We consider discrete mortality data for groups of individuals observed over time. The fitting of cumulative mortality curves as a function of time involves the longitudinal modelling of the multinomial response. Typically such data exhibit overdispersion, that is greater variation than predicted by the multinomial distribution. To model the extra-multinomial variation (overdispersion) we consider a Dirichlet-multinomial model, a random intercept model and a random intercept and slope model. We construct asymptotic and robust covariance matrix estimators for the regression parameter standard errors. Applying this model to a specific insect bioassay of the fungus Beauveria bassiana, we note some simple relationships in the results and explore why these are simply a consequence of the data structure. Fitted models are used to make inferences on the effectiveness and consistency of different isolates of the fungus to provide recommendations for its use as a biological control in the field.