Entomological data are often overdispersed, characterised by a larger variance than assumed by simple standard models. It is important to model overdispersion properly in order to avoid incorrect and misleading inferences. Outcomes of interest are often in the form of counts or proportions and we present extended models that incorporate overdispersion, methods to assess its impact and model goodness-of-fit, and techniques to test treatment differences in the presence of overdispersion.

Summary: We consider the analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on two alternative modelling approaches: over‐dispersion (OD) models and zero‐inflation (ZI) models, both of which can be seen as generalisations of the Poisson distribution; we refer to these as implicit and explicit ZI models, respectively. Although sometimes seen as competing approaches, they can be complementary; OD is a consequence of ZI modelling, and ZI is a by‐product of OD modelling. The central objective in such analyses is often concerned with inference on the effect of covariates on the mean, in light of the apparent excess of zeros in the counts. Typically, the modelling of the excess zerosper seis a secondary objective, and there are choices to be made between, and within, the OD and ZI approaches. The contribution of this paper is primarily conceptual. We contrast, descriptively, the impact on zeros of the two approaches. We further offer a novel descriptive characterisation of alternative ZI models, including the classic hurdle and mixture models, by providing a unifying theoretical framework for their comparison. This in turn leads to a novel and technically simpler ZI model. We develop the underlying theory for univariate counts and touch on its implication for multivariate count data.

A common feature of much survival data is censoring due to incompletely observed lifetimes. Survival analysis methods and models have been designed to take account of this and provide appropriate relevant summaries, such as the Kaplan–Meier plot and the commonly quoted median survival time of the group under consideration. However, a single summary is not really a relevant quantity for communication to an individual patient, as it conveys no notion of variability and uncertainty, and the Kaplan–Meier plot can be difficult for the patient to understand and also is often mis-interpreted, even by some physicians. This paper considers an alternative approach of treating the censored data as a form of missing, incomplete data and proposes an imputation scheme to construct a completed dataset. This allows the use of standard descriptive statistics and graphical displays to convey both typical outcomes and the associated variability. We propose a Bayesian approach to impute any censored observations, making use of other information in the dataset, and provide a completed dataset. This can then be used for standard displays, summaries, and even, in theory, analysis and model fitting. We particularly focus on the data visualisation advantages of the completed data, allowing displays such as density plots, boxplots, etc, to complement the usual Kaplan–Meier display of the original dataset. We study the performance of this approach through a simulation study and consider its application to two clinical examples.

In evidence-based medicine, randomised trials are regarded as a gold standard in estimating relative treatment effects. Nevertheless, a potential gain in precision is forfeited by ignoring observational evidence. We describe a simple estimator that combines treatment estimates from randomised and observational data and investigate its properties by simulation. We show that a substantial gain in estimation accuracy, compared with the estimator based solely on the randomised trial, is possible when the observational evidence has low bias and standard error. In the contrasting scenario where the observational evidence is inaccurate, the estimator automatically discounts its contribution to the estimated treatment effect. Meta-analysis extensions, combining estimators from multiple observational studies and randomised trials, are also explored.