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This paper describes methodology for analyzing data from cluster randomized trials with count outcomes, taking indirect effects as well spatial effects into account. Indirect effects are modeled using a novel application of a measure of depth within the intervention arm. Both direct and indirect effects can be estimated accurately even when the proposed model is misspecified. We use spatial regression models with Gaussian random effects, where the individual outcomes have distributions overdispersed with respect to the Poisson, and the corresponding direct and indirect effects have a marginal interpretation. To avoid spatial confounding, we use orthogonal regression, in which random effects represent spatial dependence using a homoscedastic and dimensionally reduced modification of the intrinsic conditional autoregression model. We illustrate the methodology using spatial data from a pair‐matched cluster randomized trial against the dengue mosquito vector Aedes aegypti, done in Trujillo, Venezuela. [ABSTRACT FROM AUTHOR]

Background: The ability of cluster-randomized trials to capture mass or indirect effects is one reason for their increasing use to test interventions against vector-borne diseases such as malaria and dengue. For the same reason, however, the independence of clusters may be compromised if the distances between clusters is too small to ensure independence. In other words they may be subject to spillover effects. Methods: We distinguish two types of spatial spillover effect: between-cluster dependence in outcomes, or spillover dependence; and modification of the intervention effect according to distance to the intervention arm, or spillover indirect effect. We estimate these effects in trial of insecticide-treated materials against the dengue mosquito vector, Aedes aegypti, in Venezuela, the endpoint being the Breteau index. We use a novel random effects Poisson spatial regression model. Spillover dependence is incorporated via an orthogonalized intrinsic conditional autoregression (ICAR) model. Spillover indirect effects are incorporated via the number of locations within a certain radius, set at 200m, that are in the intervention arm. Results: From the model with ICAR spatial dependence, and the degree of surroundedness, the intervention effect is estimated as 0.74—favouring the intervention—with a 95% credible interval of 0.34 to 1.69. The point estimates are stronger with increasing surroundedness within intervention locations. Conclusion: In this trial there is some evidence of a spillover indirect effect of the intervention, with the Breteau index tending to be lower in locations which are more surrounded by locations in the intervention arm. Author summary: Control methods for dengue, and other diseases which are transmitted by mosquitoes, are often tested in cluster-randomized trials. This means that whole groups of people, often defined by geographical area, are randomly allocated to receive the control method or not. These control methods often have a mass effect so that they may be stronger if applied to a whole area together. However, if the areas (clusters) are not very far apart then the effects may 'spill over' from one to another. In this paper we use a new spatial statistical method to re-analyse data from a cluster-randomized trial which was done in a town in Venezuela. The idea was to use insecticide treated curtains and water tank covers to try to control the mosquitoes which transmit dengue. To assess the spillover effect we calculate how much each location was surrounded by locations which got the control method. We found some evidence that the greater the surroundedness then the stronger the effect of the intervention. [ABSTRACT FROM AUTHOR]

One dimensional exponential families on finite sample spaces are studied using the geometry of the simplex Δ0n-1 and that of a transformation Vn-1 of its interior. This transformation is the natural parameter space associated with the family of multinomial distributions. The space Vn-1 is partitioned into cones that are used to find one dimensional families with desirable properties for modeling and inference. These properties include the availability of uniformly most powerful tests and estimators that exhibit optimal properties in terms of variability and unbiasedness. [ABSTRACT FROM AUTHOR]

This paper looks at boundary effects on inference in an important class of models including, notably, logistic regression. Asymptotic results are not uniform across such models. Accordingly, whatever their order, methods asymptotic in sample size will ultimately "break down" as the boundary is approached, in the sense that effects such as infinite skewness, discreteness and collinearity will dominate. In this paper, a highly interpretable diagnostic tool is proposed, allowing the analyst to check if the boundary is going to have an appreciable effect on standard inferential techniques. [ABSTRACT FROM AUTHOR]

. The relative frailty variance among survivors provides a readily interpretable measure of how the heterogeneity of a population, as represented by a frailty model, evolves over time. We discuss the properties of the relative frailty variance, show that it characterizes frailty distributions and that, suitably rescaled, it may be used to compare patterns of dependence across models and data sets. In shared frailty models, the relative frailty variance is closely related to the cross-ratio function, which is estimable from bivariate survival data. We investigate the possible shapes of the relative frailty variance function for the purpose of model selection, and we review available frailty distribution families in this context. We introduce several new families with contrasting properties, including simple but flexible time varying frailty models. The benefits of the approach that we propose are illustrated with two applications to bivariate current status data obtained from serological surveys. [ABSTRACT FROM AUTHOR]