Case-Deletion Diagnostics for Linear Mixed Models

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.

Data-Influence Analytics in Predictive Models Applied to Asthma Disease

Asthma is one of the most common chronic diseases around the world and represents a serious problem in human health. Predictive models have become important in medical sciences because they provide valuable information for data-driven decision-making. In this work, a methodology of data-influence analytics based on mixed-effects logistic regression models is proposed for detecting potentially influential observations which can affect the quality of these models. Global and local influence diagnostic techniques are used simultaneously in this detection, which are often used separately. In addition, predictive performance measures are considered for this analytics. A study with children and adolescent asthma real data, collected from a public hospital of São Paulo, Brazil, is conducted to illustrate the proposed methodology. The results show that the influence diagnostic methodology is helpful for obtaining an accurate predictive model that provides scientific evidence when data-driven medical decision-making.

Influence diagnostics for count data under AB-BA crossover trials

This paper aims to develop diagnostic measures to assess the influence of data perturbations on estimates in AB-BA crossover studies with a Poisson distributed response. Generalised mixed linear models with normally distributed random effects are utilised. We show that in this special case, the model can be decomposed into two independent sub-models which allow to derive closed-form expressions to evaluate the changes in the maximum likelihood estimates under several perturbation schemes. The performance of the new influence measures is illustrated by simulation studies and the analysis of a real dataset.

Influence assessment in censored mixed-effects models using the multivariate Student's-t distribution

In biomedical studies on HIV RNA dynamics, viral loads generate repeated measures that are often subjected to upper and lower detection limits, and hence these responses are either left- or right-censored. Linear and non-linear mixed-effects censored (LMEC/NLMEC) models are routinely used to analyse these longitudinal data, with normality assumptions for the random effects and residual errors. However, the derived inference may not be robust when these underlying normality assumptions are questionable, especially the presence of outliers and thick-tails. Motivated by this, Matos et al. (2013b) recently proposed an exact EM-type algorithm for LMEC/NLMEC models using a multivariate Student's-t distribution, with closed-form expressions at the E-step. In this paper, we develop influence diagnostics for LMEC/NLMEC models using the multivariate Student's-t density, based on the conditional expectation of the complete data log-likelihood. This partially eliminates the complexity associated with the approach of Cook (1977, 1986) for censored mixed-effects models. The new methodology is illustrated via an application to a longitudinal HIV dataset. In addition, a simulation study explores the accuracy of the proposed measures in detecting possible influential observations for heavy-tailed censored data under different perturbation and censoring schemes.