The impact of random-effect misspecification on percentile estimation for longitudinal growth data

Exploratory assessment of treatment-dependent random-effects distribution using gradient functions

In analyzing repeated measurements from randomized controlled trials with mixed-effects models, it is important to carefully examine the conventional normality assumption regarding the random-effects distribution and its dependence on treatment allocation in order to avoid biased estimation and correctly interpret the estimated random-effects distribution. In this article, we propose the use of a gradient function method in modeling with the different random-effects distributions depending on the treatment allocation. This method can be effective for considering in advance whether a proper fit requires a model that allows dependence of the random-effects distribution on covariates, or for finding the subpopulations in the random effects.

Fetal growth velocity: the NICHD fetal growth studies

BACKGROUND

Accurately identifying pregnancies with accelerated or diminished fetal growth is challenging and generally based on cross-sectional percentile estimates of fetal weight. Longitudinal growth velocity might improve identification of abnormally grown fetuses.

OBJECTIVE

We sought to complement fetal size standards with fetal growth velocity, develop a model to compute fetal growth velocity percentiles for any given set of gestational week intervals, and determine association between fetal growth velocity and birthweight.

STUDY DESIGN

This was a prospective cohort study with data collected at 12 US sites (2009 through 2013) from 1733 nonobese, low-risk pregnancies included in the singleton standard. Following a standardized sonogram at 10w0d-13w6d, each woman was randomized to 1 of 4 follow-up visit schedules with 5 additional study sonograms (targeted ranges: 16-22, 24-29, 30-33, 34-37, and 38-41 weeks). Study visits could occur ± 1 week from the targeted GA. Ultrasound biometric measurements included biparietal diameter, head circumference, abdominal circumference, and femur length, and estimated fetal weight was calculated. We used linear mixed models with cubic splines for the fixed effects and random effects to flexibly model ultrasound trajectories. We computed velocity percentiles in 2 ways: (1) difference between 2 consecutive weekly measurements (ie, weekly velocity), and (2) difference between any 2 ultrasounds at a clinically reasonable difference between 2 gestational ages (ie, velocity calculator). We compared correlation between fetal growth velocity percentiles and estimated fetal weight percentiles at 4-week intervals, with 32 (±1) weeks' gestation for illustration. Growth velocity was computed as estimated fetal growth rate (g/wk) between ultrasound at that gestational age and from prior visit [ie, for 28-32 weeks' gestational age: velocity = (estimated fetal weight 32-28)/(gestational age 32-28)]. We examined differences in birthweight by whether or not estimated fetal weight and estimated fetal weight velocity were <5th or ≥5th percentiles using χ².

RESULTS

Fetal growth velocity was nonmonotonic, with acceleration early in pregnancy, peaking at 13, 14, 15, and 16 weeks for biparietal diameter, head circumference, femur length, and abdominal circumference, respectively. Biparietal diameter, head circumference, and abdominal circumference had a second acceleration at 19-22, 19-21, and 27-31 weeks, respectively. Estimated fetal weight velocity peaked around 35 weeks. Fetal growth velocity varied slightly by race/ethnicity although comparisons reflected differences for parameters at various gestational ages. Estimated fetal weight velocity percentiles were not highly correlated with fetal size percentiles (Pearson r = 0.40-0.41, P < .001), suggesting that these measurements reflect different aspects of fetal growth and velocity may add additional information to a single measure of estimated fetal weight. At 32 (SD ± 1) weeks, if both estimated fetal weight velocity and size were <5th percentile, mean birthweight was 2550 g; however, even when size remained <5th percentile but velocity was ≥5th percentile, birthweight increased to 2867 g, reflecting the important contribution of higher growth velocities. For estimated fetal weight ≥5th percentile, but growth velocity <5th, birthweight was smaller (3208 vs 3357 g, respectively, P < .001).

CONCLUSION

We provide fetal growth velocity data to complement our previous work on fetal growth size standards, and have developed a calculator to compute fetal growth velocity. Preliminary findings suggest that growth velocity adds additional information over knowing fetal size alone.

Joint modeling of survival time and longitudinal outcomes with flexible random effects

Joint models with shared Gaussian random effects have been conventionally used in analysis of longitudinal outcome and survival endpoint in biomedical or public health research. However, misspecifying the normality assumption of random effects can lead to serious bias in parameter estimation and future prediction. In this paper, we study joint models of general longitudinal outcomes and survival endpoint but allow the underlying distribution of shared random effect to be completely unknown. For inference, we propose to use a mixture of Gaussian distributions as an approximation to this unknown distribution and adopt an Expectation-Maximization (EM) algorithm for computation. Either AIC and BIC criteria are adopted for selecting the number of mixtures. We demonstrate the proposed method via a number of simulation studies. We illustrate our approach with the data from the Carolina Head and Neck Cancer Study (CHANCE).

Unconditional and conditional standards for fetal abdominal circumference and estimated fetal weight in an ethnic Chinese population: a birth cohort study

BACKGROUND

Diagnosis of intrauterine fetal growth restriction and prediction of small-for-gestation age are often based on fetal abdominal circumference or estimated fetal weight (EFW). The present study aims to create unconditional (cross-sectional) and conditional (longitudinal) standards of fetal abdominal circumference and EFW for use in an ethnic Chinese population.

METHODS

In the Growing Up in Singapore Towards healthy Outcome (GUSTO) birth cohort study in Singapore, fetal biometric measurements were obtained at enrolment to antenatal care (11-12 weeks) and up to three more time points during pregnancy. Singleton pregnancies with a healthy profile defined by maternal, pregnancy and fetal characteristics and birth outcomes were selected for this analysis. The Hadlock algorithm was used to calculate EFW. Mixed effects model was used to establish unconditional and conditional standards in z-scores and percentiles for both genders pooled and for each gender separately.

RESULTS

A total of 313 women were included, of whom 294 had 3 and 19 had 2 ultrasound scans other than the gestational age dating scan. Fetal abdominal circumference showed a roughly linear trajectory from 18 to 36 weeks of gestation, while EFW showed an accelerating trajectory. Gender differences were more pronounced in the 10(th) percentile than the 50(th) or 90(th) percentiles. As compared to other published charts, this population showed growth trajectories that started low but caught up at later gestations.

CONCLUSIONS

Unconditional and conditional standards for monitoring fetal size and fetal growth in terms of abdominal circumference and EFW are available for this ethnic-Chinese population. Electronic spreadsheets are provided for their implementation.

A longitudinal study of weight gain in pregnancy in Malawi: unconditional and conditional standards

BACKGROUND

To monitor weight gain during pregnancy and assess its relation with perinatal health outcomes, both unconditional (cross-sectional) and conditional (longitudinal) standards of maternal weight are needed.

OBJECTIVE

This study aimed to develop and validate unconditional and conditional maternal weight standards for use in Malawi, Africa.

DESIGN

Longitudinal data were drawn from an antenatal care intervention study conducted in Malawi. Participants were selected for this analysis if they had a healthy profile defined by body mass index and infectious disease measures and delivered healthy singletons defined by birth weight, gestational age, and neonatal survival status. A total of 1733 measurements from 358 women were randomly split to form development and validation samples.

RESULTS

Unconditional and conditional standards were developed and validated. An electronic spreadsheet implements the calculations. Weight gain during pregnancy was substantially slower in this cohort than the US Institute of Medicine recommendation. The percentiles increased linearly; therefore, the use of the conditional standards is robust to inaccuracy in gestational age estimates.

CONCLUSION

The standards can facilitate researchers and clinicians to examine maternal weight and weight gain and estimate their associations with pregnancy outcomes in Malawi. This trial was registered at www.clinicaltrials.gov as NCT00131235.