reference will now be made in detail to the present preferred embodiment of the invention , an example of which is illustrated in the accompanying drawings . wherever possible , the same reference numbers will be used throughout the drawings to refer to the same or like parts . a system for recording electrocardiogram data in accordance with the present invention is broadly shown in fig6 as reference numeral 100 . an electrocardiogram ( ecg ) monitor 104 is connected to a patient , such as a dog 102 . preferably ecg monitor 104 uses electrodes in the lead ii position , however , a qt measurement can be calculated from other ecg vectors , including leads i and iii , a vl , a vr , a vf , and all pre - cordial leads ( v1 - v6 ). a vehicle or test compound is administered to dog 102 with a compound administration device 106 . the vehicle or test compound may be administered in various ways , including but not limited to orally , intravenously , or subcutaneous . ecg monitor 104 provides signals 110 to a data acquisition interface 108 which processes the signals 110 and provides processed signals 112 to a computing device 114 . heart rate ( rr interval ) and lead ii ecg data are collected continuously on a beat - to - beat basis at a sampling rate of 1000 hz to allow for millisecond ( ms ) resolution . using the sampled data , the qt interval and preceding rr interval are measured on individual cardiac cycles using commercially available data acquisition and analysis software . the software package used in support of the data presented here was from gould inc . ( po - ne - mah ) subsidiary . this software permits visual validation of the determination of end points used in the calculation of the ecg time intervals . the collection of data is not limited to any particular method . for example , ecg time intervals can be measured using a ecg strip chart recorder . thus , both manual and electrical data collection is possible with the present invention . computing device 114 , as shown in fig7 , includes a bus 200 interconnecting a processor 202 , a read - only memory ( rom ) 204 , a main memory 206 , a storage device 208 , an input device 210 , and an output device 212 . bus 200 is a network topology or circuit arrangement in which all devices are attached to a line directly and all signals pass through each of the devices . each device has a unique identity and can recognize those signals intended for it . processor 202 includes the logic circuitry that responds to and processes the basic instructions that drive device 114 . rom 204 includes a static memory that stores instructions and data used by processor 202 computer storage is the holding of data in an electromagnetic form for access by a computer processor . main memory 206 , which may be a ram or another type of dynamic memory , makes up the primary storage of device 114 . secondary storage of device 114 may comprise storage device 208 , such as hard disks , tapes , diskettes , zip drives , raid systems , holographic storage , optical storage , cd - roms , magnetic tapes , and other external devices and their corresponding drives . input device 210 may include a keyboard , mouse , pointing device , sound device ( e . g . a microphone , etc . ), biometric device , or any other device providing input to device 114 . output device 212 may comprise a display , a printer , a sound device ( e . g . a speaker , etc . ), or other device providing output for device 114 . as will be described below , a computing device 114 consistent with the present invention may perform a method for statistical analysis of qt interval as a function of changes in the rr interval . device 114 performs this task in response to processor 202 executing sequences of instructions contained in a computer - readable medium , such as main memory 206 . a computer - readable medium may include one or more memory devices and / or carrier waves . execution of the sequences of instructions contained in main memory 206 causes processor 202 to perform processes that will be described later . alternatively , hardwired circuitry may be used in place of or in combination with software and any such arrangement wherein the device is set to perform the tasks of the algorithms disclosed herein , either by hardwire circuitry , stored instructions , or combination thereof , would comprise a means for comparing a pre - dose curve of qt interval versus rr interval to a post - dose curve of qt interval versus rr interval , determining the incidence of points of the post - dose data that exceed an upper 95 % single - point prediction limit to determine the degree of heterogeneity of ventricular repolarization and a means for comparing the points of the post data that exceed the upper 95 % single - point prediction limit of the pre - dose curve to determine the magnitude of these points and provide a quantitative assessment of treatment - induced changes in the qt - rr relationship instructions to implement processes consistent with the present invention . thus , the present invention is not limited to any specific combination of hardware circuitry and software . the various treatments with vehicle or compounds are studied in a randomized fashion . the drugs include methanesulfonamide , n -[ 4 -[[ 1 -[ 2 ( 6 - methyl - 2 - pyridinyl ) ethyl ]- 4 - piperidinyl ] carbonyl ] phenyl ] ( i . e ., e - 4031 ), terfenadine , and cisapride . e - 4031 , an antiarrhythmic , terfenadine ( seldane ®), an antihistamine , and cisapride ( propulsid ®), a gastrointestinal prokinetic agent , clinically have all been shown to cause a clear , dose - dependent increase in qt c . the term “ vehicle ” as used herein is defined as a non - reactive solvent used in the administration of the compound . ii . analysis of qt interval as a function of the preceding rr interval the method for statistical analysis of qt interval as a function of changes in the rr interval in accordance with the present invention is performed by computing device 114 . as shown in fig8 , the method 300 of the present invention includes a plurality of steps , including the step 302 of replaying the stored data from ecg . the method further includes : a step 304 of analyzing the qt interval on individual cardiac cycles ; a step 306 of statistically analyzing the qt - rr interval relationship ; a step 308 of statistically comparing best fit curves of the qt - rr relationship ; a step 310 of statistically comparing the number of qt interval measurements exceeding the upper 95 % confidence interval ; a step 312 of statistically comparing the magnitude of the outliers ; and a step 314 of statistically comparing the qt at an rr interval of 1000 ms . each of the steps of the method 300 of the present invention is explained in the following sections in greater detail . the calibrated analog signal is replayed on computer device 114 in order to analyze qt interval measurements for individual cardiac cycles . approximately 250 to 300 consecutive cardiac cycles are analyzed for a pre - dose period and during steady - state compound exposure . this encompasses between three to five minutes of continuous data for each data collection period . a previous analysis for statistical power for the variance of the data for the dog showed that approximately 250 points were required for a probability of 0 . 15 of a false negative , β , ( i . e . determining the treatments to be the same when they are , in fact , different ) with a type i error rate ( false positive ) of α = 0 . 05 . the ( α and β values were chosen from historical precedence with physiological data . sample size determinations should be done for each type of experiment and subject . each qt measurement is monitored by a technician on a data replay screen ( e . g ., a computer monitor ) connected to computing device 114 . if there is a discrepancy between the software analysis and the technician &# 39 ; s interpretation of the end of the t wave , the cardiac cycle is reanalyzed interactively by the technician using on - screen measurement cursors . qt is then analyzed as a function of the previous rr interval for each cardiac cycle of a selected time period . an asymptotic decaying exponential growth curve fit is used to describe the relationship between qt and rr interval : the coefficients a , b , and c represent different aspects of the qt - rr relationship . the terms a , b , and c are regression coefficients that are determined by a non - linear regression technique applied to the data . the coefficients a , b , and c are unique for a given data set . the coefficient “ a ” represents the behavior of qt at very large values of rr . the coefficient “ b ” represents the behavior of qt at very low values of rr . the coefficient “ c ” represents the relationship of the intermediate points and the steepness of the curve between low and high rr values . calculation of the relationship between qt and rr interval is not limited to equation ( 1 ). rather , other curve fit equations may be used , including a log growth function , bazett or fridericia &# 39 ; s correction ( described above ), and all of the equations set forth in t . matsunaga et al ., “ qt corrected for heart rate and relation between qt and rr intervals in beagle dogs ”, journal of pharmacological and toxicological methods , 38 , pp . 201 - 209 ( 1998 ). another curve fit equation developed by the present inventors is an arc tan function qt = a + b × arctan ( c × rr ). in the interest of qt prolongation , the concern is for qt values elevated above the pre - dose value for the corresponding rr interval defined by the regression analysis - fitted curve . the null hypothesis h 0 is a one - sided hypothesis and all rejections of the null hypothesis are based on whether the dose measurements were greater than 95 % of the pre - dose data ( i . e . 0 . 05 significance level ). for treatments where the interest lies in detection of increasing qt , the one - sided hypothesis h 0 is the appropriate test . in this case , a qt value that is higher than 95 % of the pre - dose data is determined to be different , or prolonged , from the pre - dose data , and the hypothesis h 0 is rejected in favor of the alternative hypothesis h 1 . a false negative is defined as accepting hypothesis h 0 when it should have been rejected . the analysis of the vehicle or compound versus pre - dose effect on qt was accomplished by a statistically significant indication of qt prolongation by at least one of the following : ( 1 ) a significant rise in qt post - dose curve above the pre - dose curve ; ( 2 ) a significant increase in the number of episodes of qt intervals that exceed the pre - dose 95 % prediction interval threshold ; or ( 3 ) a significant increase in the magnitude by which the prolonged points exceed the pre - dose curve . equation ( 1 ) is used to fit the qt measurements to the preceding rr interval for each separate data set of consecutive cardiac cycles . the data from each sample period for each vehicle or compound dose is fit to the equation using a least squares nonlinear regression method such as , but not limited to , quasi gauss - newton . post - dose curves are inspected to determine if and at what point the dose curve becomes significantly higher than the pre - dose curve . the upper 95 % confidence limit for the difference of the curves is determined for each of the dose - to - pre - dose comparisons . if the dose curve crosses the 95 % limit , the qt and rr values and the direction of crossing is noted . if the treatment curve is significantly elevated or depressed for the entire rr range , then the curves will not cross , indicative of an overall significant rise in qt or no significant overall rise , respectively . statistical comparison of the number of qt measurements exceeding the upper 95 % confidence interval the analysis of the compound versus vehicle effect on qt is also accomplished by comparisons of the number of prolonged points exceeding the 95 % confidence interval of their respective pre - dose curves . the pre - dose curve value represents the least squares estimate of qt at that value of rr . the 95 % limits are then used to compare the overall effect of the treatment ( compound or vehicle ) to that of the pre - dose response . the confidence limits of the two curves are combined ( pooled ) to determine the standard error of the difference between the pre - dose and post - dose curves . the single - point prediction limits for the pre - dose data are used to determine whether a qt point is significantly prolonged . the extent of the confidence and prediction limits depends on the overall variability of the data and the values of the coefficients . the number of pre - dose data that exceed the upper 95 % prediction limit ( referred to herein as “ outliers ”) is compared to the number of post - dose data that exceed the limit for each of the time periods . a repeated measures test for significant difference between pre - dose and post - dose outliers is conducted to evaluate an effect . in the case of small but consistent effects , the repeated measures test detects significant differences better than individual tests . individual significance tests of the proportion of prolonged outliers , such as , but not limited to chi - square and fisher &# 39 ; s exact test , are also conducted to determine if any one treatment is significantly higher than the pre - dose results . to minimize the chance of false negatives , β , conventionally known as “ type ii errors ,” no multiple comparison adjustments are made for the individual tests . once the outliers are identified , they are compared to the pre - dose curve to estimate the magnitude of prolongation , δqt , above the qt - rr curve fit to the pre - dose data . the magnitude of prolongation is referenced to the curve rather than the upper 95 % confidence bound because the curve is the best estimate of the qt - rr functional relationship , regardless of the number of data points . the resulting δqt are then compared within treatment groups ( dose to pre - dose ) using a comparative statistical method such as , but not limited to , signed rank tests and t - test . the nonlinear curve defined by equation ( 1 ) is used to provide a least squares estimate of the qt interval at a physiologically relevant heart rate of 60 beats / min ( qt rr1000 ). a one - tailed student &# 39 ; s t - test is then used for comparison of post - dose versus the pre - dose response . when comparing two or more treatments given with the same dosing protocol , the responses are first compared to the pre - dose data and curve . treatments include , but are not limited to , different dose levels , compounds and days . the resulting outlier numbers and magnitudes ( δqt ) are then compared between treatments . for measurements at repeated intervals , a repeated measures test is conducted on the number and magnitude data for statistical significance . individual tests are conducted without multiple comparison corrections to minimize the chance of false negatives . a simultaneous overall measure of significant treatment effect over all measurement times provides increased statistical power for a consistent trend at all data collection periods . this overall measurement was done using a mantel - haenszel statistical analysis . the analysis can be done using conventional independent ( such as a chi - square ) or correlated ( such as mcnemar ) statistical tests and can include a continuity correction for low frequencies or outliers . individual measurements may also be performed to investigate each period &# 39 ; s results . other statistical tests may be performed using transformed outlier frequency data and standard repeated measures of variance ( such as anova , linear models ) or categorical methods ( such as logistic regression and generalized linear models ). the results of three tests for significance increases the sensitivity of detecting qt prolongation by testing for the incidence and magnitude of prolonged episodes . conventional methods such as bazett or fridericia may not fit the data , depending on the range of rr intervals associated with each qt interval . additionally , conventional testing does not account for the effects of increasing incidence in prolonged qt episodes nor do they test specifically for the magnitude of the determined outliers . the statistical method of the present invention evaluates individual responses to ensure sensitivity in detecting statistically significant effects in a heterogenous population that may otherwise mask changes if one evaluates only the pooled study group response . exemplary data of the qt - rr relationship for a variety of compounds known to prolong qt are shown in fig2 - 5 , with the statistical analysis summarized in table 1 . the bazett correction for the treatment curve is also included in fig2 - 5 to demonstrate how poorly this predicts the qt - rr relationship . the data in fig2 show no difference between the vehicle and the pre - dose baseline for this dog . for e - 4031 , fig3 shows a large rise in overall qt over the entire rr range . the results for terfenadine , shown in fig4 , are slightly different from those of e - 4031 . the qt values of the terfenadine data are close to the baseline values for low (& lt ; 600 ms ) rr values . however , as with e - 4031 , there is a clear rise in qt values at rr values above 1000 ms . the effect of cisapride on the qt - rr relationship is shown in fig5 . the post - dose curve is not significantly greater than the pre - dose curve for rr & gt ; 1094 ms ( the crossing point of the curves ). the rate dependence of the cisapride effect would not be shown in a simple measurement of qtc . table 1 summarizes the statistical analysis of the number and magnitude of δqt measurements exceeding the upper 95 % confidence bounds of the curve fit . e - non - breaking e - 4031 , terfenadine , and cisapride all caused a significant increase in the number and magnitude of the outliers compared to the pre - dose and vehicle response . conventional single - parameter models , such as bazett &# 39 ; s or fridericia &# 39 ; s , while able to provide one measure of prolongation , fail to adequately fit the data over the wide rr range . the single parameter model forces qt = 0 at r = 0 . qt then increases monotonically with increasing rr , resulting in overly high qt values at rr & gt ; 1000 ms . both of these models will overestimate the qtc at low rr , calling normal values prolonged , and underestimate qtc at high rr , calling almost nothing prolonged . the use of a multiparameter model of the present invention , rather than reporting the functional relationship of qt to rr , uses the pre - dose response over the rr domain as a baseline from which to measure the treatment response for a given experiment . inherent differences between subject pre - treatment qt - rr relationships should be taken into account in the response of the subject to treatment . therefore the qt response to treatment is examined within the context of the observed pre - treatment qt statistics . effects such as change in baseline level or change in qt variability , are then accounted for and valid comparisons between subjects ( or treatments ) can be done . it will be apparent to those skilled in the art that various modifications and variations can be made in the system and method of the present invention and in construction of this system and method without departing from the scope or spirit of the invention . as an example , repeated measures analysis of the number of outliers can be accomplished using transformed data or sets of 2 × 2 contingency tables ( eg . mantel - haenszel ). other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein . it is intended that the description and examples be considered as exemplary only , with a true scope and spirit of the invention being indicated by the following claims .
a system and method for statistically analyzing qt interval as a function of changes in the rr interval . the system and method utilize three statistical comparisons to fully characterize the qt response : the comparison of curves to give an overall effect ; the incidence of points exceeding a baseline upper 95 % single - point prediction bound to reflect the degree of heterogeneity of ventricular repolarization ; and the magnitude of these points to provide a quantitative assessment of treatment - induced changes in the qt - rr relationship . the system and method use the relationship between the qt interval and heart rate to reference a control baseline response . data from mammals such as humans and dogs , and pharmacological maneuvers using both cardiac and non - cardiac therapeutic agents , may be used with this multi - parameter statistical system and method . additionally , the system and method quantifies the incidence and magnitude of points lying outside the upper 95 % single - point prediction limit of the regression analysis for vehicle versus treatment .