A general approach for two-stage analysis of multilevel clustered non-Gaussian data.
In this article, we propose a two-stage approach to modeling multilevel clustered non-Gaussian data with sufficiently large numbers of continuous measures per cluster. Such data are common in biological and medical studies utilizing monitoring or image-processing equipment. We consider a general class of hierarchical models that generalizes the model in the global two-stage (GTS) method for nonlinear mixed effects models by using any square-root-n-consistent and asymptotically normal estimators from stage 1 as pseudodata in the stage 2 model, and by extending the stage 2 model to accommodate random effects from multiple levels of clustering. The second-stage model is a standard linear mixed effects model with normal random effects, but the cluster-specific distributions, conditional on random effects, can be non-Gaussian. This methodology provides a flexible framework for modeling not only a location parameter but also other characteristics of conditional distributions that may be of specific interest. For estimation of the population parameters, we propose a conditional restricted maximum likelihood (CREML) approach and establish the asymptotic properties of the CREML estimators. The proposed general approach is illustrated using quartiles as cluster-specific parameters estimated in the first stage, and applied to the data example from a collagen fibril development study. We demonstrate using simulations that in samples with small numbers of independent clusters, the CREML estimators may perform better than conditional maximum likelihood estimators, which are a direct extension of the estimators from the GTS method.
Chervoneva
Inna
I
Division of Biostatistics, Department of Pharmacology and Experimental Therapeutics, Thomas Jefferson University, Philadelphia, Pennsylvania 19107, USA. i_chervoneva@mail.jci.tju.edu
Iglewicz
Boris
B
Hyslop
Terry
T
D000818:Animals; D001699:Biometry / Q000379:methods*; D016000:Cluster Analysis; D003627:Data Interpretation, Statistical; D005838:Genotype; D016013:Likelihood Functions; D051379:Mice; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D012590:Sclera / Q000033:anatomy & histology