Diagnostics for a two-stage joint survival model.

A two-stage joint survival model is used to analyse time to event outcomes that could be associated with biomakers that are repeatedly collected over time. A Two-stage joint survival model has limited model checking tools and is usually assessed using standard diagnostic tools for survival models. The diagnostic tools can be improved and implemented. Time-varying covariates in a two-stage joint survival model might contain outlying observations or subjects. In this study we used the variance shift outlier model (VSOM) to detect and down-weight outliers in the first stage of the two-stage joint survival model. This entails fitting a VSOM at the observation level and a VSOM at the subject level, and then fitting a combined VSOM for the identified outliers. The fitted values were then extracted from the combined VSOM which were then used as time-varying covariate in the extended Cox model. We illustrate this methodology on a dataset from a multi-centre randomised clinical trial. A multi-centre trial showed that a combined VSOM fits the data better than an extended Cox model. We noted that implementing a combined VSOM, when desired, has a better fit based on the fact that outliers are down-weighted.

Ticks and tick-borne diseases: a vector-host interaction model for the brown ear tick (Rhipicephalus appendiculatus).

An analytical model is derived for the interaction of the brown ear tick (Rhipicephalus appendiculatus) with its hosts. Such models are rare due to the complexity and lack of information on the entire stages of ticks life cycles. Most models are simulations rather than analytical. The vector is categorized into a discrete number of compartments according to its life cycle. The starting model in this article consists of a system of differential equations with constant coefficients. A general model on a stage structured population with unlimited host density is developed. From the characteristic polynomial of the system a sensitivity analysis for the population parameters is carried out in detail. The model is then improved by incorporating host abundance and availability. This is done on the basis of a demand-driven and ratio-dependent functional response model. The improved model adequately represents the dynamics of a stage-structured vector population under conditions of varying host density. The model allows the qualitative evaluation of several management strategies and is expected to guide future research work.