The Heart Rate-Corrected QT Interval of Conscious Beagle Dogs: A Formula Based on Analysis of Covariance

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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 depolariza-
Dogs: 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

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   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; Gold-
compared 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 pro-
the 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 in-
QT 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 pro-
                                                                     Among the many sources of variation in the QT interval, heart
longs the QT interval by blocking the slow activating component
of the delayed rectifying potassium channel (/,„). Based on their    rate has a dominant role (Ahnve, 1985).
ability to dissociate the effects of heart rate on the QT interval, the     To account for heart rate-induced changes in the QT interval,
formulas received the following ranking: Covariate Adjustment            various correction formulas have been derived to normalize the
(preferred) = Van De Water's > Fridericia's > Bazett's (not              QT interval for heart rate (QTJ. The square root formula of
recommended). Analysis of covariance based on pretest or control         Bazett, derived from observations in 39 healthy young people, is
data is preferred for moderate to large studies where there are          the most frequently used and standardizes QT to a value predicted
adequate data for estimation of the slope parameter 0, the inves-
                                                                         at a heart rate of 60 beats per minute (Bazett, 1920). The adequacy
tigator does not have sufficient control over HR, or treatment
alters the association between HR and the QT interval. Con-              of Bazett's formula has recently been questioned since it has been
versely, for smaller studies a fixed rate adjustment formula from        shown to overcorrect the QT interval at fast heart rates and
the literature (such as Van de Water's or Fridericia's equations)        undercorrect it at slow heart rates (Van de Water et at, 1989;
may be preferable since the bias from using a fixed formula is           Ahnve, 1985; Funck-Brentano, 1992; Funck-Brentano and Jail-
likely to be smaller than the variance resulting from estimating fi      Ion, 1993; Kawataki etal., 1984). Furthermore, Bazett's formula
from a small sample, c 1998 society of Tojkotogj-                        has frequently and inappropriately been applied to QT data de-
   Key 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
   1                                                                     Hamlin, 1993). Other correction formulas have been proposed for
     To whom correspondence should be addressed at: Merck Research Labo-
ratories, WP45-118, West Point, PA 19486. E-mail: stan_spence@merek.com. anesthetized (Van de Water's) and conscious (Fridericia's; Fri-

                                                                      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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                               0.135
                                         60            78              100            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                    ance method of QT correction. The method was first presented by
or validated in a large population-based cohort Species differ-                    one of the authors (K. S.) in June 1997 at the Clinical Pathology
ences in cardiac physiology combined with the use of an inap-                      Course offered by the FDA staff college.
propriate and/or insufficiently validated correction formula may                      In addition, the use of any fixed formula based solely on
obscure drug-induced changes in the QT interval under conditions                   literature citations is problematic since variations in experi-
of moderate to highly variable heart rate (Akhras and Rickards,                    mental protocols may have an effect on the observed associa-
1981). In this paper we show one study for which the choice of                     tion between QT and HR (Funck-Brentano and Jaillon, 1993).
QT correction was critical to data interpretation. This study pro-                 This may be one reason there are multiple correction formulas
vided the impetus for our development of the analysis of covari-                   in the literature. In this regard, it is useful to show how data can

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                                         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.
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS                                                            249

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                             0.175
                                          50                75                   100      125                    150            175           200
                                                                                       HR(bpm)

             FIG. 3. Linear regression analysis of heart rate (beats per minute) vs rate-corrected QT interval (Fridericia's) of 198 beagle dogs.

be used to assess the appropriateness of a particular rate cor-              Inc. (North Rose, NY). All dogs were housed in the laboratory at least 1 monm
rection formula under the actual experimental conditions of a                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.
given study.
                                                                                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
The beagle dogs (99 females, 99 males) were obtained from Covance Research   compounds. Heart rates and QT intervals were calculated from 60-s rhythm strips
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

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                                                                                                           QTcv = QT - 0 0871(60/ HK) -1]

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                                                                                       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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                                         37   3.8   39   4.0        41    4.2       43        4.4       4.5       4.8   4.7   48    49      5.0         5.1   S2   53
                                                                                                    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.

interval calculations for each complex that was suitable for analysis (generally at                        16-day intravenous toxicity study with L-768,673. The beagle dogs used
least 90% of the complexes) during the 60-s strip (for a heart rate of 100 beats/min,                   in this study were approximately 46-54 weeks of age and weighed approxi-
this would be approximately 95 complexes). The coefficient of variation for                             mately 5.4 to 15.6 kg at the initiation of the study. Each dog was identified by
computer derived QT values was 12.7%. All electronic analyses were confirmed                            a tattoo and housed in an individual steel pen in an environmentally controlled
manually by a technician calculating intervals from representative complexes from                       room. The dogs were examined daily for adverse physical signs. Daily food
the hardcopy tracing (50 mm/s; I cm/mV) produced by the Cambridge recorder.                             consumption was measured 3 or 4 days a week. Body weights were recorded
Values that did not have an acceptable number of complexes suitable for analysis                        pretest and once a week during the study.
or had an unacceptable difference between manual and electronic analyses were                              L-768,673 is an experimental class III antiarrhythmic specific for the slow
not included in the summary. All dogs included in the analysis were considered to                       activation component of the delayed rectifying channel (l^. In pharmacology
have healthy ECGs.                                                                                      studies of conscious dogs, at relatively fixed heart rates, intravenous admin-

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                                  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.
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS                                                                         251

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                                                                                             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% prolonga-             cephalic leg vein using 22-gauge catheters and infusion pumps. The injection
tion of QT interval. L-768,673 was prepared as a microemulsion in Intralipid             sites were rotated daily between the left and right front legs. At the daily
10% (lipid weight/volume, manufactured by Pharmacia Inc., Columbus, OH)                  termination of dosing the catheters were flushed with 0.5 ml of 0.9% saline and
with 0.5% ethanol. Doses of 0.025, 0.05, 0.10, and 0.20 mg/kg/day of                     removed.
L-768,673 were administered to groups of four dogs per sex, once daily for 15               Electrocardiograms were recorded at pretest and at 10 min following the
days at a volume of 2 ml/kg. A control group consisting of four dogs per sex             completion of the last dose (Drug Day 16). Electrocardiograms were recorded
was similarly dosed with the vehicle (Intralipid 10% with 0.5 ethanol). All              while each dog was held in right lateral recumbancy at paper speeds of at 50 and
daily doses were administered over an approximate 20-min interval into the               100 mm/s. Leads I, H, m AVR, AVL, AVF, V10, and CV.RL were utilized. The

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                                                                               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.

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   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                   Fridericia's (QTa = QT/^j60/HR     or                 , and
independently read and interpreted by four individuals without prior knowledge of
the treatment regime and the consensus values were used in all analyses.                            Van de Water's         = QT - 0.087*[(60/?/«) -
   Statistical methods. The QT interval (in seconds) was adjusted for heart
rate (HR, in beats per minute) using the equations
                                                                                        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
           Bazett's (QTcb = QT/J60/HR        or   QTA =                              association of QT with HR (in pretest or control data) is analyzed by linear

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                                                                                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.
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS                                                                     253

                                021
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)

                                                           Control                   0.025             0.050                 0.100           0.200

         Bazett's ( Q T ^
          Pretest                                           0.255                    0.275             0.254                0.257           0.263
          Drug Day 16                                       0.283                    0.291             0.283                0.282           0.295NS
          p value                                                                                                                           0.424
         Fridericia's (QTrf)
          Pretest                                           0.229                    0.240             0.224                0.231           0.230
          Drug Day 16                                       0.246                    0.251             0.245                0.247NS         0.266s
          p value                                                                                                           0.944           0.043
         Van de Water's (QTCV)
          Pretest                                           0.225                    0.230             0 220                0.227           0.223
          Drug Day 16                                       0.235                    0.238             0.233                0.237NS         0.255s
          p value                                                                                                           0.858           0.005
         Analysis of covariance (QT clv )

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          Pretest                                           0.178                    0.181             0.172                0.180           0.174
          Drug Day 16                                       0.185                    0.188             0.184                0.188NS         0.206s
          p value                                                                                                           0.830           0.004

term. Successive analyses were performed in this way until p > 0.05 was                 female dogs (data not shown). Therefore, data from male and
obtained to define the largest dose not showing a statistically significant trend.      female dogs were combined for all subsequent analyses.
                                                                                           Figure 1 indicates strong negative association between un-
                                  RESULTS                                               corrected QT and HR, (r = -0.634, p < 0.0001). Note also
                                                                                        that dogs varied greatly in pretest heart rate, so that interpre-
Comparative Evaluation of Formulas Used to Derive the                                   tation of QT is virtually impossible without an appropriate
  Heart Rate-Corrected QT Interval in 198 Dogs
                                                                                        correction for HR. After correction, the correlation between
   No significant {p > 0.05) differences in QT, HR, or the                              QT and HR should be near zero (i.e., horizontal line). Figures
association between QT and HR were noted between male and                               2-4 display the association between corrected QT and heart

                                 0.38

                                 0.35

                                 0.34

                                 0.33

                                 0.32

                                 0.31

                                 0.30-
                                                                                                                            NS
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                                 0.28-

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                                0^4
                                               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.
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS                                                            255

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256                                                               SPENCE ET AL.

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                             0.15                                                                           02 MKD
                                          OMKD           0.025 MKD         0.05 MKD         0.1 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                            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
   No consistent or significant {p > 0.05) differences in QT or
                                                                            whether drug is associated with an effect on QT apart from HR.
HR were noted between male and female dogs at either pretest
                                                                            Interpretation would be problematic at best for QT^, and QTcf,
or follow-up. Moreover, males and females did not appear to
                                                                            since these parameters are known from the pretest data to be
differ with regard to the associations among QT, HR, and dose
                                                                            associated with HR (see Figs. 8 and 9), whereas QTCV and QT^
of drug (data not shown). Therefore, data from male and
                                                                            are not (Figs. 10 and 11).
female dogs were combined for all subsequent analyses.
                                                                               As expected, based on the pharmacological effects of l^
   Figure 7 shows a strong significant negative association
                                                                            blockade, there were significant increases in QTca {p = 0.004)
between uncorrected QT and HR at pretest (r = —0.561, p =
                                                                            and QTCV (p = 0.005) on Drug Day 16 at 0.2 mg/kg/day (Table
0.002). As noted in the previous study, the dogs varied greatly
                                                                            2 and Figs. 14 and 15), relative to concurrent controls. Frideri-
in pretest heart rate, so that interpretation of QT is virtually
                                                                            cia's formula also gave similar results; however, the level of
impossible without an appropriate correction for HR. Figures
                                                                            significance was approximately 10-fold less {p = 0.043) than
8-10 display the association between corrected QT and heart
                                                                            QT^ or QTCV (Fig. 13). No drug-related effects on the rate
rate at pretest using Bazett's, Fridericia's and Van de Water's
                                                                            corrected QT interval were evident when QT was corrected
equations, respectively. For these data, at least two of the
                                                                            using Bazett's formula (Table 2 and Fig. 12). The results
published equations overcorrect the QT interval, so the final
                                                                            highlight the importance of appropriate formula selection in
association between the rate correct QT interval and HR is
                                                                            interpreting potential drug-related effects on the QT interval
positive. The positive correlation between HR and QT cb (r =
                                                                            and illustrate the limitations of using Bazett's formula for these
0.713) and between QTcf and HR (r = 0.438) deviated signif-
                                                                            data.
icantly 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 be-                                          DISCUSSION
tween QTCV and HR (r = 0.202, p = 0.211). The correction
formula based on analysis of covariance fitted to these data                   Based on linear regression analysis of individual heart rate
(Fig. 11) eliminates the correlation between QTca and HR                    vs QT cb , QTcf, and QT^ from the large population cohort, it is
observed for these dogs (r = -0.016, p = 0.9221).                           clear that, of the published formulas examined, Van De Wa-
   Following 16 days of intravenous administration of L-768,673             ter's best dissociated the effects of heart rate on the QT
there were significant decreases (p = 0.006) in heart rate at a dose        interval. However, the analysis of covariance method obtained the
of 0.2 mg/kg/day (Table 1), relative to controls. There were no             optimal correction, with nearly complete dissociation of the
significant {p > 0.05) effects on heart rate at doses £ 0.10                rate adjusted QT interval from heart rate. The formulas were
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS                                              257

                                                        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           Mean               QT
   (bpm)               HR             unadjusted          Bazett's            Fridericia's           Van de Water's       Anal-Covar.

  Low-75                65              0.231              0.239                 0.236                    0.237              0.236
  76-105                92              0.206              0.255                 0.237                    0.236              0.232
  106-135              120              0.196              0.276                 0.246                    0.239              0.238
  136-165              148              0.181              0.283                 0.244                    0.232              0.233
  166-top              174              0.172              0.293                 0.246                    0.229              0.233

 ranked based on the slope of the regression line for the rate       tions and measurement protocols. The covariance-adjusted
 corrected QT interval vs heart rate [ Q T ^ = QTCV < QTcf <         mediod also allows a more complete description of treatment
 QT cb ], with Q T ^ or QTCV being the most effective formulas.      effects tiian could be obtained by separate analyses of HR and
 Functionally the impact of using these formulas is best de-         QT. For example, administration of L-768,673 at 0.20 mg/kg/
 scribed by Table 3 which was derived from die ECG measure-          day was associated widi a decrease in HR and an increase in

                                                                                                                                        Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015
 ments taken from the large cohort of beagle dogs (99 males and      QT diat was larger tiian would be expected solely from die
99 females). In Table 3, die heart rates have been subdivided        observed decrease in HR. Aldiough treatment was associated
 into five ranges of 30-beat intervals showing die mean HR, the      with effects on botii HR and QT, tiiere was no statistically
 mean unadjusted QT, and die mean corrected QT values de-            significant evidence mat die association between HR and QT
rived by die various formulas. As expected, the average unad-        observed at pretest was altered by treatment. Analysis of co-
justed QT interval decreases steadily widi an increasing HR.         variance based on pretest or control data is preferred for
Since the correction formulas are designed to eliminate the          moderate to large studies where diere are adequate data for
effect of HR on QT, die adjusted QT values should be roughly         estimation of die slope parameter /3, die investigator does not
equivalent regardless of HR. Bazett's equation shows a steady        have sufficient control over HR, or treatment alters the asso-
increase in the rate corrected QT widi increasing HR (indicat-       ciation between HR and die QT interval. Conversely, for
ing overcorrection at high HR). Fridericia's equation also           smaller studies a fixed rate adjustment formula from the liter-
shows some overcorrection of QT, aldiough not as profound as         ature may be preferable since die bias from a fixed formula
Bazett's. At die highest HRs, Van de Water's adjustment              obtained under different experimental conditions is likely to be
shows a very slight decrease in die rate correct QT diat is not      smaller tiian die variance resulting from estimating /3 from a
considered to be biologically significant given die small mag-       small sample. In light of tiiese considerations, we suggest diat
nitude of the difference. The analysis of covariance correction      Van de Water's or Fridericia's equations may be used judi-
is nearly constant diroughout all ranges of HR. Table 3 clearly      ciously as a first pass analysis of the QT interval for com-
shows diat die analysis of covariance mediod can be used to          pounds diat do not affect HR and do not affect die association
select an effective adjustment formula in an objective fashion.      between HR and QT. Neitiier formula is particularly complex,
    The estimated effects of L-768,673 (a class III antiarrhyth-     and they yield quite similar adjusted QT except when HR is
mic) varied substantially depending on die method of QT              quite high, in which case the Van de Water formula gives a
adjustment. On Drug Day 16, rate corrected QT values derived         smaller adjusted QT value. The covariance mediod may be
by Bazett's equation were equivocal across all drug-treated          used to confirm die effectiveness of a QT adjustment formula,
groups. However, rate-corrected QT values derived by Frideri-        or it can be used as die primary mediod to adjust die QT
cia's, Van De Water's, and analysis of covariance were sig-          interval. When the compound being tested is known to have
nificantly (p < 0.05) increased at 0.2 mg/kg/day (8.0, 8.7, and      cardioactive properties on both QT and HR, die covariance
11.5%, respectively) when compared to concurrent controls.           mediod is necessary to determine whedier treatment has altered
The sensitivity of each formula for detecting a drug-related         die association between QT and HR.
effect can be ranked based on die lowest p value associated             The wide variety of adjustment formulas in die literature
widi each formula [QT^ < QTCV < QT rf ], with QTM having             attest diat die association between QT and HR can be greatly
the most significant p value. These results highlight die impor-     affected by species, strain, reader, and environment. Ideally,
tance of selecting die optimal correction mediod for interpret-      measurement of die QT interval at fixed heart rates is the most
ing drug-induced changes on the QT interval, especially for          reliable mediod for assessing potential drug-related effects on
small group sizes diat are typically used in toxicity studies.       die QT interval. However, under die experimental paradigm in
   Use of a covariance-adjusted QT has die major advantage           which toxicology studies are conducted, tiiis practice is impos-
diat it is derived from data on die same dogs used for assess-       sible. Any correction formula is likely to introduce some
ment of treatment effects under identical experimental condi-        inherent error based on die shortcoming of applying a matiie-
258                                                                     SPENCE ET AL.

matical equation to a biological association. The inherent lim-                      Cellular, molecular and clinical implications. Trends Cardiovasc. Med. 3,
itations of a formula can be further confounded by the large                         149-159.
variability of small data sets. Despite these important limita-                    Kawataki, M., Kashima, T., Toda, H., and Tanaka, H. (1984). Relationship
                                                                                     between QT interval and heart rate: Applications and limitations of Bazett's
tions, the corrected QT interval remains useful in assessing the
                                                                                     Formula. J. Electrocard. 17, 371-376.
effects of drugs on the duration of repolarization.
                                                                                   Kovacs, S. J. (1985). The duration of the QT interval as a function of heart rate:
                                                                                    A derivation based on physical principals and a comparison to measured
                              REFERENCES                                             values. A. Heart J. 110, 872-878.
                                                                                   Mann, W. A., Kerns, W. D., and Kinter, L. B. (1994). Normalization of the QT
Ahnve, S. (1985). Correction of the QT interval for heart rate: Review of
                                                                                    interval (QTc) in canine electrocardiography. In Society of Toxicology
  different formulas and the use of Bazett's formula in myocardial infarction.
                                                                                    Annual Meeting Proceedings.
 Am. Heart J. 109, 568-574.
                                                                                   Motulsky, H. (1995). Intuitive Biostatistics, pp. 174-175. Oxford Univ. Press,
Ahnve, A. (1991). Is QT interval prolongation a strong or weak predictor for
                                                                                    New York.
  cardiac death? Circulation 84, 1862-1865.
Akhras, F., and Rickards, A. F. (1981). The relationship between QT interval       Nappi, J. M., and McCollam, P. L. (1993). Sotalol: A breakthrough antiar-
  and heart rate during physiological exercise and pacing. Jpn. Heart J. 22,         rhythmic? Annu. Pharmacother. 27, 1359-1368.
  345-351.                                                                         Oguchi, Y., and Hamlin, R. L. (1993). Duration of QT interval in clinically
Algra, A., Tijssen, J. G., Roelandt, J. R., Pool, J., and Lubsen, J. (1991). QTc     normal dogs. Am. J. Vet. Res. 54, 2145-2149.
  prolongation measured by standard 12-lead electrocardiography is an inde-        Peters, R. W., Byington, R. P., Barker, A., and Yusuf, S., for the BHAT Study

                                                                                                                                                                        Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015
  pendent risk factor for sudden death due to cardiac arrest. Circulation 83,        Group (1990). Prognostic value of prolonged ventricular repolanzation
  1888-1894.                                                                         following myocardial infarction: The BHAT experience. J. Clin. Epidemiol.
Bazett, H. C. (1920 An analysis of the time-relations of electrocardiograms.         43, 167-172.
  Heart 7, 353-370.                                                                Rees, S., and Curtis, M. J. (1996). Which cardiac potassium channel subtype
Colatsky, T. J., and Follmer, C. H. (1989). K + channel blockers and activators      is the preferable target for suppression of ventricular arrhythmias? Pharma-
  in cardiac arrhythmias. Cardiovasc. Drug Rev. 7, 199-209.                          col. Ther 69, 199-217.
Edwards, J. N. (1987). Bolton's Handbook of Canine and Feline Electrocar-          Schouten, E. G., Dekker, J. M., Meppelink, P., Kok, F. J., Vandenbroucke,
  diography. Saunders, Philadelphia.                                                 J. P., and Pool, J. (1991) QT interval prolongation predicts cardiovascular
Fridericia, L. S. (1920). Die sytolendauer in elektrokardiogramm bei normalen        mortality in an apparently healthy population. Circulation 84, 1516-1523.
  menschen und bei herzkranken. Ada. Med. Scand. 53, 469-486.                      Snedecor, G. W., and Cochran, W. G. (1989). Statistical Methods, 8th ed. Iowa
Funck-Brentano, C. (1992). La repolarisation ventriculaire. Arch. Mai. Coeur.        State Univ. Press, Ames, IA.
  85, 1015-1021.                                                                   Surawicz, B. (1987). The QT-interval and cardiac arrhythmias. Annu. Rev.
Funck-Brentano, C , and Jaillon, P. (1993). Rate-correct QT interval: Tech-          Med 38, 81-90.
  niques and limitations. Am. J. Cardiol. 72, 17B-22B.                             Tukey, J. W., Ciminera, J. L., and Heyse, J. F. (1985). Testing the statistical
Goldberg, R. J., Bengtson, J., Chen, Z., Anderson, K. M., Locati, E., and Levy,      certainty of a response to increasing doses of a drug. Biometrics, 41,
  D. (1991). Duration of the QT interval and total cardiovascular mortality in       295-301.
  healthy persons (the Farmingham Heart Study experience). Am. J. Cardiol.         Van de Water, A., Verheyeu, J., Xhonneux, R., and Reneman, R. S. (1989). An
  67, 55-58.                                                                         improved method to correct the QT interval of the electrocardiogram for
Kass, R. S., and Freeman, L. C. (1993). Potassium channels in the heart:             changes in heart rate. J. Pharmacol. Methods 22, 207-217.
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