Download The Heart Rate-Corrected QT Interval of

TOXICOLOCICAL SCIENCES 45, 247-258 (1998)
ARTICLE NO. TX982529
The Heart Rate-Corrected QT Interval of Conscious Beagle Dogs:
A Formula Based on Analysis of Covariance
Stan Spence,*1' Keith Soper,f Chao-Min Hoe.t and John Coleman*
'Department of Safety Assessment and tDepartment of Biometrics Research, Merck Research Laboratories, West Point, Pennsylvania 19486
Received March 9, 1998; accepted June 25, 1998
The duration of the QT interval of the electrocardiogram
The Heart Rate-Corrected QT Interval of Conscious Beagle (ECG) represents the time required for ventricular depolarizaDogs: A Formula Based on Analysis of Covariance. Spence, S., tion and repolarization to occur. Assessment of the QT interval
Soper, K., Hoe, C.-M., and Coleman, J. (1998). Toxicol. Sri. 45,
is clinically important because prolongation of this interval
247-258.
may be associated with a predisposition to tachyarrhythmias
Three frequently used and cited formulas used to rate correct (i.e., torsade de pointes) and sudden death (Peters et al, 1990;
the QT interval (Bazett's, Fridericia's, and Van de Water's) were Algra et al, 1991; Schoeten et al, 1991; Ahnve, 1991; Goldcompared and ranked using a large population-based cohort of berg et al, 1991). However, prolongation of the QT interval
beagle dogs (99 males and 99 females). In addition, analysis of may also be indicative of the antiarrhythmic activity of a
covariance was used to derive aflexiblemethod to rate correct the
compound (Colatsky and Follmer, 1989; Kass and Freeman,
QT interval for heart rate. The method isflexiblein that it utilizes
pretest or control data to determine the degree of correction. In 1993; Surawicz, 1987). Consequently, several pharmaceutical
addition, it can also be used to evaluate whether treatment alters companies are currently developing drugs that selectively prothe association between heart rate and QT. Specifically, pretest QT long the QT interval by blocking some aspect of the delayed
(unadjusted) and heart rate data were used to estimate coefficients rectifying potassium current [(/k); Kass and Freeman, 1993;
in the linear regression log(QT) = a + p\og(HR). The estimated Rees and Curtis, 1996; Nappi and McCollam, 1993]. However,
slope O) from the pretest data was used to heart rate correct the to accurately interpret drug-induced alterations of the QT inQT interval in the formula log^QT)^ = log(QT) - fi*[log(HR - terval it must be adjusted for changes in heart rate (HR) since
logfHR^)]. The term "logiHR^" is included to standardize QT^ the length of the QT interval is directly dependent on the length
to areferencevalue, either a fixed value or an average heart rate of the preceding cardiac cycle (Bazett, 1920; Van de Water et
for the data set being analyzed. These formulas were retrospec- al, 1989; Oguchi and Hamlin, 1993; Mann etal, 1994). As the
tively compared under a typical toxicity study paradigm with a heart rate increases, the QT interval decreases (Kovacs, 1985).
class III antiarrhythmic agent (L-768,673) that selectively proAmong the many sources of variation in the QT interval, heart
longs the QT interval by blocking the slow activating component
rate
has a dominant role (Ahnve, 1985).
of the delayed rectifying potassium channel (/,„). Based on their
ability to dissociate the effects of heart rate on the QT interval, the
formulas received the following ranking: Covariate Adjustment
(preferred) = Van De Water's > Fridericia's > Bazett's (not
recommended). Analysis of covariance based on pretest or control
data is preferred for moderate to large studies where there are
adequate data for estimation of the slope parameter 0, the investigator does not have sufficient control over HR, or treatment
alters the association between HR and the QT interval. Conversely, for smaller studies a fixed rate adjustment formula from
the literature (such as Van de Water's or Fridericia's equations)
may be preferable since the bias from using a fixed formula is
likely to be smaller than the variance resulting from estimating fi
To account for heart rate-induced changes in the QT interval,
various correction formulas have been derived to normalize the
QT interval for heart rate (QTJ. The square root formula of
Bazett, derived from observations in 39 healthy young people, is
the most frequently used and standardizes QT to a value predicted
at a heart rate of 60 beats per minute (Bazett, 1920). The adequacy
of Bazett's formula has recently been questioned since it has been
shown to overcorrect the QT interval at fast heart rates and
undercorrect it at slow heart rates (Van de Water et at, 1989;
Ahnve, 1985; Funck-Brentano, 1992; Funck-Brentano and JailIon, 1993; Kawataki etal., 1984). Furthermore, Bazett's formula
from a small sample, c 1998 society of Tojkotogjhas frequently and inappropriately been applied to QT data deKey Words: QT; QTC; heart rate; beagle; dog; covariate analysis; rived from the dog which, unlike man, normally has respiratory
Bazett's equation; Van de Water's equation; Fridericia's equation; sinus arrhythmia and considerable variation in conscious heart
class HI antiarrhythmic; /k; /,„; L-768,673.
rate (i.e., 70 to 190 beats per minute), depending on the physical
and emotional state of the animal (Edwards, 1987; Oguchi and
Hamlin, 1993). Other correction formulas have been proposed for
1
To whom correspondence should be addressed at: Merck Research Laboanesthetized (Van de Water's) and conscious (Fridericia's; Friratories, WP45-118, West Point, PA 19486. E-mail: [email protected].
247
1096-6080/98 $25 00
Copyright O 1998 by the Society of Toxicology.
All rights of reproduction in any form reserved.
248
SPENCE ET AL.
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0.280-
•§ 0.235-
0.210-
0.185-
0.180-
0.135
60
100
78
11S
180
175
HR(bpm)
FIG. 1. Linear regression analysis of heart rate (beats per minute) vs the uncorrected QT interval (seconds) of 198 beagle dogs. Dashed lines represent 95%
confidence intervals.
dericia, 1920; Mann et aL, 1994) dogs but have not been derived
or validated in a large population-based cohort Species differences in cardiac physiology combined with the use of an inappropriate and/or insufficiently validated correction formula may
obscure drug-induced changes in the QT interval under conditions
of moderate to highly variable heart rate (Akhras and Rickards,
1981). In this paper we show one study for which the choice of
QT correction was critical to data interpretation. This study provided the impetus for our development of the analysis of covari-
ance method of QT correction. The method was first presented by
one of the authors (K. S.) in June 1997 at the Clinical Pathology
Course offered by the FDA staff college.
In addition, the use of any fixed formula based solely on
literature citations is problematic since variations in experimental protocols may have an effect on the observed association between QT and HR (Funck-Brentano and Jaillon, 1993).
This may be one reason there are multiple correction formulas
in the literature. In this regard, it is useful to show how data can
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0.225
QTcb = QT/ JRR
0.200
SO
75
100
125
150
175
200
HR(bpm)
FIG. 2.
Linear regression analysis of heart rate (beats per minute) vs rate-corrected QT interval (Bazett's) of 198 beagle dogs.
249
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS
0.3251
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50
75
100
125
150
175
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HR(bpm)
FIG. 3. Linear regression analysis of heart rate (beats per minute) vs rate-corrected QT interval (Fridericia's) of 198 beagle dogs.
Inc. (North Rose, NY). All dogs were housed in the laboratory at least 1 monm
prior to use. They ranged in age from 36 to 50 weeks of age at die initiation of the
trials and the trials were conducted over a period of approximately 1 month.
All measurements were conducted using a computerized ECG collection and
analysis system (VecgLAB, Gateway Applied Systems, Elldns Park, PA) that was
ANTEMORTEM METHODS
interfaced to a Cambridge ECG recorder (Model CM3000). Recordings were
made from leads L IL DL aVR, aVL, aVF, CV3RL, and V10 from dogs in right
ElectrocanBogram recanting from 198 sexually mature untreated beagle dogs. lateral recumbency. All dogs were naive to treatment with any investigational
compounds. Heart rates and QT intervals were calculated from 60-s rhythm strips
The beagle dogs (99 females, 99 males) were obtained from Covance Research
Products, Inc. (Kalamazoo, ML and Cumberland, VA) and Marshall Farms USA, of leads n and aVF. Values reported are from lead U and represent the mean of die
be used to assess the appropriateness of a particular rate correction formula under the actual experimental conditions of a
given study.
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QTcv = QT - 0 0871(60/ HK) -1]
0.175
SO
75
100
125
150
175
200
HR(bpm)
FIG. 4. Linear regression analysis of heart rate (beats per minute) vs rate-corrected QT interval (Van de Water's) of 198 beagle dogs.
250
SPENCE ET AL.
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slope = -0.2839 ±0.01752
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4.7
48
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togHR
FIG. 5. Linear regression analysis of the log of heart rate (beats per minute) vs the log of the uncorrected QT interval of 198 beagle dogs. The estimated
slope (0) attained was -0.2839.
16-day intravenous toxicity study with L-768,673. The beagle dogs used
in this study were approximately 46-54 weeks of age and weighed approximately 5.4 to 15.6 kg at the initiation of the study. Each dog was identified by
a tattoo and housed in an individual steel pen in an environmentally controlled
room. The dogs were examined daily for adverse physical signs. Daily food
consumption was measured 3 or 4 days a week. Body weights were recorded
pretest and once a week during the study.
L-768,673 is an experimental class III antiarrhythmic specific for the slow
activation component of the delayed rectifying channel (l^. In pharmacology
studies of conscious dogs, at relatively fixed heart rates, intravenous admin-
interval calculations for each complex that was suitable for analysis (generally at
least 90% of the complexes) during the 60-s strip (for a heart rate of 100 beats/min,
this would be approximately 95 complexes). The coefficient of variation for
computer derived QT values was 12.7%. All electronic analyses were confirmed
manually by a technician calculating intervals from representative complexes from
the hardcopy tracing (50 mm/s; I cm/mV) produced by the Cambridge recorder.
Values that did not have an acceptable number of complexes suitable for analysis
or had an unacceptable difference between manual and electronic analyses were
not included in the summary. All dogs included in the analysis were considered to
have healthy ECGs.
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\odQTca) = \ogtQT) - Oj283?(log(//«) - log(WRm)]
0.150
50
75
100
125
150
175
200
HR(bpm)
FIG. 6.
Linear regression analysis of heart rate (beats per minute) vs the rate-corrected QT interval (covanate adjustment) of 198 beagle dogs.
251
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS
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o.^
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•
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ff-^^^o
o •
•
0165-
0150-
IX
150
170
190
Hurt H i * (bpa)
FIG. 7. Linear regression analysis of the pretest heart rate (beats per minute) and vs the uncorrected QT interval taken from the 16-day intravenous toxicity
study of L-768,673 in beagle dogs.
istration of 0.1 mg/kg of L-768,673 is associated with up to a 15% prolongation of QT interval. L-768,673 was prepared as a microemulsion in Intralipid
10% (lipid weight/volume, manufactured by Pharmacia Inc., Columbus, OH)
with 0.5% ethanol. Doses of 0.025, 0.05, 0.10, and 0.20 mg/kg/day of
L-768,673 were administered to groups of four dogs per sex, once daily for 15
days at a volume of 2 ml/kg. A control group consisting of four dogs per sex
was similarly dosed with the vehicle (Intralipid 10% with 0.5 ethanol). All
daily doses were administered over an approximate 20-min interval into the
cephalic leg vein using 22-gauge catheters and infusion pumps. The injection
sites were rotated daily between the left and right front legs. At the daily
termination of dosing the catheters were flushed with 0.5 ml of 0.9% saline and
removed.
Electrocardiograms were recorded at pretest and at 10 min following the
completion of the last dose (Drug Day 16). Electrocardiograms were recorded
while each dog was held in right lateral recumbancy at paper speeds of at 50 and
100 mm/s. Leads I, H, m AVR, AVL, AVF, V10, and CV.RL were utilized. The
0320
0J05
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0275-
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5
0.245-
0230-
0215-
0200
110
130
150
170
190
Hurt Hit> (bpa)
FIG. 8. Linear regression analysis of the pretest heart rate (beats per minute) and vs the rate corrected QT interval (Bazett's) taken from the 16-day
intravenous toxicity study of L-768,673 in beagle dogs.
252
SPENCE ET AL.
0285 -i
0270-
0255-
-S 0240
I
0225
0210-
0195-
0.1B0
110
170
190
FIG. 9. Linear regression analysis of the pretest heart rate (beats per minute) and vs the rate-corrected QT interval (Fndericia's) taken from the 16-day
intravenous toxicity study of L-768,673 in beagle dogs.
heart rate, PR, QRS, and QT interval were measured from lead II. The ECGs were
independently read and interpreted by four individuals without prior knowledge of
the treatment regime and the consensus values were used in all analyses.
Statistical methods. The QT interval (in seconds) was adjusted for heart
rate (HR, in beats per minute) using the equations
Bazett's (QTcb = QT/J60/HR
or
QTA =
Fridericia's (QTa = QT/^j60/HR
or
, and
= QT - 0.087*[(60/?/«) -
Van de Water's
Analysis of covariance (Snedecor and Cochran, 1989) is often used to adjust
a continuous variable such as QT for a covanate, in this case HR. First, the
association of QT with HR (in pretest or control data) is analyzed by linear
025002«02«
0235
0230-
°225
0220
021502100205
0200-
110
IX
19)
170
190
Hoot iato (bpc
FIG. 10. Linear regression analysis of the pretest heart rate (beats per minute) and vs the rate-corrected QT interval (Van de Water's) taken from the 16-day
intravenous toxicity study of L-768,673 in beagle dogs.
253
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS
021 <H
0.195-
0.165-
aiso110
150
130
Hurt R i b
170
190
(kpa)
FIG. 11. Linear regression analysis of the pretest heart rate (beats per minute) and vs the rate-corrected QT interval (covariate adjustment) taken from the
16-day intravenous toxicity study of L-768,673 in beagle dogs.
regression in the logarithmic scale \}og(QT) = a + 01og(///?)] to estimate the
slope parameter ft This /3 measures the degree of rate correction; for example,
Fridericia's equation sets /3 = - 1 / 3 , while Bazett's equation uses /3 = -1/2.
Second, given /3 the heart rate-adjusted QT interval is then determined from the
equation log (QTJ = log (QT - P*[\og(HR) - \og(HRJ], where HRm is the
reference heart rate. QTa (in seconds) is obtained by the inverse log function.
HRm has no effect on statistical analysis, so any convenient value can be used.
Bazett's and Fridencia's equation both set HRm = 60 bpm. When /3 has been
estimated from a single study, one may wish to choose a reference heart rate
HRm other than 60 bpm. For example, the geometric mean heart rate for the
large population cohort of 198 untreated dogs was 114 bpm, and if we use HRm
= 114 then the geometric mean of the adjusted QT over all groups will be the
same as the geometric mean of the unadjusted QT. In the 16-day intravenous
toxicity study the geometric mean at pretest was 140 bpm. If data are to be
compared across multiple studies, it is important to choose the same HRm value
for all studies.
The results of all residual analyses showed Guassian distributions and no
evidence of clusters at low or high heart rates.
A relatively precise estimate of £ was determined under one set of conditions using analysis of covariance of the data from 198 untreated dogs (see
above). However, the magnitude of the association between QT and HR may
vary depending on the experimental conditions, measurement protocol, the
stock of dogs being studied, the sample size, and other factors. To test the
utility of covariate adjustment under a typical toxicity study paradigm, ECGs
taken from a toxicity study conducted with a drug known to lengthen the QT
interval (L-768,673, see above) were retrospectively analyzed by covariate
adjustment. Cardioactive drugs like L-768,673 may have effects on HR or QT
or the nature of the association between HR and QT. Such drug-related effects
could result in a biased estimate for ft leading to an inappropriate correction
formula for QT and misleading results. To eliminate this possibility Pp^ was
estimated using the pretest data only and used to correct QT measurements
obtained after treatment by the formula log (QT^) = logQ7" — /3pre*[log(///?)
An idea] correction formula for QT should eliminate all systematic association between the corrected QT value and HR. This can be evaluated visually
by a graph of corrected QT against HR. A systematic pattern of decreasing or
increasing corrected QT with HR indicates undercorrection or overcorrection,
respectively. The strength of association between heart rate and corrected or
uncorrected QT is summarized in this paper with the Pearson correlation
coefficient (Snedecor and Cochran, 1989) and two sided p value. If a correction
formula eliminates all association between QT and heart rate, then the correlation between corrected QT and HR should be zero apart from sampling
variation. In fact, if fi is estimated from a data set by analysis of covariance,
then the correlation between the rate corrected QT interval and heart rate for
that data set is guaranteed to be zero when analyzed in the logarithmic scale.
Along with the correlation coefficient, each figure includes a regression line
(Snedecor and Cochran, 1989) of corrected QT predicted from HR. The
regression line is horizontal (has zero slope) when the correlation is zero. Since
data derived from the analysis of covariance method were plotted in the
arithmetic scale, as opposed to the logarithmic scale, minor deviations from
zero are expected and reflected in the correlation coefficient, r. The linear
regression results from the correction formulas utilized with the large population cohort of beagle dogs (99 females, 99 males) were analyzed for residuals
(data not presented) by utilizing GraphPad Prizm software (Motulsky, 1995).
- \og(HRJ].
Treatment effects were analyzed using trend contrasts in a one-way analysis
of variance (Tukey el al, 1985), using arithmetic dose scores. If statistically
significant (p :£ 0.05) through the top dose, the trend analysis was repeated
with the highest dose group deleted. Dose groups were deleted by adjusting the
vector of contrast coefficients, so all analyses used the same mean square error
TABLE 1
Mean Heart Rates Following 16 Days
of Daily Administration of L-768,673
Average heart rate
Treatment group
(mg/kg/day)
Pretest
Drug Day 16
p value
Control
0.025
0.05
0.10
0.20
112
141
138
144
126
144
112
133
0.465
136
113
0.006
254
SPENCE ET AL.
TABLE 2
A Comparison of Corrected QT Values Following 16 Days of Daily Administration of L-768,673
Treatment group (mg/kg/day)
Bazett's ( Q T ^
Pretest
Drug Day 16
p value
Fridericia's (QTrf)
Pretest
Drug Day 16
p value
Van de Water's (QTCV)
Pretest
Drug Day 16
p value
Analysis of covariance (QT clv )
Pretest
Drug Day 16
p value
0.025
0.050
0.255
0.283
0.275
0.291
0.254
0.283
0.257
0.282
0.263
0.295NS
0.424
0.229
0.246
0.240
0.251
0.224
0.245
0.231
0.247NS
0.944
0.230
0.266s
0.043
0.225
0.235
0.230
0.238
0 220
0.233
0.227
0.237NS
0.858
0.223
0.255s
0.005
0.178
0.185
0.181
0.188
0.172
0.184
0.180
0.188NS
0.830
0.174
0.206s
0.004
term. Successive analyses were performed in this way until p > 0.05 was
obtained to define the largest dose not showing a statistically significant trend.
RESULTS
Comparative Evaluation of Formulas Used to Derive the
Heart Rate-Corrected QT Interval in 198 Dogs
No significant {p > 0.05) differences in QT, HR, or the
association between QT and HR were noted between male and
0.100
0.200
Control
female dogs (data not shown). Therefore, data from male and
female dogs were combined for all subsequent analyses.
Figure 1 indicates strong negative association between uncorrected QT and HR, (r = -0.634, p < 0.0001). Note also
that dogs varied greatly in pretest heart rate, so that interpretation of QT is virtually impossible without an appropriate
correction for HR. After correction, the correlation between
QT and HR should be near zero (i.e., horizontal line). Figures
2-4 display the association between corrected QT and heart
0.38
0.35
0.34
0.33
0.32
0.31
0.30NS
P-0.424
0.280.280.27
0.280.250^4
0MKD
0.025 MKD
0.05 MKD
0.1 MKD
0.2 MXD
Dose
FIG. 12. Box and whisker graph of the rate corrected QT interval (Bazett's) assessed following 16 days of intravenous administration of L-768,673 to Beagle
dogs. The box extends from the 25th to 75di percentiles, the whiskers reflect the range of values and the horizontal lines indicate the median values (50th
percentile) for each dose group.
255
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS
0.310300.290.280.27S
P-0.043
028MS
P-0.944
0.250.240.230.220.210.20
OIlKD
0025 MKD
0.05 M<D
0.1 MKD
0.2 MKD
Dose
FIG. 13. Box and whisker graph of the rate corrected QT interval (Fridericia's) assessed following 16 days of intravenous administration of L-768,673 to
beagle dogs.
rate using Bazett's, Fridericia's, and Van de Water's equations,
respectively. Bazett's formula overcorrects these data, so the
final association between QT cb and HR is significantly positive
(r = 0.527, p < 0.0001). Fridericia's formula improves on the
dissociation of the QTcf from heart rate, so the correlation
between QTcf and HR is weak but still significantly positive
(r = 0.130, p = 0.0151). Of all three correction formulas from
the literature, Van de Water's was most effective at reducing
the correlation for these data, with a slight nonsignificant
negative correlation between QTCV and HR (r = -0.094, p =
0.079). The correction formula based on analysis of covariance
fitted to these data (Figs. 5 and 6) nearly eliminates the correlation between QTca and HR observed for these dogs (r =
-0.015, p = 0.777).
0.29-I
0.28-
0.27-
0.28-
s
FM).005
0.25-
0.24-
0.23-
022
0.21-
0.20
0M<D
0.025 MKD
0.05 MKD
0.1 MKD
0.2 MKD
Dose
FIG. 14. Box and whisker graph of the rate corrected QT interval (Van de Water's) assessed following 16 days of intravenous administration of L-768,673
to beagle dogs.
256
SPENCE ET AL.
0.24
023
022
0.21-
s
P»O.0O4
020
a °-190.18
0.17
0.180.15
OMKD
0.025 MKD
0.05 MKD
0.1 MKD
02 MKD
Dots
FIG. 15. Box and whisker graph of the rate corrected QT interval (covariate adjustment) assessed following 16 days of intravenous administration of
L-768,673 to beagle dogs.
16-Day Intravenous Toxicity Study with L-768,673
No consistent or significant {p > 0.05) differences in QT or
HR were noted between male and female dogs at either pretest
or follow-up. Moreover, males and females did not appear to
differ with regard to the associations among QT, HR, and dose
of drug (data not shown). Therefore, data from male and
female dogs were combined for all subsequent analyses.
Figure 7 shows a strong significant negative association
between uncorrected QT and HR at pretest (r = —0.561, p =
0.002). As noted in the previous study, the dogs varied greatly
in pretest heart rate, so that interpretation of QT is virtually
impossible without an appropriate correction for HR. Figures
8-10 display the association between corrected QT and heart
rate at pretest using Bazett's, Fridericia's and Van de Water's
equations, respectively. For these data, at least two of the
published equations overcorrect the QT interval, so the final
association between the rate correct QT interval and HR is
positive. The positive correlation between HR and QT cb (r =
0.713) and between QTcf and HR (r = 0.438) deviated significantly from a zero slope (p < 0.01). For these data, Van de
Water's appeared to most effective at reducing the correlation
for these data, with a nonsignificant positive correlation between QTCV and HR (r = 0.202, p = 0.211). The correction
formula based on analysis of covariance fitted to these data
(Fig. 11) eliminates the correlation between QTca and HR
observed for these dogs (r = -0.016, p = 0.9221).
Following 16 days of intravenous administration of L-768,673
there were significant decreases (p = 0.006) in heart rate at a dose
of 0.2 mg/kg/day (Table 1), relative to controls. There were no
significant {p > 0.05) effects on heart rate at doses £ 0.10
mg/kg/day. Since a decrease in HR is expected to be associated
with an increase in QT, adjustment for HR is necessary to assess
whether drug is associated with an effect on QT apart from HR.
Interpretation would be problematic at best for QT^, and QTcf,
since these parameters are known from the pretest data to be
associated with HR (see Figs. 8 and 9), whereas QTCV and QT^
are not (Figs. 10 and 11).
As expected, based on the pharmacological effects of l^
blockade, there were significant increases in QTca {p = 0.004)
and QTCV (p = 0.005) on Drug Day 16 at 0.2 mg/kg/day (Table
2 and Figs. 14 and 15), relative to concurrent controls. Fridericia's formula also gave similar results; however, the level of
significance was approximately 10-fold less {p = 0.043) than
QT^ or QTCV (Fig. 13). No drug-related effects on the rate
corrected QT interval were evident when QT was corrected
using Bazett's formula (Table 2 and Fig. 12). The results
highlight the importance of appropriate formula selection in
interpreting potential drug-related effects on the QT interval
and illustrate the limitations of using Bazett's formula for these
data.
DISCUSSION
Based on linear regression analysis of individual heart rate
vs QT cb , QTcf, and QT^ from the large population cohort, it is
clear that, of the published formulas examined, Van De Water's best dissociated the effects of heart rate on the QT
interval. However, the analysis of covariance method obtained the
optimal correction, with nearly complete dissociation of the
rate adjusted QT interval from heart rate. The formulas were
257
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS
TABLE 3
A Comparison of the Mean Unadjusted and Corrected QT Values for a Given Range of Heart Rates in the Beagle Dog
Mean rate corrected QT values
Range of HR
(bpm)
Mean
HR
QT
unadjusted
Bazett's
Fridericia's
Van de Water's
Anal-Covar.
Low-75
76-105
106-135
136-165
166-top
65
92
120
148
174
0.231
0.206
0.196
0.181
0.172
0.239
0.255
0.276
0.283
0.293
0.236
0.237
0.246
0.244
0.246
0.237
0.236
0.239
0.232
0.229
0.236
0.232
0.238
0.233
0.233
ranked based on the slope of the regression line for the rate
corrected QT interval vs heart rate [ Q T ^ = QTCV < QTcf <
QT cb ], with Q T ^ or QTCV being the most effective formulas.
Functionally the impact of using these formulas is best described by Table 3 which was derived from die ECG measurements taken from the large cohort of beagle dogs (99 males and
99 females). In Table 3, die heart rates have been subdivided
into five ranges of 30-beat intervals showing die mean HR, the
mean unadjusted QT, and die mean corrected QT values derived by die various formulas. As expected, the average unadjusted QT interval decreases steadily widi an increasing HR.
Since the correction formulas are designed to eliminate the
effect of HR on QT, die adjusted QT values should be roughly
equivalent regardless of HR. Bazett's equation shows a steady
increase in the rate corrected QT widi increasing HR (indicating overcorrection at high HR). Fridericia's equation also
shows some overcorrection of QT, aldiough not as profound as
Bazett's. At die highest HRs, Van de Water's adjustment
shows a very slight decrease in die rate correct QT diat is not
considered to be biologically significant given die small magnitude of the difference. The analysis of covariance correction
is nearly constant diroughout all ranges of HR. Table 3 clearly
shows diat die analysis of covariance mediod can be used to
select an effective adjustment formula in an objective fashion.
The estimated effects of L-768,673 (a class III antiarrhythmic) varied substantially depending on die method of QT
adjustment. On Drug Day 16, rate corrected QT values derived
by Bazett's equation were equivocal across all drug-treated
groups. However, rate-corrected QT values derived by Fridericia's, Van De Water's, and analysis of covariance were significantly (p < 0.05) increased at 0.2 mg/kg/day (8.0, 8.7, and
11.5%, respectively) when compared to concurrent controls.
The sensitivity of each formula for detecting a drug-related
effect can be ranked based on die lowest p value associated
widi each formula [QT^ < QTCV < QT rf ], with QTM having
the most significant p value. These results highlight die importance of selecting die optimal correction mediod for interpreting drug-induced changes on the QT interval, especially for
small group sizes diat are typically used in toxicity studies.
Use of a covariance-adjusted QT has die major advantage
diat it is derived from data on die same dogs used for assessment of treatment effects under identical experimental condi-
tions and measurement protocols. The covariance-adjusted
mediod also allows a more complete description of treatment
effects tiian could be obtained by separate analyses of HR and
QT. For example, administration of L-768,673 at 0.20 mg/kg/
day was associated widi a decrease in HR and an increase in
QT diat was larger tiian would be expected solely from die
observed decrease in HR. Aldiough treatment was associated
with effects on botii HR and QT, tiiere was no statistically
significant evidence mat die association between HR and QT
observed at pretest was altered by treatment. Analysis of covariance based on pretest or control data is preferred for
moderate to large studies where diere are adequate data for
estimation of die slope parameter /3, die investigator does not
have sufficient control over HR, or treatment alters the association between HR and die QT interval. Conversely, for
smaller studies a fixed rate adjustment formula from the literature may be preferable since die bias from a fixed formula
obtained under different experimental conditions is likely to be
smaller tiian die variance resulting from estimating /3 from a
small sample. In light of tiiese considerations, we suggest diat
Van de Water's or Fridericia's equations may be used judiciously as a first pass analysis of the QT interval for compounds diat do not affect HR and do not affect die association
between HR and QT. Neitiier formula is particularly complex,
and they yield quite similar adjusted QT except when HR is
quite high, in which case the Van de Water formula gives a
smaller adjusted QT value. The covariance mediod may be
used to confirm die effectiveness of a QT adjustment formula,
or it can be used as die primary mediod to adjust die QT
interval. When the compound being tested is known to have
cardioactive properties on both QT and HR, die covariance
mediod is necessary to determine whedier treatment has altered
die association between QT and HR.
The wide variety of adjustment formulas in die literature
attest diat die association between QT and HR can be greatly
affected by species, strain, reader, and environment. Ideally,
measurement of die QT interval at fixed heart rates is the most
reliable mediod for assessing potential drug-related effects on
die QT interval. However, under die experimental paradigm in
which toxicology studies are conducted, tiiis practice is impossible. Any correction formula is likely to introduce some
inherent error based on die shortcoming of applying a matiie-
258
SPENCE ET AL.
matical equation to a biological association. The inherent limitations of a formula can be further confounded by the large
variability of small data sets. Despite these important limitations, the corrected QT interval remains useful in assessing the
effects of drugs on the duration of repolarization.
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