Computing the Z Score and Centiles for Cross‐sectional Analysis: A Practical Approach

Abstract

Although Z scores have been reported in the literature, one of the problems for the nonstatistician is understanding the systematic approach used to compute the predicted mean and standard deviation, components of the Z score equation, which may vary as the independent variable changes over time (eg, gestational age). This review focuses on a step-by-step analysis using linear, quadratic, and fractional polynomials to compute the mean and standard deviation as a function of a continuous independent variable. Once the mean and standard deviation are computed, the Z score and centile can be derived and Z score calculators created that enable investigators to implement the results in the laboratory and/or clinical setting.

Evaluation of the right and left ventricles: An integrated approach measuring the area, length, and width of the chambers in normal fetuses

“…Two hundred control fetuses with accurate first‐ and/or second‐trimester dating ultrasound were examined between 20 and 40 weeks of gestation to create a normal distribution between these GAs. The fetuses were not at risk for congenital heart defects or growth restriction and were free from ultrasound‐detected malformations and growth disturbance at the time of the examination . The 200 fetuses were the same cohort used in previous studies from our group .…”

Speckle Tracking of the Basal Lateral and Septal Wall Annular Plane Systolic Excursion of the Right and Left Ventricles of the Fetal Heart

“…While computing P values between control fetuses and those with suspected abnormalities (intrauterine growth restriction, twin‐to‐twin transfusion, or structural malformation) provides insight regarding differences in fetuses categorized by disease, this approach does not allow the examiner to categorize a single fetus suspected of having cardiac dysfunction. To categorize such a fetus, reference intervals must be computed from the control group . This can only be accomplished only by computing the mean and standard deviation, followed by derivation of z score values and their equivalent centile values in fetuses with suspected abnormalities .…”

“…The gestational age determined from the last menstrual period was compared to the mean ultrasound gestational age at the time of the examination using Pearson's correlation confidence interval analysis (NCSS 11, Kaysville, UT). The lateral and septal wall APSE values were regressed against independent somatic growth and age variables (head circumference [HC], biparietal diameter [BPD], abdominal circumference [AC], femur length [FL], estimated fetal weight [EFW], ultrasound mean gestational age, and the clinical gestational age) using a curve‐fitting program previously described (NCSS 11) . The Shapiro‐Wilk normality test was used to determine if the data were normally distributed ( P > .05) between the ranges studied for the biometric and gestational age variables .…”

“…The lateral and septal wall APSE values were regressed against independent somatic growth and age variables (head circumference [HC], biparietal diameter [BPD], abdominal circumference [AC], femur length [FL], estimated fetal weight [EFW], ultrasound mean gestational age, and the clinical gestational age) using a curve‐fitting program previously described (NCSS 11) . The Shapiro‐Wilk normality test was used to determine if the data were normally distributed ( P > .05) between the ranges studied for the biometric and gestational age variables . Within subject repeated measures of variance (NCSS 11) was used to compare matched lateral and septal APSE results within and between right and left ventricles for the 200 fetuses.…”

Correlation Between the Thymic‐Thoracic Ratio and Cardiac Axis in Healthy Fetuses

“…A simple linear fit model was used to calculate the thymic‐thoracic ratio cur , the residue of which was used to calculate the SD cur . Details of this conversion were introduced in an article by DeVore …”