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 Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015 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. 0.310 n 0.285 0.280- •§ 0.235- 0.210- 0.185- 0.180- Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015 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 0.350 0.325 0.300 •g a .•-•-£: 0.25O- a* a _+ • 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.
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS 249 0.3251 0.300- 0.275- 0.250- . • • „, * . • • • ••..-- • / —->'•-—.-••A . . " - I . . • •• 0.225- ' , ' * " 0.200- Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015 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 0.325 n 0.300- 0.275- g 0 250- CT 0.225- 0-200 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. -1.0- -1.1- -1.2- -1.3- -1.4- -1.5- -1.8- -1.7 •-•—V •"•'*'•-^ -1.8 slope = -0.2839 ±0.01752 -1 9 Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015 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- 0.275-1 0.250- • . • - 0.225-1 o' • S I 0.200 • • .-'•v 0.175- \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.
HEART RATE ADJUSTMENT OF THE QT INTERVAL IN DOGS 251 0225 -i 0210- 0195- 0180- o.^ • ff-^^^o o • • • 0165- 0150- Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015 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 0320 0J05 0290 0275- I •8 0260- 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- Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015 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 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 0250- 02«- 02« 0235 0230- °225 0220 0215- 0210- 0205 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.
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 ) Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015 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 0.28- P-0.424 0.28- 0.27 0.28- 0.25- 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 0.31- 030- 0.29- 0.28- 0.27- S 028- P-0.043 MS 0.25- P-0.944 0.24- 0.23- 0.22- 0.21- Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015 0.20 OIlKD 0025 MKD 0.05 M
256 SPENCE ET AL. 0.24 023 022 0.21- s P»O.0O4 020 a °-19- 0.18 0.17 0.18- Downloaded from http://toxsci.oxfordjournals.org/ by guest on October 24, 2015 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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