharmacol 2011;51:1035–42. [4] Batchvarov VN, Ghuran A, Smetana P, Hnatkova K, Harries M, Dilaveris P, et al. QT–RR relationship in healthy subjects exhibits substantial intersubject variability and high intrasubject stability. Am J Physiol Heart Circ Physiol 2002;282:2356–63. [5] Wang Y, Pan G, Balch A. Bias and variance evaluation of QT interval correction methods. J Biopharm Stat 2008;18:427–50.
Have individual QT/RR curvatures value in QT correction? In this issue of the Journal, Ferber et al. publish their letter to the Editor [1] which makes, in principle, two points. Firstly, they state that we have made a substantial error when evaluating the effects of omitting individual curvatures of QT/RR patterns because, allegedly, we propose a QT correction technology that “has been generated and tested on the same data set”. Secondly, they express their doubts
ScienceDirect Journal of Electrocardiology 47 (2014) 385 – 393 www.jecgonline.com
Letters to the Editor Importance of subject-specific QT/RR curvatures in the design of individual heart rate corrections of the QT interval Malik and coauthors [1] investigated whether the curvature in the QT–RR relationship differs from subject to subject and recommend that an individualized correction of QT for RR should take into account individual curvature in order to obtain optimal results. The authors claim to have demonstrated that an individualized correction that takes this curvature into account is more effective than other methods (e.g., a parabolic correction) in removing the heart rate dependency of QTcI. Since the proposed methodology has been generated and tested on the same data set, we do not find the evidence convincing and certainly not conclusive and suggest how an evaluation could be performed. QT and RR are subject to variability of several sources, both technical, such as measurement errors, and biological. The latter include influences from uncontrollable or unobserved factors influencing the subject and therefore potentially the QT–RR relationship. In our view, the question of individual curvature is best addressed in the framework of statistical inference. Instead of a model with a parameter describing curvature, the authors prefer an approach that compares different functional relationships that imply different curvatures [2]. Malik et al. then use the mean squared residuals (MSR) as a criterion for goodness of fit and select the model with the lowest MSR as the best fitting. Each of the 12 models considered is described by two parameters. Therefore, the MSR criterion seems adequate for the comparison of the models and the selection of the best fitting one. The authors show that with the minimum MSR criterion, the QT–RR relationship of different subjects is best described by different models. They conclude that curvature is an important individual parameter in the description of the QT–RR relationship. We however believe that a convincing argument for this conclusion is missing and that the authors have not shown that the new approach is better than, for example, an individualized parabolic correction (referred to as log-linear in their publication). This could be shown, for example, by a statistical test of the null hypothesis that the data follow an individualized parabolic model against the alternative that different subjects follow different models. Such a test could use the MSR as measure of fit. Alternatively, showing that the individualized model is stable over time is an even more convincing argument. Indeed, the structure of the data used by Malik et al. suggests such an approach. Each subject 0022-0736/$ – see front matter © 2014 Elsevier Inc. All rights reserved.
contributed four 14-hour recordings, two in each of two periods. Within each period the recordings were separated by 2 days while there were least 22 days between the two periods. A simple but crude way to show the stability of the individualized correction is to determine the optimal correction models separately for each period and look at the proportion of subjects where the two optimal models coincide. In addition to this crude method, we propose a more quantitative approach that is inspired by the one described by Tornøe et al. [3]. As pointed out by Malik et al., there is a QT correction corresponding to each of the models considered. Indeed, the principal interest in the QT–RR relationship comes from the need for a QTc (i.e., a predicted QT at a fixed RR), which is independent of the actual value of RR. In this context, the QT–RR model is deemed optimal, if it removes the heart rate dependency the best way. Importantly and as a general principle, the quality of the prediction should be evaluated on data distinct from those used for the inference of the relationship. Let QTck designate the corrected QT using model k. Given the structure of the data used by Malik et al. [1], our proposal would be: • For each subject (subject i) use the Holter recordings of one period (learning set) to obtain the 12 models and the corresponding individual correction coefficients αik. • Determine the optimal model ki, opt as described in the article and the optimal correction formula to obtain QTci,opt. • For each subject, use the two Holter recordings of the other period as independent test set. Calculate the individually corrected QTc according to the optimal model (QTci, opt) and according to each of the 12 models (QTck = Ψk(QT, RR, αik) for k = 1,…,12) at all time points available. • For each of the 13 sets of corrected QTc values, obtained from the independent test set calculate the mean squared slopes (MSS) across subjects as suggested in Tornøe et al. [3]. Since focus is on curvature, which may not be properly represented by a slope, it will be prudent to look at the regression residuals as described [1] and determine the mean across subjects of the squared residuals (MSR). If curvature as expressed by the set of the 12 models is a subject-specific trait, the MSS and MSR for the optimal model should be smaller than those for all other
386
Letters to the Editor / Journal of Electrocardiology 47 (2014) 385–393
only one parameter. Wang et al. [5] elaborated on the balance between bias and random error in the different ways of correcting QT for RR, and their observations are likely to apply to an individual correction method based on two parameters instead of only one. We would therefore welcome if Malik et al. showed that their proposed methodology removes heart rate dependency better than others when tested on data not used for its derivation and by this way convincingly show the usefulness of curvature as an additional parameter in individual correction. Georg Ferber, PhD Statistik Georg Ferber GmbH Riehen, Switzerland E-mail address: [email protected] Meijian Zhou M., PhD iCardiac Technologies Rochester, NY, USA Fig. 1. Stability of correction coefficients: parabolic. Stability of individual correction coefficients for a parabolic correction over time. For 60 subjects who participated in a crossover TQT study, correction coefficients were calculated from the baseline days of period 2 (abscissa) and period 3 (ordinate). All beats of the respective 24-hour Holter recordings that passed a semiautomatic quality control procedure were used to derive the correction coefficients. The dashed line represents equal values for both periods. For the majority of the subjects, modest variability between the values obtained in the two periods can be observed, while a few subjects show substantial differences. Figure reproduced from J of Pharmacological & Toxicological Methods (2013). Holzgrefe et al. Preclinical QT safety assessment: crossspecies comparisons and human translation from an industry consortium, http://dx.doi.org/10.1016/j.vascn.2013.05.004.
Borje Darpo, MD, PhD iCardiac Technologies, Rochester NY, USA Karolinska Institutet Division of Cardiovascular Medicine Department of Clinical Sciences Danderyd's Hospital, Stockholm, Sweden http://dx.doi.org/10.1016/j.jelectrocard.2013.12.010 References
models. If this were not the case, we would conclude that the intra-individual variability of the QT–RR relationship is too large to warrant the use of a model with individual curvatures. Batchvarov et al. [4] showed that the inter-individual variability in the QT–RR relationship outweighs the intraindividual one. We agree with the authors that this interindividual variability most likely also extends to curvature. However, the observations of Batchvarov et al. do not preclude the existence of substantial intra-individual variability. Indeed, intra-individual variability can be seen if an individual correction (e.g., a parabolic one) is fitted to 24-hour Holter data obtained in the same subject at different occasions. In a three-period crossover TQT study with 60 subjects, we calculated parabolic QTcI based on 24-hour Holter recordings at baseline of the second and third periods respectively (Fig. 1; reproduced with permission). There is only modest agreement between the exponents of the correction formulae from different periods. There may be situations where an individual correction does not outperform Fridericia's correction if a criterion like the mean squared slope of Tornøe et al. [3] is used. Likewise, even if it can be confirmed that the intersubject variability of curvature outweighs the intraindividual one, this does not automatically imply that an individual correction optimized for both slope and curvature will outperform a simpler one that is based on
[1] Malik M, Hnatkova K, Kowalski D, Keirns JJ, van Gelderen EM. Importance of subject-specific QT/RR curvatures in the design of individual heart rate corrections of the QT interval. J Electrocardiol 2012;45:571–81. [2] Pueyo E, Smetana P, Caminal P, de Luna AB, Malik M, Laguna P. Characterization of QT interval adaptation to RR interval changes and its use as a risk-stratifier of arrhythmic mortality in amiodarone-treated survivors of acute myocardial infarction. IEEE Trans Biomed Eng 2004;51:1511–20. [3] Tornøe CW, Garnett CE, Wang Y, Florian J, Li M, Gobburu JV. Creation of a knowledge management system for QT analyses. J Clin Pharmacol 2011;51:1035–42. [4] Batchvarov VN, Ghuran A, Smetana P, Hnatkova K, Harries M, Dilaveris P, et al. QT–RR relationship in healthy subjects exhibits substantial intersubject variability and high intrasubject stability. Am J Physiol Heart Circ Physiol 2002;282:2356–63. [5] Wang Y, Pan G, Balch A. Bias and variance evaluation of QT interval correction methods. J Biopharm Stat 2008;18:427–50.
Have individual QT/RR curvatures value in QT correction? In this issue of the Journal, Ferber et al. publish their letter to the Editor [1] which makes, in principle, two points. Firstly, they state that we have made a substantial error when evaluating the effects of omitting individual curvatures of QT/RR patterns because, allegedly, we propose a QT correction technology that “has been generated and tested on the same data set”. Secondly, they express their doubts