In toxicological experiments for biological pest control, experiments frequently involve the study of cumulative mortality in a groups of insects measured at various time points. Samples of different strains, or isolates, of the compound under study are used, typically with some replication. The example considered here is from a study of a microbial control to insect damage in sugar cane. Cumulative multinomial models provide an obvious approach to the analysis of these data, however, the basic model needs to be extended to account for overdispersion. Here we consider various random effect models, including the Dirichlet-multinomial and models with random effects in the linear predictor. For some simple time trend models, fitting using a generalized estimating equation approach leads to a surprisingly simple modification of the multinomial fit and casts light on the behaviour in more complex models. Other approaches considered include quadrature methods for normal random effects. We also consider modelling isolates as a random effect, with a mixture distribution to cluster isolates with similar action, together with other replicate random effects for overdispersion.