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

Identifying unusual growth-related measurements or longitudinal patterns in growth is often the focus in fetal and pediatric medicine. For example, the goal of the ongoing National Fetal Growth Study is to develop both cross-sectional and longitudinal reference curves for ultrasound fetal growth measurements that can be used for this purpose. Current methodology for estimating cross-sectional and longitudinal reference curves relies mainly on the linear mixed model. The focus of this paper is on examining the robustness of percentile estimation to the assumptions with respect to the Gaussian random-effect assumption implicitly made in the standard linear mixed model. We also examine a random-effects distribution based on mixtures of normals and compare the two approaches under both correct and misspecified random-effects distributions. In general, we find that the standard linear mixed model is relatively robust for cross-sectional percentile estimation but less robust for longitudinal or 'personalized' reference curves based on the conditional distribution given prior ultrasound measurements. The methodology is illustrated with data from a longitudinal fetal growth study.

[1]  H. Hoffman,et al.  Pre‐pregnancy risk factors of small‐for‐gestational age births among parous women in Scandinavia , 1993, Acta obstetricia et gynecologica Scandinavica.

[2]  C. McCulloch,et al.  Misspecifying the Shape of a Random Effects Distribution: Why Getting It Wrong May Not Matter , 2011, 1201.1980.

[3]  J. Neuhaus,et al.  Prediction of Random Effects in Linear and Generalized Linear Models under Model Misspecification , 2011, Biometrics.

[4]  Edward L Korn,et al.  Application of nonparametric quantile regression to body mass index percentile curves from survey data , 2010, Statistics in medicine.

[5]  P Royston,et al.  Calculation of unconditional and conditional reference intervals for foetal size and growth from longitudinal measurements. , 1995, Statistics in medicine.

[6]  T J Cole,et al.  Smoothing reference centile curves: the LMS method and penalized likelihood. , 1992, Statistics in medicine.

[7]  George F. Corliss.  Which Root Does the Bisection Algorithm Find , 1977 .

[8]  J. Kalbfleisch,et al.  The effects of mixture distribution misspecification when fitting mixed-effects logistic models , 1992 .

[9]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[10]  B. Efron,et al.  Limiting the Risk of Bayes and Empirical Bayes Estimators—Part I: The Bayes Case , 1971 .

[11]  Patrick Royston,et al.  A Comparison of Statistical Methods for Age‐related Reference Intervals , 1997 .

[12]  S Gallivan,et al.  An investigation of fetal growth using serial ultrasound data , 1993, Ultrasound in obstetrics & gynecology : the official journal of the International Society of Ultrasound in Obstetrics and Gynecology.

[13]  Xianzheng Huang,et al.  Detecting random-effects model misspecification via coarsened data , 2011, Comput. Stat. Data Anal..

[14]  Robert W Platt,et al.  The International Journal of Biostatistics Modeling Fetal Weight for Gestational Age : A Comparison of a Flexible Multi-level Spline-based Model with Other Approaches , 2011 .

[15]  Amy H Herring,et al.  A Bayesian Latent Variable Mixture Model for Longitudinal Fetal Growth , 2009, Biometrics.

[16]  T A Louis,et al.  Random effects models with non-parametric priors. , 1992, Statistics in medicine.

[17]  G. Verbeke,et al.  A Linear Mixed-Effects Model with Heterogeneity in the Random-Effects Population , 1996 .

[18]  F. Arias,et al.  Etiology and Outcome of Low Birth Weight and Preterm Infants , 1982, Obstetrics and gynecology.

[19]  Jane E. Harding,et al.  Nutrition and fetal growth , 1995 .

[20]  E M Wright,et al.  Calculating reference intervals for laboratory measurements , 1999, Statistical methods in medical research.

[21]  E C HUGHES,et al.  Nutrition and fetal growth. , 1955, Journal of the American Dietetic Association.

[22]  A. Guihard-Costa,et al.  Optimal Standards for Fetal Biometry: To Each Measurement Its Fitting Model , 2006, Fetal Diagnosis and Therapy.

[23]  G. Verbeke,et al.  The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data , 1997 .

[24]  M Davidian,et al.  Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data , 2001, Biometrics.

[25]  V. Newman,et al.  Small-for-gestational-age birth: maternal predictors and comparison with risk factors of spontaneous preterm delivery in the same cohort. , 1991, American journal of obstetrics and gynecology.