American Journal of Epidemiology Advance Access originally published online on January 29, 2008
American Journal of Epidemiology 2008 167(6):653-666; doi:10.1093/aje/kwm348
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PRACTICE OF EPIDEMIOLOGY |
Determination of Blood Pressure Percentiles in Normal-Weight Children: Some Methodological Issues
1 Channing Laboratory, Brigham and Women's Hospital and Harvard Medical School, Boston, MA
2 University of Texas at Houston Health Science Center, University of Texas, Houston, TX
3 University of Colorado at Denver and Health Sciences Center, University of Colorado, Denver, CO
4 Department of Medicine, Jefferson Medical College, Thomas Jefferson University, Philadelphia, PA
Correspondence to Dr. Bernard Rosner, Channing Laboratory, Brigham and Women's Hospital and Harvard Medical School, 181 Longwood Avenue, Boston, MA 02115 (e-mail: bernard.rosner{at}channing.harvard.edu).
Received for publication February 7, 2007. Accepted for publication November 5, 2007.
| ABSTRACT |
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Blood pressure in children has consistently been related to adult blood pressure, with implications for long-term prevention of cardiovascular disease. The epidemic of obesity in children has resulted in corresponding increases in childhood blood pressure. In this paper, the authors develop norms for childhood blood pressure among normal-weight children (body mass index <85th percentile based on Centers for Disease Control and Prevention guidelines) as a function of age, sex, and height, using data from 49,967 children included in the database of the National High Blood Pressure Education Program Working Group on High Blood Pressure in Children and Adolescents (the Pediatric Task Force). The authors considered three types of models for pediatric blood pressure data, including polynomial regression, restricted cubic splines, and quantile regression, with the latter providing the best fit. The sex-specific norms presented here are a nonlinear function of both age and height and are generally slightly lower than previously developed norms based on Pediatric Task Force data including both normal-weight and overweight children.
blood pressure; child; models, statistical; pediatrics; regression analysis
Abbreviations: CDC, Centers for Disease Control and Prevention; CI, confidence interval; DBP, diastolic blood pressure; NHANES, National Health and Nutrition Examination Survey; OR, odds ratio; SBP, systolic blood pressure
| INTRODUCTION |
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An important trend in pediatrics is incorporation of the measurement of blood pressure in the standard pediatric examination. Recent guidelines published in the Fourth Report on the Diagnosis, Evaluation, and Treatment of High Blood Pressure in Children and Adolescents (1) provide standards for accomplishing this goal. The report supplies tables of blood pressure percentiles based on the database created by the National High Blood Pressure Education Program Working Group on High Blood Pressure in Children and Adolescents (hereafter called the Pediatric Task Force), consisting of 63,227 children seen at 83,091 physician visits over the course of 11 studies. The estimated 50th, 90th, 95th, and 99th percentiles of blood pressure are given by sex, year of age (1–17 years), and height percentile (5th, 10th, 25th, 50th, 75th, 90th, and 95th) for both systolic blood pressure (SBP) and diastolic blood pressure (DBP) (Korotkoff 5).
A decision made in constructing these tables was that although weight or body mass index is an important predictor of blood pressure in both children and adults, percentiles should not be provided as a function of weight, so as to not encourage relatively high blood pressure to be considered normal just because a child is overweight or obese. However, overweight children were still included in the normative database. A resulting issue that arises is that norms for blood pressure will continue to increase as the level of obesity changes over time. For the current report, we modified the definition of the normative database to exclude children who were either overweight (body mass index (weight (kg)/height (m)2) >95th percentile) or at risk of becoming overweight (body mass index 85th–95th percentile) (2) on the basis of 2000 Centers for Disease Control and Prevention (CDC) growth charts (3), and we redefined blood pressure percentiles using this more restrictive database. The data used for the 2000 CDC growth charts were based on reference data sets from National Health Examination Survey II (1963–1965), National Health Examination Survey III (1966–1970), the Second National Health and Nutrition Examination Survey (NHANES II; 1976–1980), and the Third National Health and Nutrition Examination Survey (NHANES III; 1988–1994) and hence were roughly contemporary with the time period of the 11 studies used in the Pediatric Task Force report (1). We also explored several different analytic strategies for estimating blood pressure percentiles.
| MATERIALS AND METHODS |
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In the Pediatric Task Force database (1), we had data available from 11 large pediatric blood pressure studies (4–18). Furthermore, the age distribution varied considerably in different studies and there were some differences in measurement techniques among studies, although all measurements were made with mercury manometers. In addition, although most studies provided cross-sectional data, other studies provided blood pressure data obtained at more than one age for a given child. Finally, the number of readings available per child varied by study. Some studies provided data from multiple readings taken at a single visit for a child, while other studies only provided data from one reading. For the sake of uniformity, we based all analyses on the first reading only. Even after accounting for age differences between studies, there were obvious study effects. We considered three different analytic approaches for relating blood pressure to age and height: polynomial regression, restricted cubic splines, and quantile regression.
Polynomial regression models
We first estimated the study effects by expressing blood pressure (BP) as a sex-specific fourth-degree polynomial function of age, height (ht) z score, and weight (wt) z score, as follows:
![]() | (1) |
N(0,
2) and Corr(eim1,eim2)=
. The study effect estimates
1,...,
G were then used to estimate the blood pressure that would be obtained in a particular child if that child were from an average study by computing the adjusted blood pressure, given by
![]() | (2) |
![]() | (3) |
N(0,
2*). The pth percentile of blood pressure for a child of age x and height z score Zht is then estimated by
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An advantage of equation 3 is that although the distribution of height varies greatly with age, the distribution of Zht does not, thus allowing one to estimate blood pressure percentiles as a function of age and height with a relatively simple polynomial model across a wide age range. However, a disadvantage of equation 3 is the assumption that the difference in average blood pressure between two children of the same age with height z scores of Z1 and Z2 is independent of age and is given by
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Restricted cubic spline models
To build a more flexible model, we fitted a restricted cubic spline model (19). Under this model, each predictor variable is modeled using a restricted cubic spline representation with five knots which correspond to the 5th, 27.5th, 50th, 72.5th, and 95th percentiles, respectively, over the entire pediatric age range, as suggested by Harrell (20). To assess study effects, we first fitted a restricted cubic spline model of the form
![]() | (5) |
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N(0,
2**),Corr(e
,e
)=
,x+=xif x>0 and x+=0 if x
0, xim,j and him,k are defined as above, zim=zim,1=(ageim–10)x(htim–
z1, ..., z5 are the knots for (age – 10)(ht –
) and
= mean height over all children of a given gender. Restricted cubic splines (also referred to as natural splines) are constrained to be linear for values less than the first knot and greater than the last knot and may provide a better fit than unrestricted cubic splines, which sometimes behave poorly in the tails (19). These models are more flexible than simply adding interaction effects of age x Zht to equation 3, since the shape of the function relating blood pressure to age and/or height is allowed to change over the range of each variable.
Quantile regression models
An assumption of the model shown in equation 6 is that the distribution of blood pressures is assumed to be normal, which implies that the effects of age and height are the same for all quantiles of blood pressure. To relax this assumption, we also considered quantile regression methods (21). To implement these methods, a separate regression is run for each quantile
and the vector of parameters
that minimize
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(g)=gx[
–I(g<0)] and I(a) = 1 if a is true and 0 if a is false. The regression is estimated using PROC QUANTREG in SAS (SAS Institute, Inc., Cary, North Carolina). Thus, the assumption of normality of the residuals is not necessary for quantile regression.
We ran these regressions for each of
= 0.01, 0.05, 0.10, 0.25, 0.50, 0.75, 0.90, 0.95, and 0.99, where
are defined in equation 6. Thus, a separate set of regression coefficients
is obtained for each
. The quantile regression approach using separate restricted cubic splines for prediction for each quantile offers the most flexibility in terms of both specification of the regression function for a specific quantile and allowing for separate regression equations for different quantiles.
Assessing goodness of fit
To assess the goodness of fit of the polynomial regression approach shown in equation 3, the restricted cubic spline approach shown in equation 6, and the quantile regression approach shown in equation 7, we subdivided the data for each age according to sex-specific predicted blood pressure percentile, divided at 1 percent, 5 percent, 10 percent, 25 percent, 50 percent, 75 percent, 90 percent, 95 percent, and 99 percent, where the cutpoints were included in the upper segment. For each sex, we then compared the observed distribution of children in these blood pressure percentile groups with the expected distribution for each 1-year age group, combined the data into three age groups (1–5 years, 6–10 years, and 11–17 years) separately for boys and girls, and performed a chi-square goodness-of-fit test for each method within each of the six age-sex groups.
| RESULTS |
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The Pediatric Task Force data were derived from 11 pediatric studies (4–18). Details on the design of these studies have been previously published (1). We included children from this database in this analysis only if their body mass index percentile was less than the 85th percentile for their 1-year age-sex group (2) based on the CDC growth charts (3). Demographic data for the study population are provided in table 1.
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The age range was 1–17 years, with heterogeneous age distributions in different studies and a broad range of ethnicities over the 11 studies, which is similar to the entire Pediatric Task Force database. Approximately 21 percent of physician visits were excluded because the body mass index was
85th percentile, with the percentage excluded being notably higher in the later studies (NHANES III and NHANES 1999–2000). Results from the polynomial regression models (equation 3) are presented separately for boys and girls in table 2. As expected, age and height z score were strong predictors of SBP and DBP for both boys and girls (p < 0.001). To allow better understanding of the relation of blood pressure to height, we display in figure 1 the predicted 90th percentile of blood pressure (prehypertensive level) by height z score for children aged 5, 10, and 15 years, separately for boys and girls. Prehypertensive blood pressure level appears to be an approximately linear function of height z score for a given age group. In addition, in figure 2 we plot the prehypertensive level by age for children at the 10th, 50th, and 90th height percentiles. The prehypertensive level shows a curvilinear increase with age, with the highest slope appearing in early childhood and adolescence and a more moderate rate of increase being evident in late childhood.
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An advantage of this approach is that the blood pressures of children of different ages can be easily accommodated in a relatively simple polynomial model. The disadvantage is that based on equation 3, the mean difference in blood pressure for two children with height z scores of Zht and Zht2 are the same for all ages. To test this assumption, we conducted additional analyses including interaction terms of (age – 10) x Zht, (age – 10) x Zht2, (age – 10) x Zht3, and (age – 10) x Zht4 for all of the models in table 2. There were significant interaction effects for three of the four models (SBP in boys: for (age – 10) x Zht, p = 0.025; SBP in girls: for (age – 10) x Zht, p = 0.002; DBP in boys: for (age – 10) x Zht, p = 0.051, and for (age – 10) x Zht2, p = 0.034).
To provide a more flexible model, we represented age, height, and age x height using restricted cubic splines, as given in equation 6. The resulting sex-specific models are presented in table 3. For illustration of the relations, plots of the prehypertensive level (
90th percentile) of SBP and DBP by age are presented by percentile of height in figure 3. The differences in prehypertensive level between the 10th and 90th percentiles of height vary somewhat by age for SBP in females and are noticeably different by age for DBP in both boys and girls.
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A limitation of the polynomial models shown in equation 3 and the spline models shown in equation 6 is that they assume that the distribution of blood pressures is normal with the same variance for all combinations of age and height. To relax this assumption, we fitted the quantile regression model in equation 7 separately by sex for the 1st, 5th, 10th, 25th, 50th, 75th, 90th, 95th, and 99th percentiles of blood pressure. The regression coefficients are given in Appendix tables 1–4. Plots of the quantile regression results for the 90th percentile of blood pressure by age and height percentile are given in figure 4.
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In general, blood pressure increased with both age and height percentile, albeit in a nonlinear manner. For DBP, effects of height were smallest at the onset of puberty (ages 10–12 years) and largest for younger children and older adolescents. In addition, effects of height tended to be larger for boys than for girls. Table 4 shows the 90th percentile of blood pressure by height percentile in 1-year age-sex-specific groups. A complete table of the 1st, 5th, 10th, 25th, 50th, 75th, 90th, 95th, and 99th percentiles of blood pressure by height percentile in 1-year age-sex groups (Web table 1) is given on the Journal's website (http://aje.oxfordjournals.org/) and at the following website: http://www.geocities.com/bernardrosner/Pediatrics.html.
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Prehypertensive levels (
90th percentile) for normal-weight adolescents (ages 13–17 years) ranged from 115 mmHg to 134 mmHg for SBP in boys, from 116 mmHg to 125 mmHg for SBP in girls, from 74 mmHg to 83 mmHg for DBP in boys, and from 75 mmHg to 78 mmHg for DBP in girls, which fits in well with the customary definition for hypertension of 140/90 mmHg for adults. Comparable levels for the Pediatric Task Force data (1) based on normal-weight and overweight children were: for SBP in boys, 118–135 mmHg; for SBP in girls, 118–127 mmHg; for DBP in boys, 75–84 mmHg; and for DBP in girls, 76–81 mmHg. These levels are slightly higher than those based on normal-weight children only. In addition, normative values vary widely by height among children of the same age (SBP in boys, 6–11 mmHg; SBP in girls, 5–7 mmHg; DBP in boys, 3–6 mmHg; and DBP in girls, 1–2 mmHg). To assess goodness of fit, we compared the observed and expected percentages of children in different blood pressure percentile groups by age (1–5, 6–10, and 11–17 years) and sex for both SBP and DBP for both the spline and quantile regression models. Web table 2, which is posted on the Journal's website (http://aje.oxfordjournals.org/), displays the observed number and percentage of children falling into each percentile category, along with the percentage expected. For each age group, the goodness of fit of the quantile regression model (Q) is generally excellent, with no significant difference between observed and expected counts. Conversely, the restricted cubic spline models (S) consistently showed a poor goodness of fit. The assumption of normality was inappropriate for both SBP, which was generally positively skewed, and DBP, which was generally negatively skewed.
In the preceding analyses in this paper, we considered SBP and DBP separately. However, the determination of prehypertension is based on both SBP and DBP and is defined as blood pressure at or above the 90th percentile for either SBP or DBP. In table 5, we present the numbers and percentages of children who were at or above the 90th percentile for SBP and DBP separately and in combination, as well as the percentage of prehypertensive children. These data were calculated for both the normal-weight Pediatric Task Force children (body mass index <85th percentile) included in this report and the overweight Pediatric Task Force children (body mass index
85th percentile) who were excluded from this report.
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Among normal-weight children, 10 percent of children had SBP
90th percentile, 10 percent of children had DBP
90th percentile, 3 percent had both SBP and DBP
90th percentile, and 18 percent were prehypertensive (either SBP or DBP
90th percentile), on the basis of a single visit. The prevalence of prehypertension was significantly higher for overweight children (odds ratio (OR) = 2.3, 95 percent confidence interval (CI): 2.2, 2.4) than for normal-weight children, as was the prevalence of elevated SBP (OR = 2.8, 95 percent CI: 2.6, 2.9), elevated DBP (OR = 1.9, 95 percent CI: 1.8, 2.0), and elevation of both SBP and DBP (OR = 3.2, 95 percent CI: 3.0, 3.5). | DISCUSSION |
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The development of norms for pediatric blood pressure is challenging because of the nonlinear relation between blood pressure levels and both age and height. Several functional forms were considered in this analysis. We determined that the use of the quantile regression model offered the most flexibility and the best fit of the models considered. The methods presented in this paper are somewhat different from the penalized likelihood LMS (lambda-mu-sigma) methods of Cole and Green (22, 23) that are used to estimate height and weight quantiles for pediatric growth data. However, Wei et al. (24) performed a study comparing quantile regression methods for fitting pediatric growth data and the LMS methods; the results indicated very similar estimated quantiles using these two approaches. An advantage of the quantile regression approach is that it is relatively easy to incorporate covariates into the analysis of growth data. In the setting in this paper, this involves estimating blood pressure quantiles as a nonlinear function of both age and height. Quantile regression has also been used to accurately assess the effects of early-life risk factors on adult body size, where adult body size is characterized by body mass index at 20 and 40 years of age (25). In general, quantile regression would be expected to be a useful analytic tool with which to study adult body mass index, which is almost always nonnormally distributed.
Another issue is that although weight is a major determinant of blood pressure in both children and adults, it is important to not raise the norm for blood pressure in an overweight child. Hence, we restricted the normative population to include normal-weight children only. Thus, the prehypertensive and hypertensive levels in this report are slightly lower than those previously published (1), which included both normal-weight and overweight children. The one exception to this rule occurs for the youngest children (ages 1–2 years), for whom the levels in this report are higher for the shortest children because of the relaxation of the criterion that the difference in mean blood pressure by z score of height is the same for all age groups.
In addition, although all studies used mercury manometers in the measurement of blood pressure, there were obvious study effects. We chose to base the norms on children from an "average" study. Whether these norms are also appropriate for oscillometric blood pressure readings remains an open question which can best be addressed by studies including both oscillimetric and mercury readings taken in the same children. Another issue is that blood pressure varies considerably in children, and it is not uncommon to find children who are prehypertensive (
90th percentile) or hypertensive (
95th percentile) at one physician visit and normotensive at a second visit. The present guidelines require confirmation of a prehypertensive or hypertensive level of blood pressure on three separate occasions (1). Whether this approach is the most efficient method of identifying prehypertensive and hypertensive children remains an open question.
APPENDIX TABLE 1. Regression coefficients for systolic blood pressure in boys, obtained from quantile regression models using Pediatric Task Force data (33,383 physician visits)
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APPENDIX TABLE 2. Regression coefficients for systolic blood pressure in girls, obtained from quantile regression models using Pediatric Task Force data (32,056 physician visits)
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APPENDIX TABLE 3. Regression coefficients for diastolic blood pressure (Korotkoff 5) in boys, obtained from quantile regression models using Pediatric Task Force data (22,897 physician visits)
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APPENDIX TABLE 4. Regression coefficients for diastolic blood pressure (Korotkoff 5) in girls, obtained from quantile regression models using Pediatric Task Force data (22,120 physician visits)
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| ACKNOWLEDGMENTS |
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This work was supported by National Institutes of Health grant HL40619.
The authors acknowledge Marion McPhee for programming assistance and Shelly Magno and Lisa Ottaviani for administrative assistance.
Conflict of interest: none declared.
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