Methods of Subject‐Specific Heart Rate Corrections

The physiologic relationship between the QT interval and the underlying heart shows both high intrasubject stability and substantial intersubject variability. This observation is some 2 decades old,1, 2 and its implications for the assessment of QTc changes by drugs changing heart rate are well understood.3 The so-called individual heart corrections (providing the QTcI intervals) that reflect the subject-specific QT/RR relationship are presently used in a number of studies.4-6 Most of the studies using the individual corrections follow the design of the very first study that utilized QTcI values.7 In that study, QT and RR readings of drug-free data points were taken in each subject separately. Based on their relationship, subject-specific formula QTcI = QT/RRα was optimized with different correction coefficients α for different study subjects. This methodology of the old seminal study is presently replicated despite repeated publications pointing out its inefficiencies and problems.3, 8, 9 The major potential problem is the limited span of heart rates found during the drug-free time points. If such time points cover only a narrow window of resting heart rates, the individual QT/RR relationship might be poorly defined, practically irrespective of how many drug-free measurements are used. Indeed, the standards of study conduct require all time-point electrocardiograms (ECGs) to be recorded while the subjects are in supine resting positions. These conditions limit the heart rate span (also depending on how strictly are the requirements enforced).10 With limited heart rate span, the confidence intervals of the regression curvatures that describe the individual QT/RR may become very wide and if the on-treatment heart rates are remote from the window of the drug-free heart rates, substantially erroneous conclusions might easily be reached3 (Figure 1). Indeed, it has been explained previously that if the on-treatment and off-drug heart rate are noticeably different, and if the off-drug heart rates cover only a narrow window, no conclusions on the drug-induced QTc changes are possible.3 The obvious solution to this problem was proposed already some decade ago.8 In addition to the ECG measurements during the drug-free time points, other drug-free QT/RR data must be obtained from continuous ECG recordings at baseline, aiming at covering as wide heart rate ranges as possible. In addition, specific procedures, for example, postural provocations, can easily be included into the drug-free baseline days of a clinical study to increase the spread of available heart rates beyond what might be found in clean and thus easily measurable ECGs recorded in freely moving study subjects.9 With all these methods that make the individual heart rate corrections more accurate and reliable, it is regrettable and disappointing that so many studies continue copying the initial simplistic design while ignoring the available advances. In addition to the problem of potentially erroneous results, any inaccuracy of heart rate corrections projects into increased variability of QTc data, which in turn decrease the statistical power of clinical studies investigating drug-induced QTc changes.11 More accurate QTcI data allow making these studies smaller and more economical. For these reasons, it is very pleasing to see the contribution by Panicker et al12 in this Journal issue reporting on a system for the design of individual heart rate corrections that incorporates some of the methodological advances. Consistent with the previous regulatory position,3 Panicker et al rightly show that by scanning through complete long-term Holter recordings and measuring QT intervals at a broad range of heart rates, the accuracy of QTcI values is substantially increased as evidenced by significant reduction of intrasubject QTcI variability in drug-free data. Increased accuracy and lesser variability of QTc data is important not only when dealing with drugs affecting heart rate but also if aiming at making the clinical studies smaller, for example, when incorporating the assessment of drug-induced QTc changes into early clinical investigations.13 While we need to commend Panicker et al12 for their implementation of the Holter scanning techniques, the actual values of the intrasubject drug-free QTcI variability that they report are puzzling. The within-subject standard deviation of QTcI of 12.2 ± 4.9 milliseconds reported by Panicker et al is substantially larger than the within-subject QTcI standard deviation of 5.7 ± 1.1 and 5.4 ± 1.1 milliseconds in women and men, respectively, that was reported with a very similar Holter scanning technique.14 An almost 2.2 times further reduction of intrasubject variability of drug-free QTcI values means that clinical studies can be made some 4.5 times smaller while maintaining the same statistical power of detecting QTcI changes. Therefore, it seems important to discuss further improvements that might be incorporated into the system described by Panicker et al to make it even more effective. Three such aspects come to mind. Panicker et al12 followed the most common practice and designed the individual corrections in the form QTcI = QT/RRα where the measurements are in seconds and the coefficient α is optimized for each subject separately based on log-transformed linear regression. It is not obvious whether the popularity of this particular formula stems from the first publication of individual corrections7 but, regrettably, the formula is far from the best choice. (Note that in the first proposal,7 the optimization of the formula did not use the log-transformed linear regression but optimized the parameter α to obtain zero correlation between QTcI and RR values in the drug-free data of each subject. Using the slope of log-transformed linear regression leads to slight departures from this zero correlation.) Different subjects not only show different slopes of their QT/RR patterns, but these patterns are also differently curved in different subjects. Logarithmic transformation does not turn such different curvatures into straight lines, and omitting the differences in the curvatures increases the intrasubject QTcI standard deviation markedly.14 Moreover, the QT/RRα formula has awkward statistical properties3, 15 since it treats the same change of QT interval differently at different heart rates, that is, (Δ + QT) / RRα ≠ Δ + QT / RRα. Previously, the difference in the curvatures of QT/RR patterns was somewhat primitively addressed by considering a family of differently curved profiles (with a possibility of changing the slope of each of them) and finding the best-fitting option for each subject.8, 9, 15 While this approach of selecting the best among different families of heart rate correction formulas was clearly unsophisticated, it showed that the QT/RRα formula is only very infrequently the best of other possibilities.15, 16 More recently, methodology was developed allowing expression of both the slope and the curvature of individual QT/RR patterns by optimizing a two-parameter correction formula, QTcI = QT + (δ/γ)(1 – RRγ), where δ represents the slope and γ the curvature.14 The previously mentioned small standard deviations of intrasubject QTcI values were obtained in this way. Changing the calculation of QTcI values to a more accurate formula should not represent a problem. Once the drug-free QT/RR data are obtained, as described by Panicker et al,12 parameters of slope and curvature can easily be found using published methods.14 While such methods are algorithmically a little more complicated than the simple log-transformed linear regression, the computational power of present personal computers makes the difference inconsequential. At the same time, as previously shown,14 this technical change makes the QTcI values more accurate and significantly less variable. Panicker et al12 acknowledge that their system does not incorporate the correction for QT/RR hysteresis, that is, the assessment of how quickly rather than how much QT interval changes after a heart rate change.10, 17 They suggest that QT/RR hysteresis needs to be considered only in situations when an investigated drug rapidly changes heart rate. That is not really true. In more detail, Panicker et al12 measure QT interval during episodes that are preceded by stable heart rates. They define this stability as no more than a 100-millisecond difference between mean RR interval for the 10-second period (during which the QT interval is measured) and the mean RR of the preceding 1-minute window. The RR interval difference of 100 milliseconds is not minuscule (corresponding roughly to a 10% heart rate change). Simple linear regressions between QT and RR intervals show that for every 100 milliseconds of RR change, QT interval changes (approximately and on average) by about 15 milliseconds. Of course, the difference of 100 milliseconds is an upper limit in the system described by Panicker et al. Still, if the average difference between the instantaneously measured RR interval and the RR interval representative of heart rate physiologically underlying the QT interval duration is only some ±30 milliseconds, inaccuracies of some ±5 milliseconds are introduced into the QTcI values. This is because the QT interval duration is influenced by the history of heart rate well beyond the preceding 10-second window. At the same time, to ascertain that the heart rate stability is within their prescribed limit, Panicker et al12 clearly do have the history of RR intervals preceding their QT interval measurements available in their system. Indeed, measuring RR intervals in continuous Holter recordings is relatively simple even in moderately noise-polluted sections that are not suitable for accurate QT measurement. This RR interval history of each QT measurement should allow Panicker et al to recalculate the RR interval used in the heart rate correction as a simple weighted average of the series of preceding RR intervals, for example, applying the universal hysteresis correction that might be applied to every study subject.10, 18 Such a calculation of the universal hysteresis profile is truly trivial. Similar to the slope and curvature of QT/RR patterns that are substantially different between different subjects, the individual QT/RR hysteresis profiles also show intrasubject reproducibility with intersubject differences.19 Nevertheless, the decrease of QTcI variability achieved by assessing subject-specific QT/RR hysteresis profiles instead of using a universal hysteresis profile is, under usual circumstances, not very large.10 In this sense, there is a substantial and principal difference between universal heart rate corrections (eg, the Fridericia formula) that may cause substantial errors in the presence of heart rate changes, and the universal QT/RR hysteresis correction that can (and always should) be safely applied unless the investigated drug leads to rapid heart rate changes. Absolute stability of heart rate preceding QT interval measurement is unachievable10 (unless guaranteed by constant atrial pacing) and the QTc inaccuracy caused by omitting hysteresis correction should not be underestimated.18 Finally, Panicker et al12 do not mention many details of the algorithms used in the automatic QT interval measurements. Nevertheless, it is known that the threshold-based measurement techniques might be influenced by low-level noise and that this influence may cause jitter on the order of some milliseconds, which is difficult to judge or even detect during visual review. Such a jitter necessarily increases the QTcI variability. To avoid this problem, a pattern adjustment technique of QT interval measurement may be proposed.20 This technique classifies ECG morphologies of the QRS complexes and T waves and repositions previous measurements (eg, those based on the threshold methods) to ensure that morphologically similar ECGs are measured systematically. This is important because each ECG measurement depends on particular interpretation of each signal. It has been shown that while the pattern classification algorithms cannot measure ECG interval on their own, they can substantially reduce measurement fluctuations.20, 21 As reported, this reduces the variability of QT interval measurements and consequently further decreases the intrasubject standard deviations of QTcI values. Similar to previous comments on the methodology reported by Panicker et al,12 the algorithms of the pattern adjustment of the QT measurements are in the public domain, and while they represent some computational demands, the present power of standard personal computers make them easy to implement. As previously stated, the report by Panicker et al12 is certainly welcome, and it can only be hoped that the more accurate implementation of the individual QT corrections will be adopted by other centers. We should all agree with Panicker et al that restricting the design of individual corrections to the data obtained only during drug-free time points of clinical studies is potentially too problematic and that more accurate techniques should be used. The comments in the previous sections merely describe possibilities of making the Holter scanning systems more accurate and thus more effective in terms of power sample calculations of drug-related QTc investigations. Hence, when the Holter scanning techniques are adopted by other centers, these possibilities should carefully be considered and implemented. The author declares no conflict of interest.