# Assessment of the stability of the individual-based correction of QT interval for heart rate.

**ABSTRACT** Modeling the relationship between QT intervals and previous R-R values remains a challenge of modern quantitative electrocardiography. The technique based on an individual regression model computed from a set of QT-R-R measurements is presented as a promising alternative. However, a large set of QT-R-R measurements is not always available in clinical trials and there is no study that has investigated the minimum number of QT-R-R measurements needed to obtain a reliable individual QT-R-R model. In this study, we propose guidelines to ensure appropriate use of the regression technique for heart rate correction of QT intervals.

Holter recordings from 205 healthy subjects were included in the study. QT-R-R relationships were modeled using both linear and parabolic regression techniques. Using a bootstrapping technique, we computed the stability of the individual correction models as a function of the number of measurements, the range of heart rate, and the variance of R-R values.

The results show that the stability of QT-R-R individual models was dependent on three factors: the number of measurements included in its design, the heart-rate range used to design the model, and the T-wave amplitude. Practically our results showed that a set of 400 QT-R-R measurements with R-R values ranging from 600 to 1000 ms ensure a stable and reliable individual correction model if the amplitude of the T wave is at least 0.3 mV. Reducing the range of heart rate or the number of measurements may significantly impact the correction model.

We demonstrated that a large number of QT-R-R measurements (approximately 400) is required to ensure reliable individual correction of QT intervals for heart rate.

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**ABSTRACT:**Of late there has been considerable interest in the efficient and effective storage of large-scale network graphs, such as those within the domains of social networks, web and virtual communities. The representation of these data graphs is a complex and challenging task and arises as a result of the inherent structural and dynamic properties of a community network, whereby naturally occurring churn can severely affect the ability to optimize the network structure. Since the organization of the network will change over time, we consider how an established method for storing large data graphs (K2 tree) can be augmented and then utilized as an indicator of the relative maturity of a community network. Within this context, we present an algorithm and a series of experimental results upon both real and simulated networks, illustrating that the compression effectiveness reduces as the community network structure becomes more dynamic. It is for this reason we highlight a notable opportunity to explore the relevance between the K2 tree optimization factor with the maturity level of the network community concerned.Computers & Mathematics with Applications 01/2012; · 2.00 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Background Reproducibility of spatial TT’ angle on the 10-second ECG and its agreement with QT variability has not been previously studied. Methods We analyzed 2 randomly selected 10-second segments within 3-minute resting orthogonal ECG in 172 healthy IDEAL study participants (age 38.1 ± 15.2 years, 50% male, 94% white). Repolarization lability was measured by the QT variance (QTV), short-term QT variability (STV(QT)), and spatial TT’ angle. Bland-Altman analysis was used to assess the agreement between different log-transformed metrics of repolarization lability, and to assess the reproducibility. Results The heart rate showed a very high reproducibility (bias 0.14%, Lin’s rho_c = 0.99). As expected, noise suppression by averaging improves reproducibility. Agreement between two 10-second LogQTV was poor (bias -0.04; 95% limits of agreement [-1.89; 1.81]), while LogSTV(QT) (0.04[-1.01;1.10], and especially LogTT’ angle (-0.009[-0.84; 0.82]) was better. Conclusion TT’ angle is a satisfactory reproducible metric of repolarization lability on the 10-second ECG.Journal of Electrocardiology 09/2014; · 1.36 Impact Factor - SourceAvailable from: diahome.org
##### Article: The Assessment of QT/QTc Interval Prolongation in Clinical Trials: A Regulatory Perspective

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**ABSTRACT:**Excessive prolongation of the QT/QTc interval creates an electrophysiological environment that predisposes the myocardium to torsade de pointes, a polymorphic ventricular tachyarrhythmia that can progress to ventricular fibrillation and sudden cardiac death. Identification of QT/QTc prolongation liability is therefore an important objective of contemporary drug development programs. Nonclinical safety pharmacology studies are useful in early identification of this cardiac safety problem and in preliminary risk assessment. Specialized clinical pharmacology studies play a critical role in characterizing the magnitude, time course, dose dependency, and concentration relationship of drug-induced QT/QTc prolongation, as well as guiding the intensity of electrocardiogram (ECG) safety evaluations in subsequent trials. The reading, analysis, and interpretation of the ECG data acquired through these studies are complex issues that present many challenges to the pharmaceutical industry and regulatory authorities alike.Therapeutic Innovation and Regulatory Science 10/2005; 39(4):407-435.

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Assessment of the Stability of the Individual-Based

Correction of QT Interval for Heart Rate

Jean-Philippe Couderc, Ph.D., M.B.A., Xia Xiaojuan, M.Sc., Wojciech Zareba,

Ph.D., M.D., and Arthur J. Moss, M.D.

From the Heart Research Follow-up Program, Cardiology Department, University of Rochester, Rochester,

New York

Background: Modeling the relationship between QT intervals and previous R-R values remains a

challenge of modern quantitative electrocardiography. The technique based on an individual regres-

sion model computed from a set of QT–R-R measurements is presented as a promising alternative.

However, a large set of QT–R-R measurements is not always available in clinical trials and there is

no study that has investigated the minimum number of QT–R-R measurements needed to obtain a

reliable individual QT–R-R model. In this study, we propose guidelines to ensure appropriate use of

the regression technique for heart rate correction of QT intervals.

Method: Holter recordings from 205 healthy subjects were included in the study. QT–R-R relation-

ships were modeled using both linear and parabolic regression techniques. Using a bootstrapping

technique, we computed the stability of the individual correction models as a function of the number

of measurements, the range of heart rate, and the variance of R-R values.

Results: The results show that the stability of QT–R-R individual models was dependent on three

factors: the number of measurements included in its design, the heart-rate range used to design

the model, and the T-wave amplitude. Practically our results showed that a set of 400 QT–R-R

measurements with R-R values ranging from 600 to 1000 ms ensure a stable and reliable individual

correction model if the amplitude of the T wave is at least 0.3 mV. Reducing the range of heart rate

or the number of measurements may significantly impact the correction model.

Conclusion: We demonstrated that a large number of QT–R-R measurements (∼400) is required to

ensure reliable individual correction of QT intervals for heart rate.

A.N.E. 2005;10(1):25–34

QT interval; heart rate; regression analysis; risk assessment; drug effects

An accurate measurement of the QT interval du-

ration from the surface ECG is a challenging task

requiring careful consideration of several technical

and physiological factors. Among these factors, the

recording technique and the measurement meth-

ods,1the lead choice,2and the subjects age and gen-

der3are easy to control. Other factors, such as the

autonomicbalance,4therepolarizationadaptation,5

the effect of QT hysteresis,6and the QT heart-rate

dependency are more difficult to assess mainly be-

cause their levels are likely to be different between

individuals. Our study relates to the heart-rate de-

pendency of QT interval duration. Correcting QT

intervals for heart rate allows for comparing repo-

larization measurements obtained at different heart

Address for reprints: J.P. Couderc, Ph.D., MBA, Research Assistant Professor of Medicine, Heart Research Follow-up Program, Car-

diology Department, University of Rochester, 601 Elmwood Avenue, Box 653, Rochester, NY 14642. Fax: 585-273-5283; E-mail:

jean-philippe.couderc@heart.rochester.edu

rates, either between subjects or within the same

subject. The most popular correction is Bazett’s for-

mula; it is implemented in all commercial ECG sys-

tems, but its validity has been highly criticized.7,8

It underestimates the QT interval at slow heart

rate and overestimates it at fast ones. The need

for a better correction method is even more impor-

tant for the safety evaluation process of new drugs

where the drug-induced QT interval prolongation

is used as a surrogate marker for the occurrence

of torsades de pointes (TdP). A prolongation of 10–

20 ms may raise some concerns and a prolongation

above 20 ms may jeopardize the future commer-

cial release of a new drug. In this case, the Bazett’s

correction may lead to both false-positive and

25

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rIndividual Rate Correction for QT Interval

false-negative observations, and thus it should not

be used.8

Among a large set of published correction for-

mulae, Fridericia’s is one that seems better than

Bazett’s.9,10Nevertheless, the use of a mathemati-

calfunctioncharacterizingtheQT–R-Rrelationship

and generalized to any patient is a questionable ap-

proach because the QT–R-R relationship was re-

ported to be subject dependent.10Today, there are

three alternatives to a general predefined mathe-

matical formula. The first one compares the QT

interval for matched heart rate; the so-called “bin

approach” does not use any correction model.11

The second alternative is a population-based for-

mulae (or pool formula) based on a QT–R-R model

designed on measurements from all subjects of

the study population.9This alternative may be the

best one when a limited number of short ECGs is

available for each subject. The third option is an

individual-basedformula.Thismethodreliesonthe

computation of a QT–R-R correction model in each

subject.10The resulting model is used to correct the

QT measurements for this subject.

The stability of the individual-based correction

model between individuals and between record-

ings within the same individual has been inves-

tigated.10However, there is no study investigat-

ing the variation of the individual-based correction

model within the same recording as a function of

(1) the number of measurements (N) used to design

this model, (2) the heart-rate range (and variance),

and (3) the T-wave amplitude, which is known to

affect the quality of the QT measurements.12In this

study, we will use the term “stability” for charac-

terizing this variation of the fitting models.

The first two components are the most relevant

ones in the assessment of the quality of a fitting

technique under the assumption that the data are

homoscedastic. Investigating the limits of stability

Table 1. Clinical Characteristics of the Study Population.

AllMalesFemalesP value

N

Age (years)

HR (bpm)

BMI (cm/kg2)

QTc (second)

205104101

38.9 ± 15.9

68.4 ± 11.5

24.4 ± 4.5

0.43 ± 0.04

37.3 ± 14.5

66.9 ± 11.8

24.9 ± 3.3

0.42 ± 0.04

40.6 ± 17.1

70.0 ± 11.0∗

23.8 ± 5.5∗∗

0.44 ± 0.04

NS

0.06

0.0002

0.016

∗P = 0.06;∗∗P = 0.0002 (Wilcoxon two-sample test).

QTc values are average values from the first10-minute ECG in lead Z. Bazett’s formula was used

for the heart rate correction.

of individualized formula may help to better under-

stand the limits of the utility of this concept in drug

safety investigations.

METHOD

The study population consists of 205 healthy

subjects from the Intercity Digital Electrocar-

diogram Alliance (IDEAL) database. Table 1

reports clinical characteristics of this study popula-

tion. Twenty-four-hour Holter recordings were ac-

quired using the SpaceLab-Burdick digital Holter

recorder (SpaceLab-Burdick, Inc., Deerfield, WI).

This equipment provides 200 Hz sampling fre-

quency signals (5-ms time resolution) with 16-bit

amplituderesolution(2.5µVamplituderesolution).

Electrocardiograms were acquired using three

pseudoorthogonal lead configuration (X, Y, and Z).

The QRS detection and beat annotations were ob-

tained using Vision PremierTM(SpaceLab-Burdick).

The QT measurements were automatically mea-

sured using the software for COMPrehensive

Analysis of the repolarization Signal (COMPAS)

developed at the University of Rochester, Heart

Research Follow-up Program (ECG Core Lab,

Rochester, NY). The measurements of repolariza-

tion in Holter recordings require the use of an

averaging technique as well as a filtering process

based on preceding heart rate values as reported

by Maison-Blanche et al.13Median cardiac beats

were computed based on 11 consecutive beats in

which abnormal beats were removed and heart-

rate stability was assessed (less than 10% variation

in heart rate was required). Then, QT measure-

ments from a set of six median cardiac beats

were averaged providing one measurement for a

set of 66 continuous beats (close to a 1-minute

period). This averaging procedure allows for sta-

bilizing QT measurements when measured from

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rIndividual Rate Correction for QT Interval

r27

Holter recordings. The issue of QT adaptation to

heart rate changes was addressed using a detec-

tion threshold on rapid heart rate changes (?R-R >

250 ms), all the cardiac beats in the following

1-minute segment were excluded from further

analysis.

The validation of QT measurements using this

software has been done in a previous study.9Iden-

tification of the end of the T wave was done us-

ing the maximum slope method where the end

of the T wave is located at the crossing point

between the maximum slope and the isoelectric

line.14The QT–R-R relationships were analyzed

using Matlab software (MathWorks, Inc., Natick,

MA). Two models were used: (1) a linear model:

(QT = αR-R + β) and (2) an exponential models

(QT = βR-Rα), referenced as a parabolic model in

previous works.10

Forbothlinearandparabolicmodels,westudied:

(1) the values of α for the population, considering

the entire 24-hour ECG recording, (2) the stability

of α (standard deviation of α: STDα) as a function

of N, and (3) the changes in STDα according to

the HR range on which the correction model was

designed.

Study of the Entire 24-Hour ECG

Recordings

Let N be the number of QT–R-R measurements

included in the design of an individual correction

model. We computed QT–R-R relationships in all

subjects. We investigated the differences occurring

in this relationship between males and females.

Stability of Individual Correction Model

Related to ECG Length

We computed the stability of the correction

model when it is based on a set of measurements in-

cluding N = 5–800 measurements (5 measurement

increment). We assumed these measurements to be

homoscedastic over a heart-rate range equal to 60–

100 bpm (R-R = 1000–600 ms). Twenty sets of N

measurements were randomly resampled with re-

placement from the 24-hour pool of QT–R-R mea-

surements for each value of N. The stability of the

correction model for a given N was computed as the

standard deviation of α within these 20 estimates

(STDα). Then, for a given N, we extracted the min-

imum and maximum values from these 20 values

of α (α min and α max). The two models based on

α min and α max provide two curves we used to

identify the so-called “maximum error’’ (Max. Err.)

defined as the largest separation between the two

curves at any given heart rate. Maximum error pro-

vides a quantitative assessment (expressed in mil-

liseconds) of the effect of the variation in the design

of the correction model on the correction of the QT

interval.

We expect STDα to vary as a function of N fol-

lowing the

ˆ σ2

mate of the residual variance and ˆ σ2

ance of R-R. We confirmed this variation of STDα

as a function of N using ˆ σ2

N = 50.

?

e/Nˆ σ2

R−Rmodel, where ˆ σ2

eis the esti-

R−Ris the vari-

eand ˆ σ2

R−Rcomputed for

Stability of Individual Correction Model

Related to Heart-Rate Range

A 24-hour Holter ECG (or a few-hours recording)

may have a limited range of heart rate. Thus, we

studied the stability of α values according to the

heart-rate range for a fixed number of measure-

ments (N = 200). The heart-rate range was quan-

tified using the variance of R-R values used in the

design of the correction model. The smallest heart-

rate range was 750 < R-R < 850 ms, the largest was

600 < R-R < 1000 ms. The upper and lower limits

of the R-R interval were incrementally changed by

steps of 25 ms.

In addition, we investigated the stability of the

models for QT–R-R values using measurements

from the entire 24-hour recordings.

STATISTICAL METHOD

The estimated residual variance (ˆ σ2

gression line reflects the stability of the fitting

model. The higher ˆ σ2

To compare the stability between gender, we used

a point estimate of the true residual variance ra-

tio (R) where R is defined as the ratio of the

residual variance of the two compared groups R =

ˆ σ2

ee

vidual estimated residual variances. On the basis

of a bootstrapping technique using a number of

replication equal to 1000, we empirically computed

the 0.05 and 0.95 quantiles of R. Then, we tested

the null hypothesis that the residual variances are

equal (R = 1) at 0.05 significance level. The statis-

tical analysis was realized using Matlab software

(MathWorks).

e) of the re-

e, the lower the stability is.

??

women/ ˆ σ2

??

men, where ˆ σ2

eis the mean of indi-

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rIndividual Rate Correction for QT Interval

Table 2. Results from QT–R-R Analysis on the Overall 24-Hour Recordings from Lead Z.

GroupNR-R (ms) T Amp (mV)

α Linear

α Parabolic

All

Male

Female

Day

Night

205

104

101

205

197

798 ± 107

815 ± 108

781 ± 105

759 ± 102

947 ± 152

0.36 ± 0.29

0.46 ± 0.32

0.26 ± 0.21

0.37 ± 0.29

0.33 ± 0.27

0.17 ± 0.08

0.16 ± 0.07

0.18 ± 0.08

0.16 ± 0.08

0.12 ± 0.12

0.34 ± 0.14

0.33 ± 0.13

0.36 ± 0.15

0.33 ± 0.14

0.26 ± 0.20

N is the number of subjects in each group, T Amp: Amplitude of T wave, α for Linear and Parabolic

Models.

RESULTS

QT–R-R Relationship in 24-Hour Holter

Analysis

Table 1 provides a description of the study pop-

ulation for age, average heart rate, body mass in-

dex (BMI) and QTc when measured from the 12-

lead ECGs and corrected using Bazett’s formula.

BMI was somewhat higher in males than in fe-

males (24.9 ± 3.3 vs 23.8 ± 5.5 cm/kg2, P = 0.095).

The heart rate was slightly higher in females; this

difference was close to the statistical threshold for

significance (70 ± 11 vs 67 ± 12 bpm, P = 0.06).

Ages were similar between genders. QTc intervals

based on Bazett’s formula were significantly higher

in females than in males (0.44 ± 0.04 vs 0.42 ±

0.04 second, P = 0.016).

Table 2 reports average values of R-R intervals, T

amplitude,andα forlinearandparaboliccorrection

model for five groups (all subjects, male, female,

day, and night) for lead Z. The values are in accor-

dance with previous studies.10,15The amplitude of

T wave was computed between leads (not reported

in Table 2) and it was significantly higher in lead

Z than in other leads (X: 0.36 ± 0.29 vs 0.30 ±

0.26 mV, P = 0.02 and Z: 0.46 ± 0.32 vs 0.30 ±

0.30 mV, P = 0.0001). The amplitude was also sig-

nificantly lower in females than in males (0.26 ±

0.21 vs 0.46 ± 0.32 mV, P < 0.001).

The variations of QT–R-R slope between linear

andparabolicmodelswereconsistent.Alphavalues

were significantly higher in females than in males

(P = 0.047) for the linear model in accordance with

previous studies.10For the logarithmic model, this

increase did not reach significance (P = 0.13).

The autonomic nervous system affects the QT–

R-R relationship, and the slope of the linear re-

lationship is steeper during the day than during

the night revealing a sensitivity of repolarization to

the vagal tone.16–18The slopes were significantly

higher for both linear and parabolic models during

day than during the night (P = 0.0001).

Stability of Individual Correction Model

Related to ECG Length

Table 3 provides examples of the effect of the

number of measurements included in the design of

the individual HR correction models for both lin-

ear and parabolic models and for two values of N

(N = 50 and 300). The number of subjects (n), the

values of the averaged slope (α), the average stan-

dard deviation of the slope within a subject (STDα),

and the maximum correction error due to insta-

bility of the model are reported for models built

on a number of measurements N = 50 and 300.

Figure 1 describes STDα as a function of N for lin-

ear models based on empirical and theoretical vari-

ation of α (

ˆ σ2

ues decrease in a similar manner as STDα.

?

e/Nˆ σ2

R−R). The Maximum Error val-

Table 3. Number of Subjects (n), the Averaged α

Value and its Averaged Standard Deviation STDα

Within Subjects.

LinearParabolic

N = 50

n

α (n.u.)

STDα (n.u.)

Max. Err. (ms)

127128

0.17

0.014

13.4

0.36

0.029

43.6

N = 300

n

α (n.u.)

STDα (n.u.)

Max. Err. (ms)

75

0.18

0.006

4.9

74

0.37

0.013

18.1

The Maximum Variation in milliseconds the model can gener-

ate (Max. Err.) for both linear and parabolic models in lead

Z. These values are reported for a number of measurements

(N) equal to 50 and 300. Values are based on the overall

24-hour Holter recordings. n.u.: no unit.

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rIndividual Rate Correction for QT Interval

r29

Figure 1. Curves describing the variation of stability (STDα) in upper panel

and the variation of Max. Err. in the lower panel for lead Z, according to the

number of points included in the design of the correction model. These graphs

rely on the models designed with measurements spreading in a similar manner

on the overall heart-rate ranges (equal variance on heart-rate range for all

experiment). These curves follow the expected theoretical

(bold line).

?

ˆσ2

e/Nˆσ2

R−Rpattern

According to the lower panel in Figure 1, to in-

sure an error less than 10 ms, more than 100 mea-

surements must be included in the design of the

linear correction model. The parabolic model leads

to higher Max. Err. values according to Table 3 re-

vealing that the parabolic model is more likely to

generate on average much larger error on the QTc

values.

Stability of Individual Correction Model

Related to Heart-Rate Range

The analysis of the effect of heart-rate ranges on

STDα is based on models designed using 100 QT–

R-R measurements (N = 100). The variance of R-R

values is used as a measure of the spread of the R-R

interval on which the correction model is designed.

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rIndividual Rate Correction for QT Interval

Figure 2. The upper panel is the evolution of stability of the slope of the linear

correction model according to the R-R ranges (expressed as the variance of

the R-Rs). Each point is labeled using the corresponding heart-rate ranges

expressed in both R-R (ms) and HR (bpm). The smaller the R-R variance, the

less stable the correction model is. The lower panel describes the values of

STDα in lead Z between genders.

The upper panel of Figure 2 describes the varia-

tion of STDα as in function of the variance of R-R.

The larger the R-R variance the more stable the

model is. Each point of the graph is labeled using

the corresponding heart-rate ranges expressed both

in R-R (ms) and heart rate (bpm). For N = 100 and

R-R within the range 600–1000 ms, the STDα level

for a large HR range is expected to be close to 0.008

(Figs. 1 and 2). When the heart-rate range shrinks,

R-R variance diminishes and the STDα value in-

creases; thus the stability of the correction model

decreases. Having a model based on 100 mea-

surements spanning heart rates between 100 and

60 bpm provides two-times higher stability than if

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rIndividual Rate Correction for QT Interval

r31

the 100 measurements were spanning only 83 and

69 bpm.

Under the assumption that the QT values used

for designing the QT–R-R model are homoskedas-

tic, the stability of a correction model is dependent

on the spread of R-R values. Limiting the heart-rate

range of QT–R-R measurements used in the design

of an individual correction model leads to a correc-

tion model with lower stability.

Role of the T-Wave Amplitude

on the Stability of the Individual

Correction Model

The slope method for the identification of the

end of the T wave is dependent on the mor-

phology of the T wave and on its amplitude as

well.12,19We investigated the role of the ampli-

tude on the stability of the correction model by

computing the values of ˆ σ2

for N = 200 measurements including T-wave am-

plitude in two different ranges: low T amplitude

<0.3 mV and high T amplitude ≥0.3 mV. Table 4

summarizes the results and demonstrates that the

stability of the correction model is different be-

tween the two levels of T-wave amplitude. QT–R-R

slopes based on low-amplitude T waves are associ-

ated with a less stable regression line [T ampl. <

0.3 mV : ˆ σ2

wave amplitude is high [T ampl. ≥ 0.3 mV : ˆ σ2

0.1 ± 0.1(10−3s2)]. Thus, the choice of leads for

computing individual correction model should be

based on leads where the amplitude of the T-wave

is the largest.

e, ˆ σ2

R−Rand

?

ˆ σ2

e/ˆ σ2

R−R

e= 1.0 ± 1.2?10−3s2?] than when the T-

e=

Effect of Gender on the Stability of the

Individual Correction Model

Differences in T-wave amplitude have been re-

ported between genders20and are confirmed in

Table 4. Table Providing the Averaged Values ofˆσ2

Groups: for All Subjects, for Subjects with T-Wave Amplitude < 0.3 mV, and for

Subjects With T-Wave Amplitude ≥ 0.3 mV.

All AmplitudeT Amp < 0.3 mV

e, ˆσ2

R−R, and

?

ˆσ2

e/ˆσ2

R−R, in Three

T Amp ≥ 0.3 mVP

ˆσ2

ˆσ2

?

P values are given for the comparison between the third and fourth column.

e(10−3s2)

R−R(10−3s2)

ˆσ2

0.5 ± 0.9

19 ± 13

0.16 ± 0.12

1.0 ± 1.2

16 ± 10

0.24 ± 0.14

0.1 ± 0.1

20 ± 15

0.09 ± 0.03

<0.0001

0.33

<0.0001

e/ˆσ2

R−R(ν)

our study (Table 2). This difference in amplitude is

highly significant (in lead Z: 0.46 ± 0.32 vs 0.26 ±

0.21 mV, P < 0.001). In Figure 2 (lower panel),

the values of STDα for an increasing number of

QT–R-R measurements are given for females and

males. Again based on the ratio of variance (R), we

computed Rmf (male vs female), the ratio (95% CI:

0.827–0.846) was significantly different from 1 (P <

0.0001) revealing that the stability of the models

are different by gender and this difference is due

to differences in the amplitude of the T wave.

The theoretical variation was also modeled as in

Figure 1.

DISCUSSION

The individual heart rate correction for QT in-

terval measurements has been introduced as an al-

ternative method to Bazett’s and Fredericia’s cor-

rection formulae which generally fail to provide

appropriate correction.9Although the reproducibil-

ity of the QT–R-R relationship has been studied by

several authors who have reached similar conclu-

sions,21,22there is no study investigating the vari-

ous factors that may affect the stability of the in-

dividual QT–R-R models. In this experiment, we

demonstrated, as expected, that the stability of in-

dividual correction formula is mainly dependent

on three components: (1) the number of measure-

ments included in the model design; (2) the spread

of heart rate on which the correction model has

been built; and (3) the amplitude of the T wave (as-

sociated with gender). The dependence on T-wave

amplitude is linked to the method used for identi-

fying the end of the T wave. The two other com-

ponents are intrinsically related to the regression

analysis and must be taken into account regardless

of the technique used to measure the QT intervals.

Previous publications emphasized the importance

of the number of measurements but ignored the

effect of the R-R variance (or spread of heart rate

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rIndividual Rate Correction for QT Interval

into the computation of the individual regression

analysis).8Our study demonstrates that these two

factors (number of points and R-R variance) affect

the quality of the individual heart rate correction.

Thus, both should be examined carefully before us-

ing any individual correction factor based on re-

gression models.

The use of a filtering technique for identify-

ing stable QT measurements discarded in aver-

age 24.8% of measurements in an overall 24-hour

recording. The range of the rejection rate was 98.7–

2.0%. Which means that only few measurements

were available in several ECGs due to the strin-

gency of criteria for QT measurement selection. To

decrease this rate of rejection, one could use less

stringent criteria on rapid changes of heart rate or

reduced the repolarization adaptation period. How

this would affect the stability of the QT–R-R mea-

surement can only be hypothesized and could be

investigated in further studies.

We studied both linear and parabolic models.

Our results show that the parabolic model is less

stable and can lead to larger errors in QTc than the

linear model. The values of STDα for the parabolic

model are higher than the linear model: 0.029 ver-

sus 0.014 for 50 measurements and 0.013 versus

0.006 for the 300 measurements (Table 3). Thus, in

this discussion we will focus mainly on the linear

model.

From our results, the standard deviation of α

values within subjects for the linear model was

close to 0.005, which is twofold lower than what

was reported in Batchvarov et al. study (in males,

average intrasubject standard deviation of α was

0.011).22The higher stability of our approach may

be explained by several factors: the preselective fil-

tering algorithm (considering only stable QT mea-

surements), the imposed homoscedasticity of our

models or simply a different number of measure-

ments included in the design of the models. Never-

theless, the intrasubject QTc error associated with

instability is not negligible and it may play a rele-

vant role when small QT interval changes are be-

ing evaluated. For a model based on few minute

recordings (300 measurements), one should note

that individual-based correction formula might

lead, in the worth-case scenario, to a 5-ms mea-

surement error on an individual basis, which is

the level of prolongation that one might look for

in certain compounds associated with polymor-

phique ventricular tachycardia (moxifloxacin is an

example).23

Wereportα valuesfrom205HolterECGs.Inlead

Z (highest amplitude), the average 24-hour α value

wasequalto0.18±0.08and0.16±0.07forfemales

and males, respectively. According to Dower’s ma-

trix,onewouldextendourresultsbasedonleadZto

a lead V2 in the 12-lead system.24Our investigation

of lead X reflecting lead I and lead Y reflecting aVF

were similar than in lead Z. The slight differences

were associated to difference in T wave amplitude.

In the overall population, average α values are

equal to 0.17 ± 0.08. When comparing our results

to previous reports, Batchvarov et al. reported in

50 healthy subjects, α = 0.203 ± 0.031 in women

and 0.163 ± 0.018 in men.22Fei et al. have found α

values for their groups of healthy subjects equal

to 0.12 ± 0.04 (n = 8) α and 0.14 ± 0.08 (n =

20).25,26Stramba-Badiale et al. evaluated the QT–

R-R relationship in 40 healthy subjects in whom

they found α values equal to 0.13 ± 0.03 in males

(n = 20) and 0.16 ± 0.04 in females (n = 20).3

Rasmussen et al. investigated the largest group of

healthy with 60 subjects, average α value was 0.14

(variation between subjects was not reported).27

Malik et al. found slightly higher values (0.17) in

50 healthy subjects with 0.19 ± 0.03 and 0.15 ±

0.03 for females and males, respectively.10Conse-

quently, there are slight differences in average val-

ues of QT–R-R slopes between studies that may be

explained by numerous factors (QT measurement

techniques, T wave amplitude, etc.). Ensuring that

QT–R-R measurements are based (1) on the lead

with the highest T-wave amplitude and (2) on a

large set of QT–R-R measurements is important.

The heart-rate range plays an important role too. As

expected, the use of ECGs including a large range

of R-R values is required to obtain a stable correc-

tion model. This means the smaller the range of

R-R values, the larger the number of QT–R-R mea-

surement needed to compensate for the lack of R-R

variance as shown in Figures 1 and 2.

Because the QT–R-R slope has also been used as

a potential marker for predicting an increased risk

for cardiac events,28our analysis may be relevant

for any risk-stratification method based on QT–R-R

dynamicity. Recently, Chevalier et al. reported that

increased diurnal QT dynamicity (α > 0.18) could

be used as a risk stratifier for sudden cardiac death

in post-MI patients.10,17Previously, Fei et al. in-

vestigated changes in α values from the overall

24-hour recordings in patients after a sudden car-

diac death,25QT–R-R slope was significantly in-

creased in both groups (0.19 ± 0.07 in sudden

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rIndividual Rate Correction for QT Interval

r33

cardiac death survivors and 0.12 ± 0.04 in healthy

subjects).Thus,ourrecommendationsforobtaining

a valid evaluation of the QT–R-R relationship might

be useful for future investigation of the prognostic

significance of α.

Our study demonstrates that heart-rate ranges,

number of QT–R-R measurements and T-wave am-

plitude are fundamental factors affecting the stabil-

ity of the individual correction models. One would

recommend insuring that there is an appropriate

balance between these factors. On the basis of our

experiment, designing a correction model using 400

QT–R-R measurements (6-hour recordings accord-

ing to our method) from a lead with an average

T-wave amplitude of 0.3 mV and with heart rate

rangingfrom60to100bpmwouldprovidelessthan

5 ms error on the corrected QT at any heart rate.

LIMITATION OF THE STUDY

Our study population is one of the largest used

to analyze the QT–R-R dynamicity in normal sub-

jects based on digital Holter recordings. However,

most of our study is based on regression analyses in

which the QT–R-R measurements were chosen in

order to obtain equal variance of QT values across

all R-R values (homoskedastic data) thus our exper-

iments do not represent real data but rather ideal

situations minimizing the level of stability found in

our experimental models. In addition, the results

are dependent on our QT algorithm that is, in this

case, a derived version of the slope method.

In addition, we assessed the stability by ran-

domly choosing QT–R-R measurements from the

24-hour recording without distinction between di-

urnal and nocturnal periods. We agree that limiting

the QT–R-R measurements to the diurnal or noctur-

nal period could help stabilizing the correction be-

cause the QT–R-R relationship is different between

these two periods (Table 2).

CONCLUSION

Our study investigates the stability of the

QT–R-R individual-based correction formula in re-

lation to the number of measurements used to de-

sign the correction model, the heart-rate range and

the T-wave amplitude. All factors had an effect on

the stability of the model. On the basis of our exper-

iment, we recommend using the individual-based

correction formula with caution and ensure that

both the number of QT–R-R measurements (≥400)

and the range of HR values (60–100 bpm) are large

enough. The choice of the lead for the design of

the correction model is important too. If all leads

cannot be combined, the use of the lead with the

highest amplitude (∼0.3 mV) of T-wave helps in

stabilizing the model.

Acknowledgments: The authors acknowledge Dr. Derick R. Pe-

terson for its valuable contribution in the design of the statistical

analysis presented in this study.

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