Analysis of a Toxicological Experiment Using a Generalized Linear Model with

Summary This paper is concerned with the modeling and analysis of data collected in a large experiment designed to study the mortality in gypsy moths exposed to a mixture of two toxicants and observed over three time periods. The stochastic survival model employed is based on a pertinent biological model that describes the mode of action of synergism between the toxicants. Conditional probability of death in an interval, given survival up to that interval, is fitted by a binary response model with nested random effects added to fixed treatment effects. The random effects factors are used to account for intercorrelation and extravariation. Approximate maximum likelihood estimates of the parameters are evaluated by adapting the iteratively weighted least squares algorithm within GLIM. Results from the nested random effect model are compared with those from the quasi-likelihood procedure for overdispersed data. Analysis of the gypsy moth data suggests that the addition of an enzyme to an environmentally safe, but not very potent, microbial control agent produces a mixture that is a more effective toxicant for the gypsy moth than the microbial agent used alone.

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