Which QT Correction Formulae to Use for QT Monitoring?

Background Drug safety precautions recommend monitoring of the corrected QT interval. To determine which QT correction formula to use in an automated QT‐monitoring algorithm in our electronic medical record, we studied rate correction performance of different QT correction formulae and their impact on risk assessment for mortality. Methods and Results All electrocardiograms (ECGs) in patients >18 years with sinus rhythm, normal QRS duration and rate <90 beats per minute (bpm) in the University Hospitals of Leuven (Leuven, Belgium) during a 2‐month period were included. QT correction was performed with Bazett, Fridericia, Framingham, Hodges, and Rautaharju formulae. In total, 6609 patients were included (age, 59.8±16.2 years; 53.6% male and heart rate 68.8±10.6 bpm). Optimal rate correction was observed using Fridericia and Framingham; Bazett performed worst. A healthy subset showed 99% upper limits of normal for Bazett above current clinical standards: men 472 ms (95% CI, 464–478 ms) and women 482 ms (95% CI 474–490 ms). Multivariate Cox regression, including age, heart rate, and prolonged QTc, identified Framingham (hazard ratio [HR], 7.31; 95% CI, 4.10–13.05) and Fridericia (HR, 5.95; 95% CI, 3.34–10.60) as significantly better predictors of 30‐day all‐cause mortality than Bazett (HR, 4.49; 95% CI, 2.31–8.74). In a point‐prevalence study with haloperidol, the number of patients classified to be at risk for possibly harmful QT prolongation could be reduced by 50% using optimal QT rate correction. Conclusions Fridericia and Framingham correction formulae showed the best rate correction and significantly improved prediction of 30‐day and 1‐year mortality. With current clinical standards, Bazett overestimated the number of patients with potential dangerous QTc prolongation, which could lead to unnecessary safety measurements as withholding the patient of first‐choice medication.

T he QT interval is a measure of the duration of ventricular repolarization. It approximates the time interval between the start of depolarization and the end of repolarization of the ventricular myocardium. 1 QT prolongation is associated with a risk for cardiac arrhythmias given that it can result in early after depolarizations, provoke Torsades des Pointes, and lead to ventricular fibrillation, causing sudden cardiac death. 2 The risk assessment for QT prolongation of in-hospital patients is based on their medication profile, demographic risk factors, electrolyte disturbances, and monitoring of the corrected QT (QTc) interval. 3,4 Large population studies have shown a relation between QTc and all-cause mortality, cardiac mortality, and sudden cardiac death. [5][6][7] For correct interpretation, the QT interval should undergo adequate rate correction (QTc) to compare measurements at different time points and at different heart rates. To perform optimal risk stratification, this rate correction has to be reliable. The current clinical standard is the most widely used Bazett formula, but with this formula, there is a known overcorrection at high heart rates and undercorrection at lower heart rates. 8 In developing an automated patient-specific drug safety algorithm applicable in the electronic medical record, QTc together with clinical, biochemical, and pharmacological risk factors should be included. We wanted to determine which QT correction formula would be the best to use in such an automated algorithm. We first compared the heart rate correction performance of 5 commonly studied QT correction formulae. Second, we aimed to study the impact of the implementation of different QT correction formulae on risk assessment for mortality. To rule out a potential effect of the normal range or reference value for QTc in our population, we determined the reference values of the different formula in a healthy subset. We used this reference value to study the risk stratification for mortality for each QT correction formula separately. Finally, we investigated whether implementation of these different formulae would influence clinical decision making in a retrospective analysis of patients receiving haloperidol.

Study Population
All electrocardiograms (ECGs) taken in patients ≥18 years of age at the University Hospitals of Leuven (Leuven, Belgium) during a 2-month period (January 1, 2014 until February 28, 2014) were collected retrospectively using the MUSE Cardiology Information System (GE Medical Systems, Menomonee Falls, WI). All ECGs were standard 12-lead resting ECGs (25 mm/s paper speed, 10 mm/mV amplitude, and 250 Hz sampling rate). ECGs were recorded using MAC 5500 of GE Healthcare with automated analysis by the "GE Marquette 12SL ECG Analysis Program." Age, sex, contact type (emergency department, ambulatory, or hospitalized), heart rate, RR interval, QRS duration (QRSd), and QT interval were registered. On May 19, 2015, patients' mortality status was checked using the electronic medical records determining 30day and 1-year all-cause mortality.
ECGs were inspected visually for quality, rejecting ECGs with missing leads and excessive noise interfering with analysis. Next, for every patient, only the first ECG was retained and the underlying rhythm was visually controlled.
Patients were excluded from further analysis when not in sinus rhythm, a QRS duration >120 ms, or when the heart rate was >90 beats per minute (bpm). The limitation on heart rate was introduced to minimize overcorrection when correcting the QT interval for RR in case of tachycardia and thereby minimizing outliers influencing further statistics.
The study was approved by the University Hospitals of Leuven ethical committee and obtaining informed consent was waived.

QT Correction
QT correction for heart rate was performed using 5 previously published formulae: The Hodges correction formula was originally developed based on heart rate; however, for uniform interpretation, all formulas above are shown for calculations based on QT and RR interval measured in seconds. However, values presented in tables and figures are expressed in milliseconds (ms) conform to clinical use.
Using a population-based approach, the relation between QTc and RR was determined using scatterplots for QTc/RR pairs per subject. QTc/RR linear regression slopes were calculated with the template: QTc=BxRR+intercept. Given that optimal QTc correction should be independent of the RR interval, the slope of the linear regression (B) and R 2 should be zero. Therefore, the best performing QT correction formula has a slope value and R 2 closest to zero, indicating the least remaining influence by the RR interval. However, the true relationship between QTc and RR cannot be exactly linear for all correction formulae simultaneously, but linear QTc/RR regression is a commonly used technique providing a good estimate of remaining influence of the RR interval on the corrected QT values. 14,15 Reference Interval From this cohort, an age-and sex-matched population of 212 healthy patients, ranging from 18 to 70 years of age, was identified. Selection was performed blinded of ECG measurements such as heart rate and QTc. Patients were selected to fulfill the following criteria: 1 No cardiovascular medical history 2 No significant medical history, such as diabetes mellitus, chronic obstructive pulmonary disease, etc. 3 No cardiovascular medication 4 No QT or repolarization influencing medication Based on this healthy subset, the 99% reference interval, defined as lower and upper limit of normal (LLN and ULN, respectively) and their 90% CI, were calculated for each QT correction formula using the most recent guidelines of the Clinical and Laboratory Standards Institute. 16

Retrospective Clinical Analysis
Data from a point-prevalence study on the use of haloperidol, 17 a known QT-prolonging drug with associated risk on Torsade des Pointes, in the University Hospitals of Leuven, were used to perform a clinical simulation of in-hospital risk stratification based on the previously described 5 correction formulae for QTc. ECGs performed before the administration of a first dose of haloperidol were collected, together with clinical variables. Patients were excluded for further analysis using identical exclusion criteria as stated above. Risk stratification was performed based on clinical standards, 450 and 470 ms cutoffs for men and women, respectively. The number of patients identified above clinical standards was compared between the different correction formulae. The study was approved by the ethical committee of the University Hospitals of Leuven in a separate protocol.

Statistical Analysis
All continuous variables are given as meanAESD and proportions as percentages. Means were compared using Student t tests and proportions using chi-squared analysis. QTc values between correction formulae were compared using repeated-measurements 1-way ANOVA followed by pair-wise comparison with Tukey correction. QTc/RR linear regression was performed calculating the slope (B value) and the intercept with their 95% CI. Comparison of slopes between correction formulas was performed using 1-way ANOVA with Tukey correction for multiple comparisons based on the slope, SE of the slope, and the number of comparisons. Bland-Altman plots with calculation of bias and limits of agreement were performed to illustrate differences between correction formulae. For each QT correction formula, the sensitivity, specificity, and positive (PPV) and negative predictive value (NPV) for predicting 30day all-cause mortality were calculated. Multivariate Cox regression analysis, using the ENTER method, for prediction of 30-day and 1-year mortality, was performed separately for each QT correction formula for significant univariate parameters. Interpretation of the models was performed by analyzing the log likelihood ratio (À2 LLR) results by analyzing the difference in À2 LLR with QTcB using chisquared analysis. P<0.05 was considered significant. All statistical analysis was performed using SPSS (IBM Statistics, version 22; IBM Corp, Armonk, NY) and GraphPad (Prism, version 6; GraphPad Software Inc., La Jolla, CA).

Demographics
A total of 6609 patients were included in the analysis. Demographics are shown in Table 1. There was a nearly equal distribution of sex (53.6% male vs 46.4% female). Female patients were significantly older, had a higher heart rate, and a shorter QRS duration. There was no sex difference in uncorrected QT interval, but for all QT correction formulae, QTc was significantly longer in females. Results of the QTc values comparison between correction formulae are shown in Table 2. QTcB was significantly longer than all other correction formulae (P≤0.0001); only QTcFri and QTcFra did not differ significantly (P>0.050).

QTc/RR Analysis
The QTc/RR analysis identified the Fridericia and Framingham correction formulae as the best rate correction in this population, with slopes of 0.004 and À0.005, respectively (shown in Table 3 and Figure 1). All slopes of the correction formulae differed significantly from one another, as summarized in Table 4. Bazett's correction formula performed worst, with a slope of À0.071, indicating significant over-and underestimation of QTc at high or low heart rates, respectively. Bland-Altman plots and data on the bias and limits of agreement between correction formulae are available as Table 5 and Figure 2. This is illustrated when selecting patients at the extremities of the heart rate spectrum. Selecting the 1190 patients (18.0%) with a heart rate ≥80 bpm (49.0% male; age, 57.7AE16.6 years; QRSd, 89AE11 ms; heart rate, 84.5AE3.2 bpm), the difference between QTcB and QTcFri is 24 ms (QTcB 438 ms and QTcFri 414 ms; P<0.001).

Reference Interval
The reference intervals, LLN and ULN, of the healthy subset are shown with their 90% CIs in Table 6. For LLN, there was only a limited difference for the different QT correction formulae, and sex did not seem to affect the LLN value. For the ULN, there were, as expected, a difference between males and females. Bazett had the highest ULN values in both sexes, up to 472 ms for men and 482 ms for women. The QT correction formulae with the best rate adaptation, Fridericia and Framingham, produced an ULN similar to current clinical values.
The number of patients with a QTc below LLN was limited: from 5 patients (0.07%) for QTcFri and QTcH to 12 patients (0.18%) using QTcFra. The correction formulae with a morenegative slope identified more patients as having a short QTc, using QTcB 14 patients (0.21%) and for QTcR 26 patients (0.39%). Table 7 shows the proportion of patients with a QTc higher than the ULN.

Mortality Analysis
In total, 0.9% of the patients died at 30 days and 4.0% at 1 year. The 30-day mortality did not differ significantly for contact type (emergency department, ambulatory, or hospitalized; P=0.224). However, 1-year mortality was more frequent (P<0.001) in hospitalized patients (6.0%) than ambulatory (3.8%) and patients presenting at the emergency department (2.7%).
In Table 7, the sensitivity, specificity, PPV, and NPV for mortality prediction for QTc>ULN are shown. There were no deaths occurring in patients with a QTc<LLN. At 30 days, QTcB had a far lower sensitivity with equal specificity compared to the best performing correction formulae. After 1 year, the differences became less, but remained consistent.
The Cox regression analysis is summarized in Table 8; the complete results are available in Tables S1 through S4. The 30-day mortality model included age, heart rate, and a QTc>ULN as univariate significant predictors. Multivariate analysis identified age, heart rate, and QTc>ULN as independent predictors of 30-day all-cause mortality. Comparing the LLR analysis, all QTc formulae were significantly better predictors, compared to QTcB (QTcFri, P<0.005; QTcH, P<0.005; QTcR, P<0.010), with the model containing QTcFra (P<0.001) performing the best. The model with QTcFra was also significant better than these with QTcH and QTcR (P<0.050), but did not differ significantly with QTcFri.
The 1-year mortality model also included QRSd as a univariate significant predictor. Age, heart rate, and QTc>ULN (and QRSd in the model with QTcFri) were identified as independent predictors. The models with QTcFri and QTcFra remained significant better predictors compared to QTcB (QTcFra, P<0.050; QTcFri, P<0.005). All other models did not differ significantly from one another.
Subgroup analysis for cause of death was performed at 1year given the low number of events at 30 days (available in  Tables S1 through S4). For cardiac mortality, a longer QRS duration, even in a population with QRS <120 ms, was an independent predictor of mortality, and the models did not differ significantly for QT correction formulae. Whereas for noncardiac mortality, the opposite was true and a shorter QRS duration seemed an independent predictor of noncardiac mortality and models with QTcFri and QTcH were significantly better predictors. Comparison of QRSd between patients from the healthy cohort (88.13AE11.21 ms), with these dying from cardiac causes (94.88AE12.39 ms; P<0.001) and noncardiac causes (88.66AE11.82 ms; P=0.663), showed that the QRSd in patients who died of noncardiac causes was not shorter than normal. Taken together, these data showed that, in our hospital, population QRS duration was related with a worse cardiovascular prognosis. Patients with a "broader" QRS complex have a higher mortality and die more often of cardiac causes than those with a more "narrow" QRS complex, who have a better survival, and if they die, this was caused more often by noncardiac causes.

Retrospective Clinical Analysis
In total, 212 patients were included in the haloperidol pointprevalence study.

Discussion
This analysis confirms the inferiority of QTcB for rate correction compared to QTcFri or QTcFra, even in patients in sinus rhythm and normal heart rate ranges. In a healthy subset of our study population, this inferior rate correction of QTcB led to the calculation of reference values with a ULN far higher than current clinical standards, whereas formulae with near optimal rate correction approximate the current clinical standards for both males and females. Moreover, QTcFri and QTcFra showed to be better predictors of 30-day and 1-year all-cause mortality.

QT Correction
The inferiority of QTcB has already been widely documented in smaller population studies. 15,18 Also, alternative approaches in which the QT correction formula was chosen based on sex and heart rate range have been suggested. 19 Within different populations, it can be expected that certain formulae perform better in rate correction, which could be based on sex composition, ethnicity, age, exclusion of higher or lower heart rates, etc. Sex analysis in our population confirmed the difference in rate correction between male and females for different QT correction formulae. The largest differences were observed with QTcFri (slope, 0.002 vs 0.016 in males vs females, respectively) and QTcFra (slope, À0.010 vs 0.011 in male vs females, respectively). The switch from a negative to a positive slope observed in QTcFra indicates a switch from a slight overcorrection in males toward a slight undercorrection in females at higher heart rates. Notwithstanding these changes, QTcFri and QTcFra remained the best performing correction formulae for both sexes.
Thus, different studies have suggested different formulae to be superior, but all had one thing in common: the inferiority of QTcB. 8,15,19,20 The introduced difference by using QTcB instead of a superior rate-correcting formula might be clinically significant. We observed an overcorrection with a mean difference of 24 ms between QTcB and QTcFri in patients with a heart rate ranging 80 to 90 bpm. This difference could lead to changes in clinical practice, for example, withholding a patient from clinically indicated firstchoice medication. If we keep in mind that thorough QT/QTc studies should be designed to detect QTc changes of 5 ms, the observed difference between formulae should lead to a reconsideration of current clinical practice in which QTcB is still the most used formula. 21 Besides a population-based approach and choosing the best performing formula within this population, an individual QT correction could be obtained. It was stated by Malik et al. that a mathematical QT/RR relation that fits for all persons individually is unobtainable. 22 Individual-or subject-specific correction methods have proven to be superior to populationbased formulas. 8,22,23 However, the reliability of a subjectspecific correction depends on the number of data points, the range of heart rates between different data points, and the time interval between data points and possible intervening changes in between, such as medication, physical activity, and the interplay between sympathetic and parasympathetic tone. Adding the recently described nonlinearity of subjectspecific QT/RR relations and the problem of QT hysteresis makes the subject-specific QT correction currently rather a scientific tool suited for thorough QT/QTc studies and further

Reference Interval
The determined LLN within the healthy subpopulation corresponded to the proposed lower limit of 350 ms, with a maximal variation of only 6 ms for both men and women for all QT correction formulae studied. 25 This is in contrast to the ULN, where approximation of the clinical standard of 450 ms for QTcFri (448 ms), QTcFra (449 ms), and QTcH (446 ms) was observed. However, correction formulae with morenegative slopes, QTcB (472 ms) and QTcR (464 ms), have far higher ULNs than the clinical standard. Again, this indicates the impact of suboptimal rate correction, even in a healthy population. In women, the ULN approximates the clinical standard of 470 ms, except for QTcB with 482 ms. A comparable analysis was performed by Luo et al. (n=10 303) excluding only the top 2% of QTc values. 19 They reported a 2% ULN within heart rate ranges of 60 to 90 bpm of 480 ms in men and 486 ms in women for QTcB, whereas the other reported formulae approximated the clinical standards.
A careful clinical interpretation of these findings suggest that using the clinical standards of 450 ms in men and 470 ms in women leads to an overestimation of patients with prolonged QT when using QTcB. Applying these clinical standards in our population with QTcB would triple the proportion of patients with a QTc>ULN from 3.2% to 9.4%. This in contrast to the 4.6% using QTcFra, which is still twice the amount of patients requiring attention for a prolonged QTc.

Prediction of Mortality
We report that a prolonged QTc is related to an increased 30day and 1-year mortality and that the use of QTcFri or QTcFra would significantly improve all-cause mortality risk stratification compared to QTcB. A prolonged QRSd is related to 1-year mortality. We hypothesize that the apparent association between a shorter QRSd and a higher risk of noncardiac mortality is an illustration of the concept of conversion of mode of death (a decrease of cardiovascular mortality leads to an increase in noncardiovascular death) within this hospital-based population, but should be interpreted with caution because this finding could be influenced by our design and the study limitations.
In a healthy population study by Schouten et al., a QTcB above 440 ms was associated with a significant relative risk The major difference with the previous studies of the Framingham Heart Study population and the study by Schouten et al. is that our analysis was performed on a hospital-based population, which cannot be interpreted as a healthy or normal population. Also, these studies reported long-term follow-up, and only the Framingham Heart Study reported both QTcB and QTcFra, but still showed a significant association with all-cause mortality. The primary care study by Nielsen et al. reported only a population ages between 50 and 90 years of age and therefore could have shown higher HR. The high HR of our analysis could be caused by the fact that we studied a hospitalbased nonhealthy population, including 21.5% hospitalized patients, and by the fact that we analyzed 30-day and 1-year mortality instead of multiple years of follow-up.

Retrospective Clinical Analysis
Haloperidol should not be used in patients with QT prolongation. The data from the haloperidol point-prevalence study illustrated that when using optimal QT correction, the proportion of patients with QTc values above clinical standards before the prescription of this QT-prolonging drug could be reduced with up to 50%. This implies that a hospital-wide automated algorithm, which uses QTcB for assessment of a possible dangerous QT prolongation, would generate double the amount of alerts compared to an algorithm using the optimal QT correction formula. This could lead to alert fatigue and avoiding clinically indicated first-choice drugs because of potential QTprolonging effects. 26 Hence, using an optimal QT correction formula could reduce the workload and improve patient safety.

Limitations
One of the main limitations of this study is its single-center retrospective character. The survival status of the patients was based on the electronic medical record at our institution, without a link to a public register. Although our electronic medical record is linked to multiple regional hospitals, the number of events might be underestimated. We limited current analysis to patients in sinus rhythm with a narrow QRS and a heart rate <90 bpm in order to avoid the number of outliers. The number of parameters included in the risk stratification modeling was limited; however, the data set yielded no missing values. Furthermore, prospective population studies should be used to study population-based rate correction in abnormal heart rhythms, such as sinus tachycardia, atrial fibrillation, or ventricular conduction defects.

Conclusion
The current use of Bazett's QT correction formula in clinical standards should be questioned. The use of QTcFri or QTcFra in a hospital-based population would significantly increase risk stratification for all-cause mortality. Therefore, the question arises of whether QTcFri, as in thorough QT/QTc studies, should become the next clinical standard replacing QTcB for hospital-based QT monitoring.