Equations describing percentiles for birth weight, head circumference, and length of preterm infants

Abstract

Charts to describe the appropriate growth of children who completed 37 weeks of gestation were standardized by the World Health Organization (WHO) almost 30 years ago.1 Besides being used by health care providers to track growth, the information obtained from growth charts can be used as a basis in epidemiologic research and for allocation of resources. Normative data to describe appropriate growth of prematurely born infants have not been established. An expert committee of the WHO2 recommended using the birth weight curves reported by Williams3 for classifying premature infants as small for gestational age (SGA), appropriate for gestational age (AGA), or large for gestational age (LGA). However, Williams' curves do not describe the infants from the neonatal intensive care unit (NICU) at Vanderbilt University Medical Center (VUMC). The growth charts used in most neonatal intensive care units today are derived from studies of predominantly white, middle class, liveborn infants born prematurely during the time from 1948 to 1966.4, 5, 6, 7 These studies lacked cultural diversity and had small numbers of infants with gestational ages less than 29 weeks. These early growth charts are not suitable when evaluating the growth of extremely premature infants. The purpose of this study was to use retrospective data from our NICU to create a growth chart adequate to assess growth of infants with less than 29 completed weeks of gestation. With the approval of the Institutional Review Board at Vanderbilt University Medical Center, we retrieved and analyzed birth measurements of all infants of 37 weeks of completed gestation that were admitted to the regional NICU at VUMC from 1985 through 1997. These were from a longitudinal database maintained by the neonatology division. There were 7425 liveborn preterm infants (including 1234 infants of less than 29 weeks of gestation) with 89% singleton, 55% male, 76% Caucasian, 18% African American and 6% other races. Birth weight was recorded for all of the infants, head circumference was recorded for 90% of the group, and length was recorded for 89%. Birth weight, head circumference and length were measured by the admitting nurse while gestational age, gender and race were assigned by the admitting neonatologist. Birth weight (BW) was measured in grams with an electronic scale; head circumference (HC) and length (LEN) were measured in centimeters with a paper tape. Gestational age (GA), expressed in completed weeks,8 was assigned after evaluating the maternal history and assessing the infant. Race was based on the mother's race. The data were exported into an Excel spreadsheet and sorted by weeks of gestation. After determining that the values for BW, HC and LEN were normally distributed at each week of gestation, we calculated percentiles for each measurement. Percentile values were chosen rather than mean and s.d. because percentiles are less susceptible to occasional outlier values. Based on the recommendations of a report by a WHO Expert Committee,2 we have reported the 3rd, 5th, 10th, 15th, 25th, 50th, 75th, 85th, 90th, 95th and 97th percentiles. In comparison, when mean and s.d. measures are provided, one s.d. from the mean represents the 16th and 84th percentiles and two s.d. from the mean represents the 2nd and 98th percentiles. These percentile values were then used for mathematical modeling. Mathematical models are used to summarize and smooth data, and have been used in prior investigations of growth.9, 10 We evaluated several mathematical models: exponential (y=a exp(b x)), power (y=a xb), linear (y=a x+b), quadratic (y=a x2+b x+c) and cubic (y=a x3+b x2+c x+d). An exponential function analysis fits a linear function to semi-logarithmic data (logarithm Y axis) and a power function analysis fits a linear function to full-logarithmic data (logarithm X and Y axes). Regression analyses utilizing least squares methods were used to define the coefficients of each mathematical model. The mathematical models were evaluated with SAS statistical software to calculate the Akaike's Information Criterion11 and the Bayesian Information Criterion.12 The 3rd, 5th, 10th, 15th, 25th, 50th, 75th, 85th, 90th, 95th and 97th percentiles for birth weight are provided in Table 1. Based on the Akaike and Bayesian Information Criteria, the exponential function was the best model for birth weight. The percentiles for BW were fit to the following function: where GA is gestational age in weeks, A has units of grams and B is the growth velocity for birth weight in units of grams/day per kilogram of body weight. The growth rate (the first derivative of Equation (1)), in terms of g/day, has the following form: Dividing Equation (2) by Equation (1) (in kg) will produce the constant B at all gestational ages. To calculate the growth velocity with the exponential model, the daily weight gain (in grams) is divided by current weight (in kilograms). The 3rd, 5th, 10th, 15th, 25th, 50th, 75th, 85th, 90th, 95th and 97th percentiles for head circumference and length are provided in Tables 2 and 3. Based on the Akaike and Bayesian Information Criteria, power functions best described head circumference and length. When the power functions for the 50th percentile of HC and LEN were compared to the linear functions with zero intercept, the largest difference between the two models was 1 mm. The simpler linear model with zero intercept was selected to describe HC and LEN and the percentiles were fit to the following functions: where GA is gestational age in weeks, C is the growth velocity for head circumference in cm/week, and D is the growth velocity for length in cm/week. We determined the constants of the modeling equations for the 3rd, 5th, 10th, 15th, 25th, 50th, 75th, 85th, 90th, 95th and 97th percentiles and values of A, B, C and D are given in Table 4. Figures 1, 2 and 3 show the best-fit equations for the percentiles for birth weight, head circumference and length and the 10th,...