# Dose Response Models with Natural Mortality and Random Effects

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DOI: 10.1007/s13253-013-0150-1

- Cite this article as:
- Urbano, M.R., Hinde, J. & Demétrio, C.G.B. JABES (2013) 18: 594. doi:10.1007/s13253-013-0150-1

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## Abstract

When fitting dose–response models to entomological data it is often necessary to take account of natural mortality and/or overdispersion. The standard approach to handle natural mortality is to use Abbott’s formula, which allows for a constant underlying mortality rate. Commonly used overdispersion models include the beta-binomial model, logistic-normal, and discrete mixtures. Here we extend the standard natural mortality model by including a random effect to account for overdispersion. Parameter estimation is based on a combined EM Newton–Raphson algorithm, which provides a simple framework for maximum likelihood estimation of the natural mortality model. We consider the application of this model to data from an experiment on the use of a virus (*PhopGV*) for the biological control of worm larvae (*Phthorimaea operculella*) in potatoes. For this natural mortality model with a random effect we introduce the likelihood ratio test, effective dose, and the use of a simulated residual envelope for model checking. Comparisons are made with an equivalent beta-binomial model. The procedures are implemented in the R system.