Development and cross-validation of a prediction equation for ...

European Journal of Clinical Nutrition (2004) 58, 474–480

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ORIGINAL COMMUNICATION Development and cross-validation of a prediction equation for estimating resting energy expenditure in healthy African-American and European-American women MW Vander Weg1*, JM Watson1, RC Klesges1, LH Eck Clemens2, DL Slawson1 and BS McClanahan1 1 The University of Memphis Center for Community Health, Memphis, TN, USA; and 2Department of Consumer Science and Education, University of Memphis, Memphis, TN, USA

Objective: To develop, validate, and cross-validate a formula for predicting resting energy expenditure (REE) in AfricanAmerican and European-American women. Design: A cross-sectional study of REE in women. Participants were randomly assigned to one of two groups. One group served to develop and validate a new equation for predicting REE while the second was used to cross-validate the prediction equation. The accuracy of the equation was compared to several existing formulae. Setting: University metabolic laboratory, Memphis, TN, USA. Subjects: Healthy, premenopausal African-American and European-American women between 18 and 39 y of age. The validation sample included 239 women (age: 28.4 y, wt: 70.7 kg, body mass index (BMI): 25.2 kg/m2, REE: 5840 kJ/day), while the cross-validation sample consisted of 232 women (age: 27.5 y, wt: 70.7 kg, BMI: 25.2 kg/m2, REE: 5784 kJ/day). Results: The prediction equation derived from the current sample, which included adjustments for ethnicity, was the only formula that demonstrated a high level of accuracy for predicting REE in both African-American and European-American women. The mean difference between REE predicted from the new formula and measured REE was 28 kJ/day (s.d. ¼ 668) for European-American women and 142 kJ/day (s.d. ¼ 584) for African-American women. Conclusions: Previous equations for predicting energy needs may not be appropriate for both African-American and EuropeanAmerican women due to ethnic differences in REE. A new equation that makes adjustments in predicted REE based on ethnicity is recommended for determining energy needs in these groups (Predicted REE (kJ/day) ¼ 616.9314.9 (AGE (y)) þ 35.12 (WT (kg)) þ 19.83 (HT (cm))271.88 (ETHNICITY: 1 ¼ African American; 0 ¼ European American)). Sponsorship: Support for this study was provided by Grant #HL53261 from the National Heart, Lung, and Blood Institute. European Journal of Clinical Nutrition (2004) 58, 474–480. doi:10.1038/sj.ejcn.1601833 Keywords: resting energy expenditure; energy metabolism; ethnicity; prediction equations

*Correspondence: MW Vander Weg, The University of Memphis Center for Community Health, 5050 Poplar Avenue, Suite 1800, Memphis, TN 38157, USA. E-mail: [email protected] Guarantor: MW Vander Weg. Contributors: MWV was the primary author and data analyst. JMW also contributed to data analysis and interpretation, as well as data collection and management. RCK was the Principal Investigator for the parent study, and was responsible for its design and methodology. LHEC was Co-Principal Investigator, and assisted with the administration and scientific oversight of the study. DLS was the Project Coordinator, and supervised the day-to-day management of the study. BSM was director of the metabolic laboratory, and supervised all aspects of metabolic data collection. All six authors contributed to the preparation of the manuscript. Received 4 October 2002; revised 22 January 2003; accepted 7 February 2003

Introduction The most accurate procedures for measuring REE include direct and indirect calorimetry. However, such methods are costly and are not feasible in most clinical settings (Foster & McGuckin, 2001). Therefore, prediction equations that provide accurate estimates of REE based on easily obtained variables such as height, weight, and age have greater clinical utility. Several equations have been developed to estimate REE based on readily available physical measures. The most widely used equations to predict REE were developed more than 80 y ago by Harris and Benedict (1919). Although initial

Estimates of resting energy expenditure in women MW Vander Weg et al

475 investigations of these equations found them to provide a relatively good estimate of REE, recent validation studies have determined that they often overestimate energy needs, particularly among individuals who are overweight (Daly et al, 1985; Heshka et al, 1993; Frankenfield et al, 1998). Consequently, other equations have been developed in an attempt to improve estimates of REE (eg, Owen et al, 1986; Mifflin et al, 1990). Among these are a series of prediction equations developed by Schofield et al, (1985) that were adopted by the World Health Organization (FAO/WHO/ UNU, 1985) and that have since gained widespread use internationally. Unfortunately, the ethnicity of the samples in which these equations were developed was not considered in any of the previously mentioned formulae. There is a growing literature suggesting that, on average, African-American women have a lower REE than European-American women (eg, Weyer et al, 1999; Gannon et al, 2000; Kimm et al, 2001; Sharp et al, 2002). While there is debate regarding the precise nature of this difference (Kumanyika, 1999), factors such as decreased leptin concentrations (Nicklas et al, 1997), reduced levels of metabolic activity in lean tissue (Albu et al, 1997; Jakicic & Wing, 1998), and increased energy efficiency due to variations in uncoupling proteins (Kimm et al, 2002) may contribute to the lower levels of REE among AfricanAmerican women. None of the formulae developed to date have accounted for these ethnic differences. The prediction equations developed from a primarily European American sample might not be appropriate for AfricanAmerican women, and may overestimate energy needs in this group. Consequently, there is a need to develop an equation that can accurately predict REE for both ethnic groups. The purpose of the present investigation was to develop and cross-validate a new equation for estimating REE in African-American and European-American women, and to compare the accuracy of this equation with several existing formulae to determine their utility in a biethnic sample of women.

Method Participants and recruitment Participants were healthy, premenopausal women between the ages of 18 and 39 y who were taking part in a 2-y prospective study of factors associated with weight gain in women. Women with chronic health problems (eg, hypertension, diabetes) and those who had been pregnant or breastfeeding in the previous 6 months were not eligible for the study. Additional exclusionary criteria included longterm medication use, irregular menstrual cycle length (ie, o23 or 435 days), and being on a special or weight reducing diet. Participants were recruited from several sources including newspaper, radio, and television advertisements, flyers, health fairs, and recorded telephone hold messages. A total of 487 women were recruited for the parent study. Of these,

16 were excluded from the present investigation due to missing data, for a resultant sample size of 471 (205 African American, 266 European American). The study protocol was approved by The University of Memphis Institutional Review Board.

Procedure Participants attended an orientation session during which they completed consent forms as well as demographic and health-related questionnaires. Participants were instructed to contact the laboratory on the first day of their next menstrual cycle, at which time they were scheduled for a laboratory session. Owing to variation in REE across the menstrual cycle (Webb, 1986), all assessments were obtained between the 8th and 10th days of participants’ menstrual cycles (during the menstrual and follicular stages). The following approach was taken to compare the accuracy of the new equation for estimating REE against existing formulae. First, participants in the sample were randomly assigned to one of two groups consisting of a validation (n ¼ 239) and a cross-validation sample (n ¼ 232). The characteristics of the two groups are presented in Table 1. Data from the first group were used to develop and validate the new equation for predicting REE. The second group served as a calibration sample for cross-validating the new formula and comparing it to existing equations. Four previously developed equations for estimating REE in women were included in the present study (Schofield et al, 1985 Predicted REE (kcal): 18–30 y ¼ 14.7(WT) þ 496; 30– 60 y ¼ 8.7 (WT) þ 829; Owen et al, 1986 Predicted REE (kcal) ¼ 795 þ 7.2 (WT); Mifflin et al, 1990 Predicted REE (kcal) ¼ 161 þ 10 (WT) þ 6.25 (HT)5 (AGE); Harris & Benedict, 1919 Predicted REE (kcal) ¼ 665 þ 9.6 (WT) þ 1.85 (HT)4.68 (AGE)). Since we were interested in predicting REE across a broad range of body weight, equations developed from samples of exclusively overweight women were not included. Although additional formulae for predicting REE based on body composition (eg, fat-free mass) have been developed, the current investigation was restricted to equations consisting of readily available measures (eg, height, weight, age), as these have greater clinical utility.

Measures Self-report measures. Demographics, reproductive health history, and smoking status were assessed via self-report. An individual was considered to be African American if she was born in the United States and reported she had at least three grandparents of African heritage. Similarly, participants were classified as European American if they were born in America and had at least three grandparents of Euro-Caucasian heritage. Body composition. Weight was measured to the nearest 0.25 pound using a leveled platform scale with a beam and European Journal of Clinical Nutrition


476 Table 1 Characteristics of the validation and cross-validation samples Validation sample African American (n=97) Variable

Mean (s.d.)

Age (y) 29.5 Weight (kg) 76.1 Height (cm) 164.3 2 BMI (kg/m ) 27.3 REE (kJ/day) 5835.8

Range

Cross-validation sample

European American (n=142) Mean (s.d.)

(5.8) 18–39 27.7 (18.7) 48.9–136.4 67.1 (6.8) 143.5–179.1 165.6 (6.2) 17.3–50.0 23.7 (894.4) 4164.2–8774.9 5843.4

Range

Mean (s.d.)

(5.5) 18–37 28.2 (14.7) 46.2–112.7 76.4 (6.4) 151.8–181.0 164.6 (5.0) 16.9–39.6 27.3 (813.0) 4331.8–8315.0 5729.9

moveable weights. Participants were weighed in light clothing (shorts and T-shirt) with shoes removed. Height was measured to the nearest 0.25 in using a wall-mounted stadiometer. Measures of weight and height were subsequently converted to kilograms and centimeters. BMI was calculated using a standard formula (kg/m2).

Resting energy expenditure. REE was estimated through indirect calorimetry using a Critical Care Monitor Desktop Analysis System (Medical Graphics, St Paul, MN, USA). Participants’ heads were placed in a ventilated canopy in which they breathed ambient air and exhaled into a collection tube connected to a gas analyzer. Expired air was continuously sampled in order to provide a breath-by-breath analysis of O2 consumption, CO2 production, and respiratory rate. Measurements were obtained in a thermoneutral (231C) and humidity-controlled, quiet, semidarkened environment. The calorimeter was calibrated prior to each testing session using gas mixtures of precisely known O2 and CO2 concentrations. Validation was verified on a weekly basis using the Medical Graphicss gas exchange system validator (GESV). The GESV utilizes a pump to inspire and expire a combination of atmospheric air mixed with precisely measured concentrations of calibration gas in a manner that simulates human respiration (Huszczuk et al, 1990). The system allows for a variety of combinations of tidal volume, respiratory rate, and metabolic rate in order to reproduce a wide range of physiologic states. Laboratory visits were scheduled at a uniform time of day (between 0600 and 0900). Assessments were conducted on an outpatient basis, with participants transporting themselves to the laboratory on the morning of testing sessions. Participants were instructed to fast and to refrain from exercise for at least 10 h prior to their laboratory visit, and to abstain from smoking for at least 12 h. Adherence to instructions to keep from smoking was verified by measuring alveolar carbon monoxide using a cutoff of 12 parts-permillion. Upon arriving at the laboratory, participants sat for a period of approximately 20 min while self-report measures were reviewed. Participants then were measured at rest in a supine position for a period of at least 25 min, including a European Journal of Clinical Nutrition

African American (n=108) Range

European American (n=124) Mean (s.d.)

(5.8) 18–38 26.9 (19.7) 44.0–122.0 65.7 (6.4) 142.2–178.4 165.4 (6.9) 13.8–41.9 23.3 (873.1) 4508.2–8738.9 5831.6

Range

(5.8) 18–37 (14.3) 40.1–120.6 (6.5) 149.9–182.9 (4.6) 15.7–39.1 (799.3) 4519.5–9045.7

5-min acclimation period (Isbell et al, 1991). Data from the initial 5 min of measurement, along with periods of movement by the participant, were eliminated from the calculation of mean REE. Estimates of REE per 24 h were calculated by computer from the O2 and CO2 gas exchange using the abbreviated Weir (1949) formula. REE was measured in kcal and then converted to kJ. The coefficient of variation in REE across multiple assessments for the laboratory has been measured at 5.1% (median ¼ 4.6%).

Statistical methods An equation for predicting REE was developed using multiple regression analysis. Measured REE served as the dependent variable. Age, height, weight, and ethnicity were included as independent variables using a forced entry procedure (Separate regression equations for African-American and European-American women also were considered. However, because the overall accuracy of predicted REE was greater when a single equation was utilized, this approach was chosen.). The regression equation was cross-validated in the second sample in the following manner. First, the crossvalidity of the regression equation was examined by calculating the amount of shrinkage in the predictive power of the equation (Pedhazur, 1982). This was carried out by applying the regression equation derived from the validation sample to the cross-validation sample to obtain a predicted REE for each participant. Measured REE was then regressed on predicted REE to obtain an estimate of the variance accounted for in the cross-validation sample. The adjusted R2 for the cross-validation sample was subtracted from that of the validation sample to arrive at an estimate of shrinkage, an indication of how much the predictive ability decreases when the equation is applied to other samples. Measured REE was next regressed on predicted REE using the Harris–Benedict, Mifflin–St Jeor, Owen, and Schofield equations. The relation between predicted and measured REE was examined by testing the results for each equation against the line of identity, which represents perfect agreement between predicted and measured REE (Bland & Altman,


477 1986). Equations with an intercept and slope that did not differ from 0 and 1, respectively, suggested a good fit between predicted and measured REE (Heshka et al, 1993; Finan et al, 1997). Although tests of linear relationships provide a good indication of the strength of the relationships between variables, they do not indicate the level of agreement between them (Bland & Altman, 1986). Therefore, limits-of-agreement analysis comparing predicted and measured REE also was conducted (Bland & Altman, 1986). Limits-of-agreement analysis involves calculating the bias associated with each prediction equation, defined as the difference between measured REE and predicted REE obtained from each formula. The level of precision for each equation was determined by calculating the s.d. of the difference scores. Differences in the level of bias associated with each equation were then examined following the procedures recommended by Bland (2001). Error scores for each equation were squared and then compared using pairedsamples t-tests. Since the distribution of squared difference scores was highly skewed, values were log transformed prior to analysis (Bland, 2001). To adjust for conducting multiple comparisons between prediction equations, a Bonferroni correction was applied to arrive at a revised alpha level of 0.005 (0.05/10 comparisons).

Results Participants The 471 participants included in the study averaged 28.0 y of age (s.d. ¼ 5.8; range: 18–39), weighed 70.7 kg (s.d. ¼ 17.4; range: 40.1–136.4), and had a mean BMI of 25.2 kg/m2 (s.d. ¼ 5.9; range: 13.8–50.0). REE averaged 5813 kJ/day (s.d. ¼ 839; range: 4164–9046). Approximately 43% of participants reported taking birth control pills, while 1% used Depo Provera or a Norplant implant. A larger percentage of European Americans (47.9%) than African Americans (35.6%) reported using birth control pills (w2 (1) ¼ 7.17, P ¼ 0.007). Most participants (98.5%) had obtained their high school diploma, and 85.5% had attended college. In total, 52% had a family income of o$25 000. Among all participants, 40% were married, and 14% were smokers.

Prediction equation The regression model generated from the validation sample accounted for approximately half of the variance in measured REE (adjusted R2 ¼ 0.51, Po0.001). Each of the variables included in the equation provided a significant independent contribution to the model (P’so0.05). Not surprisingly, the best predictor of REE was body weight (squared partial correlation (pr2) ¼ 0.448). Interestingly, of the remaining variables, ethnicity demonstrated the next strongest relationship to REE (pr2 ¼ 0.045), followed by height (pr2 ¼ 0.042) and age (pr2 ¼ 0.018).

The results of the multiple regression analysis produced the following equation for predicting REE in kJ/day: Predicted REE ðkJ=dayÞ ¼616:93 14:9 ðAGE ðyÞÞ þ 35:12 ðWT ðkgÞÞ þ 19:83 ðHTðcmÞÞ 271:88 ðETHNICITYÞ where 1 ¼ African American and 0 ¼ European American. For predicting REE in kcal/day, the corresponding equation is as follows: Predicted REE ðkcal=dayÞ ¼147:45 3:56ðAGEÞ þ 8:39ðWTÞ þ 4:74ðHTÞ 64:98 ðETHNICITYÞ

Cross-validation of prediction equation We next examined how well the formula predicted REE in a separate sample, and how its predictive ability compares to established equations. This was accomplished by first examining the amount of variance accounted for in the cross-validation sample. The amount of shrinkage when the prediction formula was applied to the cross-validation sample was minimal (0.08), indicating that it provided a good estimate of measured REE in this sample, and suggesting that it can be considered reliable. The relationship between REE predicted from each equation and measured REE was investigated through simple regression analysis to determine the amount of variance accounted for by each formula, and by testing the slope and intercept against 1 and 0, respectively. Results are presented in Table 2. The new equation, hereafter referred to as the University of Memphis equation, did not differ from the line of identity for either group, suggesting a good relationship between measured and predicted REE. Of the other prediction equations, only the Owen formula did not deviate significantly from the line of identity for either African Americans or European Americans. The slope for the Harris– Benedict equation differed from 1 for African-American women, suggesting that the accuracy of the prediction equation varied as a function of measured REE. For the Mifflin–St Jeor and Schofield equations, the slope and intercept both differed significantly from 1 and 0, respectively, for both groups.

Limits-of-agreement analysis The results of the limits-of-agreement analysis are presented in Table 3, which shows the bias and precision for each equation according to ethnicity. The absolute percent error of each of the formulae, along with the percentage of predicted values that fell within 710% of measured REE, a level commonly used to determine the accuracy of prediction equations (Glynn et al, 1999; Foster & McGuckin, 2001), also are included. The University of Memphis equation, which demonstrated good predictive value for both AfricanEuropean Journal of Clinical Nutrition


478 Table 2 Comparison of each prediction equation to the line of identity (n=232) Prediction equation

Intercept (kJ/day)

University of Memphis African American European American Harris–Benedict (1919) African American European American Owen et al (1986) African American European American Mifflin–St Jeor (1990) African American European American Schofield et al (1985) African American European American

Slope (95% CI)

Adjusted R2

419.1 1038.5

0.90 (0.75–1.06) 0.83 (0.61–1.04)

0.55** 0.31**

299.6 874.3

0.83 (0.69–0.97)* 0.81 (0.60–1.01)

0.57** 0.33**

267.1 255.8

1.07 (0.87–1.26) 1.05 (0.78–1.33)

0.52** 0.31**

1020.3* 1848.9**

0.76 (0.63–0.88)** 0.68 (0.50–0.86)**

0.56** 0.31**

1638.0** 2190.0**

0.63 (0.53–0.74)** 0.61 (0.44–0.77)**

0.57** 0.29**

*

Po0.05; **Pp0.001.

American and European-American women, was the only formula to provide accurate estimates of REE for both groups. The Mifflin–St Jeor equation was highly accurate for predicting energy needs in European-American women, but was considerably less accurate for African-American women. The Schofield and Harris–Benedict equations also were considerably less accurate at predicting REE among AfricanAmerican women. The opposite pattern was observed using estimates derived from the Owen equation, which was highly accurate among African-American women, but which significantly underestimated REE among European-American women. Comparisons of the squared error scores for each prediction equation revealed the following. Among EuropeanAmerican women, error rates did not differ significantly between any of the prediction equations (all P’s40.10). For African-American women, the University of Memphis equation was associated with a lower level of error than the Harris–Benedict, Mifflin–St Joer, and Schofield equations (P’so0.005), but did not differ from the Owen equation

(P ¼ 0.68). The Owen equation produced an error rate that was below that of both the Harris–Benedict and Schofield equations (P’s o0.001), and marginally lower than that of the Mifflin–St Joer equation (P ¼ 0.013). Finally, the error associated with the Mifflin–St Joer equation was significantly lower than that of the Harris–Benedict equation (Po0.001). None of the other paired comparisons between prediction equations was significant. For a prediction equation to be most useful, it must provide accurate estimates across a broad range of REE. To determine whether the accuracy of the new prediction equation varied as a function of REE, the bias associated with predicted REE was plotted against the mean REE values (ie, (measured REE þ predicted REE)/2). The results are presented in Figure 1. The reference lines represent the mean error (bias) and the limits of agreement, defined as 72 s.d. from the mean (Bland & Altman, 1986). Values outside of this range represent individuals for whom the prediction equation did not accurately estimate REE. A slightly negative association between the bias associated with the University of Memphis equation and mean REE is evident from the graph. Overall, it appears that the equation was generally accurate across a broad range of REE values. However, predicted values that were outside of the limits of agreement appeared to be slightly more common among individuals at the upper range of REE. This suggests that there may be a slight tendency for REE predicted from the University of Memphis equation to be underestimated among those with very high levels of REE.

Discussion This study compared the accuracy of a new equation for predicting REE in a biethnic sample of African-American and European-American women against several previously developed formulae. Overall, the new equation, which included adjustments for ethnicity, was the only formula that was accurate at predicting REE in both African-American and European-American women. Although the equation developed by Owen et al (1986) was highly accurate among African-American participants, and the Mifflin–St Jeor

Table 3 Bias, precision, and percent error of prediction equations by ethnicity for the cross-validation sample African American (n=108)

Prediction equation University of Memphis Harris–Benedict (1919) Mifflin–St Jeor (1990) Owen et al (1986) Schofield et al (1985) a

Biasa (kJ) 142.2 801.9 508.2 101.0 763.6

Precisionb (kJ) 584.2 588.3 616.1 604.8 690.2

% Error

% Values accurate within 710%c

Bias (kJ)

Precision (kJ)

% Error

% Values accurate within 710%

8.0 15.6 11.4 7.5 15.1

67.6 35.2 52.8 74.1 33.3

27.7 302.7 7.4 525.0 163.2

666.7 660.6 693.4 659.9 726.3

8.9 10.3 9.1 10.2 10.0

65.3 55.6 63.7 54.0 53.2

Mean difference between measured and predicted REE. s.d. of the bias. c Percentage of predicted values that were within 710% of measured REE. b

European Journal of Clinical Nutrition

European American (n=124)


479

Figure 1 Degree of bias of the University of Memphis prediction equation at different levels of REE (n ¼ 232).

(Mifflin et al, 1990) formula provided good estimates of REE among European-American women, both equations provided biased estimates of REE in the other ethnic group. The Schofield et al (1985) and Harris–Benedict (1919) equations also were considerably more accurate among EuropeanAmerican than African-American women. These results highlight the importance of considering ethnicity when estimating energy needs. Numerous studies have reported lower levels of energy expenditure in AfricanAmerican compared to European-American women (Weyer et al, 1999; Gannon et al, 2000; Sharp et al, 2002), suggesting greater energy efficiency and, perhaps, reduced energy needs in this group. Equations that fail to consider ethnicity may result in inappropriate nutritional recommendations. Considering that the most widely used equations have been based on samples of primarily European heritage, estimates of REE in African-American women are likely to be overestimated. This study has several positive features worth noting. First, the prediction equation developed in this study is the first, to our knowledge, to provide adjustments for ethnicity based on differences in REE between African-American and European-American women. Second, evidence supporting the accuracy of the prediction equation was obtained by cross-validating the formula in a separate sample. Third, the study included women representing a broad range of body weight, which may increase its generalizability to other samples. Finally, the effects of several potentially important confounders, such as menstrual cycle, menopausal status, pregnancy/lactation, medical conditions, and the thermogenic effects of food and nicotine, were carefully controlled. There are, however, several limitations to the present study. First, the investigation was restricted to women.

Whether equations for estimating REE in men should be adjusted for ethnicity is unclear, and should be the focus of future study. Second, the sample was limited to women between the ages of 18 and 39 y. The predictive value of the equation for estimating REE among older women is uncertain. The impact of ethnicity on the accuracy of prediction equations that have been developed for older women (eg, Arciero et al, 1993) should be the focus of future investigation. Third, the study included only EuropeanAmerican and African-American women. Studies of other racial and ethnic groups have similarly demonstrated ethnic differences in REE (Benedict, 1932; Henry & Rees, 1991). Future studies should examine whether equations for predicting REE should be modified for use in other ethnic groups. Additionally, although the University of Memphis prediction equation provided good estimates of resting energy needs, there was still a nontrivial amount of variance in REE left unaccounted. Nevertheless, the variance in REE accounted for by the prediction equation was consistent with previous studies. In addition, REE was measured on an outpatient basis, which may slightly overestimate REE compared to in-patient assessments (Berke et al, 1992). The equation also demonstrated a slight tendency to underestimate REE among women at the upper range of REE. As a result, estimates of REE based on this equation may not be as accurate for women who are overweight or obese. Another limitation was that menstrual cycle phase was determined by self-report rather than measures of hormone levels or body temperature, which may have introduced variability in the timing of laboratory assessments. Finally, while the prediction equation, on average, provided good estimates of REE for both groups, it was, like all prediction equations, less accurate at predicting REE at the individual level. Consequently, the fact that it may accurately predict the mean REE for a sample does not ensure that it will be accurate for a given individual (Foster & McGuckin, 2001).

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