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A random effects continuation-ratio model for replicated toxicological data

Marie-José Martinez 1 John Hinde 2 
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : Discrete survival times can be considered as ordered multicategorical data. In the ordinal data modelling context, a variety of multinomial regression models can be used. In this work, we consider a continuation-ratio model, which is particularly appropriate when the ordered categories represent a progression through different stages, such as survival through various times (Agresti, 2002). This particular model has the advantage of being a simple decomposition of a multinomial distribution as a succession of hierarchical binomial models. The property of conditional independence enables to fit it by adapting the methods available for binary response data. To account for uncontrolled experimental variation (this may be apparent through overdispersion of multinomial responses across the replicates), we include random effects into the linear predictor. To fit the proposed random effects models, we consider different approaches to maximum likelihood estimation. As in the general case of generalized linear mixed models, the likelihood of the observed data is obtained by integrating out of the random effects. Unfortunately, this marginal likelihood does not generally have a closed form expression and approximation estimation methods are needed. Assuming a normal distribution for the random effects, we use ordinary and adaptive Gaussian quadrature methods combined with an EM-algorithm to estimate the model parameters. To relax this assumption, we also consider the use of a mixture of normal distributions for the random effects (Molenberghs and Verbeke, 2005). This model which reflects the prior believe of presence of unobserved heterogeneity among the replicates is also used in this work for classification purposes. This approach is applied to grouped toxicological data. More precisely, the data considered here have been obtained from a biological control assay where different isolates of a fungus are used as a microbial control for a species of termite which causes a lot of damage in sugarcane fields in Brazil (De Freitas, 2001). The obtained data compares different isolates of the fungus. A solution of each isolate is applied to several groups of termites and the cumulative mortality in each group is measured at various time points. Clearly, the data shows different isolates efficacities and different degrees of variability among the replicates within the different isolates. Thus, the aim of this study is to determine effective isolates for use in the field by taking into account the replicated data structure.
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Submitted on : Wednesday, February 13, 2013 - 3:41:22 PM
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  • HAL Id : hal-00788043, version 1



Marie-José Martinez, John Hinde. A random effects continuation-ratio model for replicated toxicological data. ISI 2011 - 58th World Statistics Congress of the International Statistical Institute, ISI, Aug 2011, Dublin, Ireland. pp.6175-6180. ⟨hal-00788043⟩



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