Statistical analysis of honeybee survival after chronic exposure to insecticides

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Abstract
Studies concerning long-term survival of honeybees raise the problem of the statistical analysis of mortality data. In the present study, we used a modeling approach of survival data of caged bees under chronic exposure to two pesticides (imidacloprid and deltamethrin). Our model, based on a Cox proportional hazard model, is not restricted to a specific hazard functional form, such as in parametric approaches, but takes into account multiple covariates. We consider not only the pesticide treatment but also a nuisance variable (variability between replicates). Moreover, considering the occurrence of social interactions, the model integrates the fact that bees do not die independently of each other. We demonstrate the chronic toxicity induced by imidacloprid and deltamethrin. Our results also underline the role of the replicate effect, the density-dependent effect, and their interactions with the treatment effect. None of these parameters can be neglected in the assessment of chronic toxicity of pesticides to the honeybee.