Finite mixture regression model with random effects: application to neonatal hospital length of stay

A two-component mixture regression model that allows simultaneously for heterogeneity and dependency among observations is proposed. By specifying random effects explicitly in the linear predictor of the mixture probability and the mixture components, parameter estimation is achieved by maximising the corresponding best linear unbiased prediction type log-likelihood. Approximate residual maximum likelihood estimates are obtained via an EM algorithm in the manner of generalised linear mixed model (GLMM). The method can be extended to a g-component mixture regression model with the component density from the exponential family, leading to the development of the class of finite mixture GLMM. For illustration, the method is applied to analyse neonatal length of stay (LOS). It is shown that identification of pertinent factors that influence hospital LOS can provide important information for health care planning and resource allocation. (C) 2002 Elsevier Science B.V. All rights reserved.

A Mixture model with random-effects components for clustering correlated gene-expression profiles

Motivation: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. Results: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation) and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too.

Modelling inpatient length of stay by a hierarchical mixture regression via the EM algorithm

The modelling of inpatient length of stay (LOS) has important implications in health care studies. Finite mixture distributions are usually used to model the heterogeneous LOS distribution, due to a certain proportion of patients sustaining-a longer stay. However, the morbidity data are collected from hospitals, observations clustered within the same hospital are often correlated. The generalized linear mixed model approach is adopted to accommodate the inherent correlation via unobservable random effects. An EM algorithm is developed to obtain residual maximum quasi-likelihood estimation. The proposed hierarchical mixture regression approach enables the identification and assessment of factors influencing the long-stay proportion and the LOS for the long-stay patient subgroup. A neonatal LOS data set is used for illustration, (C) 2003 Elsevier Science Ltd. All rights reserved.

Effects of physical disturbance on infaunal and epifaunal assemblages in subtropical, intertidal seagrass beds

We assessed the impact of large-scale commercial and recreational harvesting of polychaete worms Marphysa spp. on macrobenthic assemblages in a subtropical estuary in Queensland, Australia, by examining: (1) the spatial extent of harvesting activities and the rate of recovery of the seagrass habitat over an 18 to 20 mo period; (2) the recovery of infauna in and around commercial pits of known age; (3) the indirect effects of physical disturbance from trampling and deposition of sediments during harvesting on epibenthos in areas adjacent to commercial and recreational pits; (4) impacts of potential indirect effects through manipulative experimentation. Harvesting caused a loss of seagrass, changes to the topography and compaction of the sediments associated with the creation of walls around commercial pits, and the deposition of rubble dug from within the pit. The walls and rubble were still evident after 1.8 to 20 mo, but comprised only a small proportion of the total area on the intertidal banks. There was a shift from an intertidal area dominated by Zostera capricorni to one with a mixture of Z. capricorni, Halophila spp. and Halodule uninervis, but there was no overall decline in the biomass of seagrass in these areas. There were distinct impacts from harvesting on the abundance of benthic infauna, especially amphipods, polychaetes and gastropods, and these effects were still detectable after 4 mo of potential recovery. After 12 me, there were no detectable differences in the abundances of these infauna between dug areas and reference areas, which suggested that infauna had recovered from impacts of harvesting; however, an extensive bloom of toxic fireweed Lyngbya majsucula may have masked any remaining impacts. There were no detectable impacts of harvesting on epifauna living in the seagrass immediately around commercial or recreational pits.