The “One‐Step” approach for QT analysis increases the sensitivity of nonclinical QTc analysis

Abstract

Whether a compound prolongs cardiac repolarization independent of changes in beat rate is a critical question in drug research and development. Current practice is to resolve this in two steps. First, the QT interval is corrected for the influence of rate and then statistical significance is tested. There is renewed interest in improving the sensitivity of nonclinical corrected QT interval (QTc) assessment with modern studies having greater data density than previously utilized. The current analyses examine the effects of moxifloxacin or vehicle on the QT interval in nonhuman primates (NHPs) using a previously described one‐step method. The primary end point is the statistical sensitivity of the assessment. Publications suggest that for a four animal crossover (4 × 4) in NHPs the minimal detectable difference (MDD) is greater than or equal to 10 ms, whereas in an eight animal crossover the MDD is ~6.5 ms. Using the one‐step method, the MDD for the four animal NHP assessments was 3 ms. In addition, the one‐step model accounted for day‐to‐day differences in the heart rate and QT‐rate slope as well as drug‐induced changes in these parameters. This method provides an increase in the sensitivity and reduces the number of animals necessary for detecting potential QT change and represents “best practice” in nonclinical QTc assessment in safety pharmacology studies.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

Nonclinical corrected QT interval (QTc) assessment in nonhuman primates (NHPs) currently uses a two‐step analysis method and has a sensitivity to detect a change in QTc interval of around 10 ms with four animals. There are assumptions in the rate correction method for QTc which may confound analysis in cases when there is a strong circadian pattern of heart rate change or where drug changes rate.

• WHAT QUESTION DID THIS STUDY ADDRESS?

This study addressed the question of whether a one‐step analysis method could improve sensitivity while also making fewer erroneous assumptions in rate correction.

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

The study showed it was possible to increase the sensitivity to detect small QTc changes with fewer animals and demonstrated an increased QTc change, and an improved QTc time profile likely to translate into an improved concentration‐QTc profile.

• HOW MIGHT THIS CHANGE CLINICAL PHARMACOLOGY OR TRANSLATIONAL SCIENCE?

These findings will improve our ability to translate QTc findings from NHP to man.

INTRODUCTION

Assessing a potential new drug for liability to prolong human cardiac repolarization is critical in drug research and development. This topic has both clinical and nonclinical International Council for Harmonization guidelines with regular updates through 2022. ¹ , ² , ³ , ⁴ The latter updates are particularly important because they have triggered the integration of nonclinical and clinical information for an overall assessment. This provides an alternative or substitute pathway to typical clinical thorough QT (TQT) study‐based characterization, which was the mainstay to fulfill a regulatory requirement for labeling as well as to inform monitoring in subsequent late phase clinical studies. The 2022 updates provide formal illustration of how integration of nonclinical and clinical information can inform risk. The use of nonclinical data to potentially discharge clinical QT risk has focused the statistical and discriminatory performance of the nonclinical in vivo corrected QT interval (QTc) assessment, bringing it closer to the level of scrutiny associated with the clinical evaluations. ⁵ , ⁶ Critical to the use of nonclinical in vivo assessment is the statistical sensitivity. A negative nonclinical result is only reassuring when the sensitivity of the study to detect a QT change is understood.

The present analyses used data from a large group (n = 48) of telemetry implanted nonhuman primates (NHPs), to facilitate the understanding of alternative assessment paradigms. This made the study ideal to re‐evaluate the “One‐Step” analysis method described previously. ⁷ The current industry standard analysis uses two models in sequence. First, the QT interval is corrected for the influence of heart rate. In the case of NHPs, this often involves a linear regression model of QT and RR intervals to determine an individualized slope of the QT‐RR relationship for each animal during vehicle treatment or a pretreatment period. ⁸ Second, the effect of compound on the corrected QT interval is assessed in an analysis of variance (ANOVA) model considering the period (e.g., hourly), the dose of compound, and the individual animal identity. ⁹ As the name suggests, the “One‐Step” method combines a heart rate correction with fewer limiting assumptions and statistical analysis into a single step estimated marginal means process.

There are advantages to the One‐Step method in two important areas of the in vivo QT study. In modern studies, a large proportion of the available electrocardiogram (ECG) complexes yield QT and RR interval values. These are summarized as 1‐min mean values and most of the 1440 potential values available in 24 h/animal are used in the analysis. The conventional method of analysis uses the 1‐min mean values collected during vehicle treatment or a pretreatment period to derive an individual animal's QT‐RR slope. Every 1‐min mean QT value for that animal is then arithmetically adjusted to a QTc value by adding an amount to the QT value proportional to the animal's QT‐RR slope multiplied by the difference between the reference RR interval and the observed 1‐min mean RR intervals. The resulting 1‐min QTc values are arithmetically averaged over the desired period (e.g., hourly) to derive a single value per animal per treatment period. Averaging all the data representative of an animal on that treatment in that period is a statistical convention (treating the 1‐min data as replicate measurements) and it is not generally accepted to take all these individual values into the hourly statistical model. In a 4 × 4 Latin Square crossover study, using hourly means this would result in only 16 values per hour. To detect differences among the four treatment groups, the statistical model has very limited data and degrees of freedom. Using the One‐Step method, there is no pre‐analysis and no determination of QTc using arithmetic. Instead, all 1‐min mean QT and RR interval data points are used and inform the statistical model of the relationship between the dependent variable (QT interval) and the independent variable (RR interval). Thus, for the same 4 × 4 crossover study, ~960 data points per hour are supplied to the statistical model. Supplying 60 times more data to derive the same ordinary linear squares model increases the confidence in the model‐derived estimated marginal or least‐squares means.

Legacy corrected QT interval analysis uses a fixed QT‐RR relationship based on data from the population of animals. In the case of NHPs, Bazett's correction (QTcB) was a reasonable approximation (an exponent of 0.5 compared to an exponent of 0.576 ¹⁰ ). This adjusts the QT interval by dividing QT by the square root (exponent of 0.5) of reference RR divided by the RR interval. The traditional reference RR for QTcB was 1000 ms (corresponding to a heart rate of 60 beats per minute), but a more realistic RR reference of 500 ms (consistent with later correction methods) can also be used. The fixed QT correction like QTcB assumes that the QT‐RR relationship is fixed across animals, across days in the same animal, across hours in the same day, and is constant in the presence of drugs. Conventional QT correction using an animal's individual QT‐RR slope recorded in the presence of vehicle treatment or a pretreatment period acknowledges the differences between animals. However, this assumes the slope of the relationship is fixed for that animal across each day and across hours within each day. Critically, it assumes that drug treatment does not change the slope of the relationship. The One‐Step method fits a slope to the QT‐RR relationship within the time period evaluated (e.g., hourly), the slope and intercept can vary by animal, by day, by hour, and by treatment. The method finds the predicted QTc value for each animal, day, hour, and treatment. The method, therefore, makes none of the assumptions inherent in the Legacy and Conventional methods. The assumptions of constant QT‐RR relationships across individual subjects, days, time within day, and drug treatment are erroneous ¹¹ , ¹² , ¹³ , ¹⁴ (see also Appendix S1 and Tables S1–S3). The One‐Step method, uses an estimated marginal means approach where the RR interval is considered as a covariate and, therefore avoids the pitfalls associated with these assumptions. Figure 1 is provided to illustrate some of the issues when using an inappropriate slope to correct for a rate effect. No data from Line A is needed to predict the data at 500 ms for Line B and vice versa. The impact on precision of QTc when corrected with the wrong slope is also obvious. With a change in heart rate, the primary reason for using a correction model, the correction also impacts accuracy as the balance of RR values on each side of the reference rate change. As there is also a time‐dependence to heart rate, any rate‐dependent impact on precision and accuracy will carry over into the QTc versus time course. This confounds any drug effect versus time course. Using the appropriate slope avoids these issues.

FIGURE 1.

Importance of correction with the appropriate slope. This figure illustrates two different QT‐RR relationships as lines A or B, or treatments A or B. Upper left: Illustrates two different linear relationships. There is a gap at an RR interval of around 500 ms. The primary question posed with this panel is “do you require any data from line A to predict the data at 500 ms RR interval for line B, or vice versa?” Upper right: Illustrates the same linear relationships with some added uniform variability. Lower left: Illustrates the QTc values – corrected QT interval if all the points were corrected using the slope for treatment A (blue solid and dashed lines). The spread of the points at 500 ms RR is widest for treatment B. Correction by this method reduced the precision of the data. Lower right: Illustrates correction of the data along its own slope. In this case, the precision is comparable for both treatments. The mean QTc value is the same in both lower panels – the method did not impact accuracy. Not illustrated is the impact of treatment B changing the heart rate. This would change the proportion of points on either side of the correction line. This would impact the mean QTc value for the lower left panel but not for the lower right. Thus, the method illustrated in the lower left panel does not account for heart rate changes as intended.

The current analyses revisit the One‐Step method to explore if the anticipated benefits of improved sensitivity and shift in QTc time course were evident.

MATERIALS AND METHODS

Materials

Moxifloxacin hydrochloride (supplier Matrix Scientific) was prepared as a suspension with 0.5% methylcellulose in distilled water. The vehicle used was 0.5% methylcellulose in distilled water and administered as 5 mL/kg. Moxifloxacin was administered by oral gavage at 80 mg/kg. The observed maximum plasma concentration (C _max) value ¹⁵ (5010 ng/mL) was approximately twofold the C _max observed ¹⁶ for the 400 mg oral dose of moxifloxacin commonly used as a positive control in human TQT studies.

Animals and procedures

All procedures in this study complied with all applicable sections of the Final Rules of the Animal Welfare Act regulations (Code of Federal Regulations, Title 9), the Public Health Service Policy on Humane Care and Use of Laboratory Animals from the Office of Laboratory Animal Welfare, and the Guide for the Care and Use of Laboratory Animals from the National Research Council. All procedures were approved by the Institutional Animal Care and Use Committee.

Study design

A total of 48 (24 male and 24 female) cynomolgus monkeys (Macaca fascicularis) of Cambodian origin were used on this study. All animals were implanted with M11 telemetry devices (Harvard Biosciences). Further details of the study design are available elsewhere. ¹⁵ Briefly, the study was split into four equally sized single sex cohorts for evaluation. Each cohort underwent the entire study design before initiation of the next cohort of 12 animals. The cohort assessment order was: 12 females, 12 females, 12 males, and 12 males. QT and RR data were collected in five periods. Period 1 was a 24‐h telemetry recording prior to any treatment. Period 2 was 2 h of baseline data and 48 h of postdose vehicle data. Period 3 was 48 h of collection after an 80 mg/kg oral dose of moxifloxacin. Periods 4 and 5 were repeats of periods 2 and 3. As a result, there were four treatment periods: vehicle 1, moxifloxacin 1, vehicle 2, and moxifloxacin 2. Consistent with most conventional in vivo QT studies and with the pharmacokinetic profile of moxifloxacin, in these animals, only the first 24 of the 48 h collected in each treatment period were used in the current analyses.

Data analysis

All telemetry data were analyzed utilizing the Review module within the Ponemah software (version 5.2; Harvard Biosciences) and ECG pattern recognition option for the ECG data, providing a comprehensive, library‐based, waveform analysis. Initial aggregation of the data was 1 min means, reducing 24 h of recording to a potential total of 1440 min mean values per day.

Effect independent of rate correction assumptions

In comparing correction methods, it would be very useful to know the effect independent of the correction method assumptions. In the current analyses, there is sufficient data to consider only data around the RR reference value which needs no correction. There were 14,368 QT interval values associated with RR intervals from 490 to 510 ms. These 14,368 data points were used as the QT effect of treatment in a statistical comparison which considered treatment and animal ID. The model was used to derive the effect of treatment relative to vehicle 1.

$$\mathrm{QT}~\text{Treatment}+\mathrm{ID}$$

QT and QTc are equivalent in this case.

Legacy analysis

The different analyses conducted are summarized in Table 1. The legacy analyses involved correcting the QT intervals for the influence of rate using Bazett's correction.

$$\mathrm{QTc}=\mathrm{QT}/{\left(500/\mathrm{RR}\right)}^{0.5}.$$

TABLE 1.

Contrasting methods of rate‐correction and statistical analysis.

	Legacy	Conventional	Hybrid	One‐Step
	e.g., QTcB	e.g., Individual vehicle period linear correction
Prior analysis	Calculate QTcB based on QT and RR Create hourly arithmetic mean QTcB value	Find individual slope in vehicle period Adjust all QT values based on the slope and RR Create hourly arithmetic mean QTc value	Find individual slope in vehicle period	None
Statistical model	QTcB ~ Drug + ID	QTc ~ Drug + ID	QT + Individual Slope*(500‐RR) ~ Drug + ID	QT ~ Drug × RR + ID × RR
Assumptions	Shape of QT‐RR relationship is constant for all animals, times, and treatments	Slope is constant day‐to‐day Slope is constant hour‐to‐hour Slope is unaffected by drug	Slope is constant day‐to‐day Slope is constant hour‐to‐hour Slope is unaffected by drug	None
Inputs to statistical model	ID, Hour, QTcB	ID, Hour, QTc	ID, minute, hour, QT, RR, dose, individual slope	ID, minute, hour, QT, RR, dose
Number of data points (for a 4 × 4 Latin Square)	16/h	16/h	~960/h	~960/h
Output from statistical model	The model derived drug effect (and CIs) on QT at 500 ms RR	The model derived drug effect (and CIs) on QT at 500 ms RR	The model derived drug effect (and CIs) on QT at 500 ms RR	The model derived drug effect (and CIs) on QT at 500 ms RR
MDD (n = 4)	9 ms	10.6 ms	2.9 ms	3.3 ms
MDD (n = 8)	5.3 ms	6.3 ms	1.7 ms	2 ms

Note: This table contrasts four different analysis methods. The desired output for the statistical models is the same for all methods. The amount of data which would be supplied to the statistical analysis for a 4 × 4 Latin Square crossover design is illustrated. The inherent assumptions about QT‐RR relationships differ across the analysis methods as does the prior analysis required before the statistical model. The outcome is much higher sensitivity, as MDD (80% power at p = 0.05), for the single step methods.

Abbreviations: CI, confidence interval; MDD, minimum detectable difference.

Rather than using a reference RR interval of 1000 ms for this correction the reference value of 500 ms was used to be consistent with other analyses.

The subsequent statistical analyses involved an ANOVA model:

$$\mathrm{QTc}~\text{Treatment}+\mathrm{ID}$$

The model was used to derive the effect of treatment relative to vehicle 1. The residual error from the model was also determined. The analyses were conducted at hourly intervals.

Conventional analyses

The conventional analyses involved correcting the QT interval for the influence of heart rate at the time of primary data aggregation using a linear QT‐RR regression. Briefly, an individual animal correction factor (iacf) for each animal was derived from the individual's 1 min mean QT and RR data for the vehicle treatment period (0–24 h). The QTc was derived as follows:

$$\mathrm{QTc}=\mathrm{QT}+\text{iacf}*\left(500-\mathrm{RR}\right),$$

where 500 ms is the RR reference value for correction.

The subsequent statistical analyses were the same as that used for the Legacy analysis. Baseline can be included in the analyses as an additional covariate. Adding in a baseline in a crossover analysis makes only a very modest impact. Overall, adding a baseline in this study would not have changed the conclusions appreciably.

A hybrid model

The two elements of the conventional analysis were combined into a single step provided the animal's individual QT‐RR slope was calculated and available. This model took the form:

$$\begin{array}{c}\mathrm{QT}+\text{iacf}*\left(500-\mathrm{RR}\right)~\text{Treatment}+\mathrm{ID}.\hfill \end{array}$$

Again, the model was used to derive the effect, at an RR value of 500 ms, of treatment relative to vehicle 1. The residual error from the model was also determined. The analysis was conducted at hourly intervals. The Hybrid model is effectively identical to the conventional analysis. The same individual animal QT‐RR slope used to arithmetically correct the QT interval prior to the statistical model in the “Conventional” method is used within the “Hybrid” method model. The Hybrid method is provided to demonstrate how supplying 60× more data to the statistical model influences sensitivity.

One‐Step model

The One‐Step method did not require a previous determination of the individual animal's QT‐RR slope or arithmetically determining a corrected QT interval. The method includes RR as a covariate in the statistical model.

$$\mathrm{QT}~\left(\text{Treatment}\mathrm{X}\mathrm{RR}\right)+\left(\mathrm{ID}\mathrm{X}\mathrm{RR}\right),$$

where X signifies the interaction of Treatment or ID with the QT‐RR slope.

Again, the model was used to derive the effect, at a reference RR value chosen by the model or at 500 ms, of treatment relative to vehicle 1. The residual error from the model was also determined. The analysis was conducted at hourly intervals. Comparisons between models used a standard 500 ms reference RR interval.

The One‐Step model is an estimated marginal mean approach using RR as a covariate. Although for the purposes of comparison and concentration‐QTc analysis, making the determination of treatment effect at an RR of 500 ms is necessary, the default estimate of QT effect of treatment is made at the overall mean RR value for the hourly data used. Thus, each hour could be comparing QT at different RR intervals, but the objective of determining whether there is a significant effect of treatment independent of RR remains the same.

The residual error from all analyses was used to determine the minimal detectable differences (MDD; 80% power at p < 0.05) and the power curves for studies of four or eight animals.

All analyses were conducted in R, ¹⁷ the estimated marginal means were determined using the package Emmeans, ¹⁸ and the power calculations used the package EnvStats. ¹⁹

Sensitivity and specificity assessment

Two different statistical hypotheses are used in nonclinical and clinical QTc assessment. In safety pharmacology (SP) studies, the common null hypothesis is: no effect on QTc. In a clinical TQT study, the common null hypothesis is: there is a small QTc effect, but it is not larger than 10 ms. These can be depicted as follows:

$$\mathrm{SP}\text{Study}–\text{H0}:\mathrm{\mu }=0\mathrm{ms}$$

$$\mathrm{TQT}\text{Study}–\text{H0}:0\mathrm{ms}<\mathrm{\mu }<10\mathrm{ms}$$

The 48 original animals in this study were repeatedly randomly sampled into 1000 studies of four animals. The 1000 studies on each treatment at each hour were then examined to assess whether the upper bound of the 95% confidence interval for the predicted effect exceeded 10 ms (TQT null hypothesis) or whether the lower bound of the 95% confidence interval exceeded 0 ms (SP null hypothesis). In the case of the moxifloxacin treatments, the proportion of values meeting these criteria gives a measure of the sensitivity of the hypothesis in detecting a moxifloxacin effect. In the case of vehicle 2 treatment “1 – the proportion” meeting these criteria gives a measure of the specificity of the QTc assessment.

RESULTS

Illustrative One‐Step model example

Figure 2 illustrates a sampled group of four animals at postdose hour 4 (time to C _max [T _max]). The figure illustrates that all the lines have different slopes and represent subtly different ranges in RR value. The figure also illustrates that based on the 60 data points for each line (960 points in total) the confidence intervals for the QT‐RR relationships are such that the QT interval at a reference RR value of 500 ms can be effectively and reliably estimated. This is the quantitative “core” of the One‐Step method. The estimated marginal means method by default makes the comparison of the dependent variable at the mean of the overall independent variable or covariate. In the illustrated example, the “model‐chosen” RR reference value was 514 ms, the mean RR for all data being compared.

FIGURE 2.

An example four (IDs = 22, 28, 37, 44) study at hour = 4. This figure illustrates for four animals at the 4 h timepoints (181–240 min postdose) the 1 min mean data recorded for all four treatments. There are four regression lines for QT‐RR for each animal. The confidence intervals around these lines at RR = 500 ms are sufficient to make confident predictions of the QT value independent of rate. The reference rate of 500 ms is indicated by the red vertical solid line. The estimated marginal means method by default uses the overall mean RR interval for the data being compared. In this case, this is 514 ms and is indicated by the black dashed vertical line.

Contrasting QTc time course

As illustrated in Table 1, the intended statistical output from all four methods is the same. The key output is the mean predicted QT effect of treatment relative to vehicle at an RR interval of 500 ms. In addition, the 95% upper and lower confidence intervals are useful in illustrating the sensitivity of the analysis. Figure 3 illustrates the time course of treatment effect derived using the five different analytical methods. This study represents a rare opportunity in having 48 animals in a crossover design and 276,480 QT‐RR pairs. This means there were 718 instances where the RR value was 500 ms, and 14,368 QT‐RR pairs where the RR interval was between 490 and 510 ms (see Figures S1 and S2). These data, around the Reference RR value, need no correction and the hourly mean effect of treatment can represent the effect of treatment on the QT interval independent of the assumptions in the heart rate correction method. The time course of effect in this case is also shown in Figure 3 (QT @ 500). There is inevitably more variability in this effect comparison. It used only a fraction of the overall data and may not reflect all animals equally at all times. It also spanned 21 ms of RR interval and so there will be some small error (<5 ms) owing to this small RR range. The primary importance of these effect data is the time course of the mean effect. The panels in Figure 3 show the derived data follow two broad patterns. The Legacy and Conventional methods are two‐step methods, and the output is derived from the second step, the statistical model. As a result of the limited amount of input data (Table 1), the residual error is relatively large and gives rise to wide confidence intervals. The Hybrid method takes all the data and the Conventional method assumptions and uses only a single step analysis. This gives rise to mean treatment effects on QTc identical to those of the Conventional analysis. However, the residual error is smaller, and the confidence intervals are narrower. The One‐Step method uses all the data and makes no assumptions about the slope of the QT‐RR relationship (Table 1). The mean QTc effect rises quickly with time, achieves a higher maximum value than the Conventional and Hybrid methods, and falls relatively quickly. In common with the Hybrid method, the confidence intervals are narrow. The time course of the One‐Step method moxifloxacin effect on QTc follows the QT @ 500 effect and achieves a higher maximum effect than the hybrid method more consistent with the QT @ 500 effect. The QT @ 500 effect minus the model‐derived effect for the Legacy, Conventional, and One‐Step methods are shown in Figure S3.

FIGURE 3.

Comparison of the analysis models. This figure illustrates for all 48 animals the mean treatment effect on QTc relative to vehicle 1. Sufficient data for a restricted range of RR interval (490–510 ms) was available. These QT data were not corrected for RR interval and represents the effect at the reference RR without the influence of correction method assumptions (“QT @ 500”) of treatment on the QT interval. Vehicle 2 should have no consistent effect on QTc. Moxifloxacin (80 mg/kg) caused a dose‐ and concentration‐dependent prolongation of QTc compared to vehicle 1. A solid red line at 10 ms QTc effect is provided for reference along with red dashed lines at ±5 ms.

FIGURE 4.

Power curves for four or eight based on the analysis models. This figure illustrates the power (for p = 0.05) to detect a QTc effect for the different methods and for group sizes of four or eight animals. Dotted lines at 5 (blue) and 10 ms (red) are provided for reference. The solid horizontal line represents 80% power.

Power assessments

The residual error derived as the median of the hourly model residual error by each method can be used to determine the power of the analysis methods for studies of four or eight NHPs. The power curves are shown in Figure 4. From Figure 4, the power of the Legacy and Conventional methods is similar, as are the Hybrid and One‐Step methods. The power of the Hybrid and One‐Step methods is significantly greater than that for the two‐step methods. The MDDs (80% power at p < 0.05) for four animal studies are 9, 10.6, 2.9, and 3.3 ms for the Legacy, Conventional, Hybrid, and One‐Step methods, respectively (Table 1).

Sensitivity and specificity

There is potential for false positive effects owing to increased sensitivity in the One‐Step method. This was examined by generating 1000 “pseudostudies” of four animals from the original 48 animals. The mean treatment effect and the mean upper and lower confidence intervals for the Conventional and One‐Step analysis models are depicted in Figure 5. The mean QTc effects in this figure are consistent with Figure 3 for the methods applied to the whole 48 animal data set. The smaller four study has much more evident impact on the confidence intervals for the Conventional method. The improved sensitivity of the One‐Step method is such that even with small numbers of animals the method is robust and sensitive. These effects on the confidence intervals are consistent with the power curves shown in Figure 4.

FIGURE 5.

Mean effect and mean confidence intervals based on 1000 sampled four studies, using the One‐Step model or Conventional analysis. The mean effect of treatment relative to dose A for 1000 sampled n = 4 studies, using either the Conventional or One‐Step analysis. The ribbons illustrate the mean upper and lower 95% confidence intervals for the 1000 studies. Reference lines for 10 ms (red solid line) and ±5 ms (red dashed line) are provided for reference. The mean effects are consistent with those in Figure 3. The wider confidence intervals are consistent with the number of animals and with the power curves in Figure 4.

The sensitivity and specificity for TQT and SP null hypotheses are depicted in Figure 6. The left panels illustrate the proportion of the 1000 replicates where the upper bound of the confidence interval exceeds 10 ms (TQT null hypothesis). In the panels on the right, the proportion of studies where the lower bound of the confidence interval exceeds 0 ms is depicted (SP null Hypothesis). The uppermost panels show the data for 1000 studies analyzed with the conventional approach. The lower panels examine the One‐Step model using a fixed RR interval reference value of 500 ms common in NHP studies. The middle panels examine the effect of dose using an RR reference value chosen by the model optimized for that hourly evaluation. The method by default chooses the mean of the RR values for all the data being compared. Thus, the reference RR interval could be different for each hour, but the statistical model still determines whether there is a statistically significant effect on the QT interval independent of RR within that hour. As the RR interval range within each hour can shift across the recording duration, the model chosen RR reference value minimizes the number of occasions where the extremes of any linear regression between QT and RR are used for comparison. A forced reference value (e.g., 500 ms) may have hours where this RR value is an extreme of RR values and the QTc value is estimated with greater uncertainty. A model chosen RR value is optimal for statistical evaluation while the fixed RR value is optimal for exploring the QTc versus time relationship and ultimately the concentration‐QTc relationship.

FIGURE 6.

Proportion of 1000 four studies where UCI exceeds 10 ms or LCI excludes 0 ms, using the conventional or One‐Step model (O‐S). The one‐step model can also be used with a fixed RR reference value (500 ms; O‐S 500) or a model‐chosen value (O‐S Model Chosen). This figure illustrates the proportion of the 1000 studies where the UCI exceeds 10 ms (left) or the LCI exceeds 0 ms (right). Reference lines for sensitivity of 90% (at 0.9) and specificity of 90% (at 0.1) are provided for reference. LCI, lower confidence interval; UCI, upper confidence interval.

Upper limit of confidence interval greater than 10 ms

The C _max for moxifloxacin occurred at 4 h and the exposures exceeded those associated with 10 ms clinical QTc prolongation from 0.5 to 18 h. ¹⁵ The sensitivity to detect an effect of moxifloxacin for the TQT null hypothesis is high for all three analyses across a wide time span: Conventional, One‐Step with fixed 500 ms RR reference, and One‐Step with model‐chosen RR reference. However, when specificity is considered, it is poor for the Conventional analysis where most studies have long periods where the upper limit exceeds 10 ms for Vehicle 2 treatment. Specificity is improved using the One‐Step method and is best when that method has a model‐chosen RR reference value.

Lower limit of confidence interval greater than or equal to 0 ms

In the case of conventional analysis, the proportion where the lower limit exceeds 0 ms is below 80% for most of the postdose period and is generally below 50% after 10 h. In the cases of moxifloxacin treatments, using the One‐Step method and a fixed reference RR, the proportion is above 75% for most of the first 18 h following treatment. When a model‐chosen RR reference is used the proportion approximates 100% for those same 18 h. In the case of treatment with vehicle (Vehicle 2) the specificity is very high for the Conventional analysis but poorer when using the One‐Step method. The proportion of 1000 studies meeting the criterion is higher for a model‐chosen RR reference value than for a fixed RR interval.

Overall, the Conventional analysis cannot test the TQT null hypothesis as the sensitivity is very high, but the specificity is impractically low and has a very high false positive rate. The commonly used SP null hypothesis allows a reasonable proportion of studies to have adequate sensitivity but consistent with the power curves (Figure 4) less than 80% of studies can detect 10 ms QTc change (as determined by the data between 12 and 20 h when the mean effect is around 10 ms). The One‐Step method using a model‐chosen RR interval improves both the sensitivity and specificity of assessment against the TQT null hypothesis but improves sensitivity at the detriment of specificity for assessments against the SP null hypothesis. In balancing the false positive and false negative burdens, it appears the best balance is offered by the One‐Step method using a model‐chosen RR reference value and the TQT null hypothesis. This is the default estimated marginal means method, in this case, simply using RR as a covariate.

DISCUSSION

Figures 1 and 2 highlight potentially erroneous assumptions of the Legacy and Conventional QTc analysis, they also provide insight into the ability of the One‐Step method to detect, with confidence, changes in cardiac repolarization independent of heart rate. Appendix S1 provided with this reported analysis further highlights the potentially erroneous assumptions.

The day‐to‐day and hour‐by‐hour variability in QT‐RR slope and the balance of RR values relative to the reference value, mean that even for treatments with no effect on cardiac repolarization or heart rate, there can be an increase in variability that impacts statistical sensitivity. It is well known that drugs which block the hERG potassium channel are associated with reverse‐rate dependent effects on action potential duration and QT interval. ¹³ , ¹⁴ This corresponds to a steepening of the QT‐RR relationship in the presence of a hERG blocker. Using a vehicle slope‐based correction will underestimate the effects of the compound during the day and overestimate effects during the night. This distortion of the QTc‐time course can distort the concentration‐QTc profile, and the distortion would be increased in the presence of a drug‐induced heart rate change. Figures S3–S9 and Table S1 illustrate the difference between the effect independent of the influence of the correction method (QT @ 500) and the effect determined by different methods, daily and hourly QT‐RR relationships, QT‐RR relationship slopes in the presence of different treatments, and the success of rate correction. Figure S12 demonstrates that the hourly slope of the QT‐RR relationship was shifted to steeper values in the presence of moxifloxacin. Taken together, this Appendix S1 further illustrates the importance of making the correct assumptions. It is also the case that the statistical test should be addressing the presence or absence of an effect of treatment on cardiac repolarization independent of heart rate in a given period (e.g., hourly). This is most appropriately addressed by examining the QT‐RR relationship within that period. Appendix S1 and Figures S10, S11, S13, and S14 are provided to illustrate that modern conscious ambulatory NHP data sets are rich enough to allow such analysis without resorting to potentially limiting assumptions.

In 2006, the amount of data used in the One‐Step method was modest. ⁷ It was described as around 20 cardiac cycles on three or more occasions, per animal and per treatment. This would be at least 60 cardiac cycles for eight animals given four different treatments in the replicated Latin square as described. Using the One‐Step method, even on such limited data, moved the threshold for detecting QT interval change from 7% (at 70% power and p = 0.05) to 5%–6%. This represented 11–13 ms absolute QT interval change. Recently similar replicated (n = 8) Latin square analyses in dogs using all the available data with conventional two step analysis showed a minimal detectable difference of 4.7 ms ²⁰ (80% power at p = 0.05). This is a clear improvement since 2006, but it appears a scant reward for now using around 100,000 cardiac cycles per animal per treatment. If the One‐Step method provided an improvement in sensitivity based on such limited data in 2006, it seemed certain it would provide increased sensitivity when more data are available. The current analysis showed that both the Hybrid and One‐Step methods, by increasing data density in the statistical model increased the sensitivity by approximately three to fourfold compared to conventional analyses. An eight animal crossover study in NHPs detected a QTc change of 6.5 ms ²⁰ (80% power at p = 0.05) using conventional analysis that threshold was 6.3 ms (Table 1) in the present analysis. The Hybrid and One‐Step analysis reduced that threshold to 1.7 and 2 ms, respectively.

Consideration of the potential false positive and false negative evaluations suggests that, as in the sensitive TQT assessment, acknowledging small QTc differences is pragmatic. Using the null hypothesis (0 ms < μ < 10 ms) would appear reasonable as this detected the effect of moxifloxacin at T _max and through most of the 18 h where the exposure exceeded the value associated with a 10 ms QTc change in man. ¹⁵ Although the peak effect of moxifloxacin was greater than 20 ms, it is possible to infer the sensitivity and specificity of the method with changes around 10 ms by examining Figure 6 and considering times between 12 and 18 h where the mean QTc effect is around 10 ms.

In addition to the increased sensitivity, the One‐Step method provides there were discernible changes in the time course and magnitude of the QTc effect. The maximum QTc change increased from around 21 ms to around 25 ms when comparing the Hybrid and One‐Step methods. Even dividing the maximum QTc change by the C _max value, the ~20% increase in QTc effect would increase the slope of the concentration‐QTc relationship. The faster rise in QTc and faster fall suggested an overall shift in time course and that conventional analysis may have a correction hysteresis artifact. Figure S3 supports a systematic underprediction with the Conventional method when RR intervals are relatively short. Beyond the sensitivity advantage, the One‐Step method should be evaluated to assess its impact in concentration‐QTc analyses, and this is a planned follow‐up evaluation. Overall, the One‐Step method offers the best discriminatory performance possible in small NHP studies.

AUTHOR CONTRIBUTIONS

D.J.L. wrote the manuscript. D.J.L., D.A.L., and M.B.B. designed the research. B.M.R. and D.L.H. performed the research. D.J.L. and D.L.H. analyzed the data.

FUNDING INFORMATION

No funding was received for this work.

CONFLICT OF INTEREST STATEMENT

The authors declared no competing interests for this work.

Supporting information

Appendix S1

Figure S1

Leishman DJ, Holdsworth DL, Lauver DA, Bailie MB, Roche BM. The “One‐Step” approach for QT analysis increases the sensitivity of nonclinical QTc analysis. Clin Transl Sci. 2023;16:2253‐2264. doi: 10.1111/cts.13625