Implications of Individual QT/RR Profiles—Part 1: Inaccuracies and Problems of Population-Specific QT/Heart Rate Corrections

Figures

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  Fig. 1. a Modeled plasma concentration profile used in the experiments of the second type (see text for details). b Schema of the modeled QT and heart rate changes. In each study subject, the full profile of the relationship between QT intervals and underlying heart rates (derived from hysteresis-corrected RR intervals) was obtained during previous investigations (small yellow dots). Their distribution allows curve-linear modeling of the QT/RR relationship (shown in the QT/heart rate plot as the solid red curvature). Replicated baseline measurements (green circles) coincide with the drug-free profiles. Their distribution and the curve-linear model of the QT/RR relationship allow simulation of different combinations of heart rate and QT changes. The figure shows three such simulations: heart rate increases of 10 bpm combined with QT increases of 15 ms are shown as blue circles; heart rate increases of 20 bpm combined with QT increases of 25 ms are shown as red circles; heart rate increases of 30 bpm with no QT increases are shown as black circles. Note that the black circles again coincide with the drug-free profile because no QT interval change was modeled. Cmax maximum concentration

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  Fig. 2. Example of experiments of the first type showing that the inaccuracies of heart rate corrections are practically independent of the programmed corrected QT (QTc) interval changes. In the experiments shown here, QTc changes programmed between − 25 and + 25 ms (horizontal axes) were all combined with heart rate acceleration of 15 beats per minute (bpm). The vertical axes of all panels show the errors in the QTc interval changes reported by the different correction formulas (reported minus actually programmed QTc interval change). Shown in this figure are linear heart rate correction optimized for individual subjects separately (a); linear heart rate correction optimized for study population (b); log-linear heart rate correction optimized for individual subjects separately (c); and log-linear heart rate correction optimized for study population (d). In all panels, the distribution of the correction errors in repeated experiment is shown (see text for details): the red lines show the median value and the pink, green, and blue bands show the ranges between 20th and 80th percentiles, 10th and 90th percentiles, and 5th and 95th percentiles, respectively

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  Fig. 3. Example of experiments of the first type showing that the inaccuracies of heart rate corrections are practically independent of the programmed corrected QT (QTc) interval changes combined with heart rate deceleration of 10 beats per minute (bpm). Shown in this figure are linear heart rate correction optimized for individual subjects separately (a); linear heart rate correction optimized for study population (b); log-linear heart rate correction optimized for individual subjects separately (c); and log-linear heart rate correction optimized for study population (d). In all panels, the distribution of the correction errors in repeated experiment is shown (see text for details): the red lines show the median value and the pink, green, and blue bands show the ranges between 20th and 80th percentiles, 10th and 90th percentiles, and 5th and 95th percentiles, respectively. Compared with Fig. 2, it can be noted that (i) the spread of the results of the experiments modeling the corrections optimized for study population were wider than the experiments modeling the corrections optimized for individual subjects; and (ii) whilst the results of the linear corrections are truly independent on…

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  Fig. 4. Dependency of the errors of investigated heart rate corrections on the programmed heart rate change. In the experiments shown, heart rate changes ranging from − 10 to + 25 beats per minute (bpm) were combined with programmed corrected QT (QTc) interval changes of 0 ms (a, b), + 8 ms (c, d), and + 12 ms (e, f). The graphs show the distribution of reported QTc interval changes obtained from linear corrections optimized for each subject separately. a, c, and e show the experiments of the first type (constant plasma concentrations in a larger group of subjects); b, d, and f show the experiments of the second type (variable plasma concentrations in a smaller group of subjects). In each panel, the distribution of the results in the repeated experiment is shown (see text for details): the red lines show the median value and the pink, green, and blue bands show the ranges between 20th and 80th percentiles, 10th and 90th percentiles, and 5th and 95th percentiles, respectively. The highlighted horizontal line in c–f shows the standard regulatory threshold of + 10 ms QTc interval change

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  Fig. 5. Dependency of the errors of investigated heart rate corrections on the programmed heart rate change. In the experiments shown, heart rate changes ranging from − 10 to + 25 beats per minute (bpm) were combined with programmed corrected QT (QTc) interval changes of 0 ms (a, b), + 8 ms (c, d), and + 12 ms (e, f). The graphs show the distribution of reported QTc interval changes obtained from log-linear corrections optimized for each subject separately. a, c, and e show the experiments of the first type (constant plasma concentrations in a larger group of subjects); b, d, and f show the experiments of the second type (variable plasma concentrations in a smaller group of subjects). In each panel, the distribution of the results in the repeated experiment is shown (see text for details): the red lines show the median value and the pink, green, and blue bands show the ranges between 20th and 80th percentiles, 10th and 90th percentiles, and 5th and 95th percentiles, respectively. The highlighted horizontal line in c–f shows the standard regulatory threshold of + 10 ms QTc interval change

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  Fig. 6. Dependency of the errors of investigated heart rate corrections on the programmed heart rate change. In the experiments shown, heart rate changes ranging from − 10 to + 25 beats per minute (bpm) were combined with programmed corrected QT (QTc) interval changes of 0 ms (a, b), + 8 ms (c, d), and + 12 ms (e, f). The graphs show the distribution of reported QTc interval changes obtained from linear population corrections (optimized for the groups of subjects pooled together). a, c, and e show the experiments of the first type (constant plasma concentrations in a larger group of subjects); b, d, and f show the experiments of the second type (variable plasma concentrations in a smaller group of subjects). In each panel, the distribution of the results in the repeated experiment is shown (see text for details): the red lines show the median value and the pink, green, and blue bands show the ranges between 20th and 80th percentiles, 10th and 90th percentiles, and 5th and 95th percentiles, respectively. The highlighted horizontal line in c–f shows the standard regulatory threshold of + 10 ms QTc interval change. Compared with Fig. 4, note the substantial increase in the spread of the…

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  Fig. 7. Dependency of the errors of investigated heart rate corrections on the programmed heart rate change. In the experiments shown, heart rate changes ranging from − 10 to + 25 beats per minute (bpm) were combined with programmed corrected QT (QTc) interval changes of 0 ms (a, b), + 8 ms (c, d), and + 12 ms (e, f). The graphs show the distribution of reported QTc interval changes obtained from the log-linear population corrections (optimized for the groups of subjects pooled together). a, c, and e show the experiments of the first type (constant plasma concentrations in a larger group of subjects); b, d, and f show the experiments of the second type (variable plasma concentrations in a smaller group of subjects). In each panel, the distribution of the results in the repeated experiment is shown (see text for details): the red lines show the median value and the pink, green, and blue bands show the ranges between 20th and 80th percentiles, 10th and 90th percentiles, and 5th and 95th percentiles, respectively. The highlighted horizontal line in c–f shows the standard regulatory threshold of + 10 ms QTc interval change. Compared with Fig. 5, note the substantial increase in the spread of…