Bayesian estimation and case influence diagnostics for the zero-inflated negative binomial regression model

In recent years, there has been considerable interest in regression models based on zero-inflated distributions. These models are commonly encountered in many disciplines, such as medicine, public health, and environmental sciences, among others. The zero-inflated Poisson (ZIP) model has been typically considered for these types of problems. However, the ZIP model can fail if the non-zero counts are overdispersed in relation to the Poisson distribution, hence the zero-inflated negative binomial (ZINB) model may be more appropriate. In this paper, we present a Bayesian approach for fitting the ZINB regression model. This model considers that an observed zero may come from a point mass distribution at zero or from the negative binomial model. The likelihood function is utilized to compute not only some Bayesian model selection measures, but also to develop Bayesian case-deletion influence diagnostics based on q-divergence measures. The approach can be easily implemented using standard Bayesian software, such as WinBUGS. The performance of the proposed method is evaluated with a simulation study. Further, a real data set is analyzed, where we show that ZINB regression models seems to fit the data better than the Poisson counterpart.     

Expanded renal transplantation: a competing risk model approach

Multi-state models (MSMs) are useful to analyze survival data when, besides the event of main interest, one or more intermediate states of the individual are identified. These models take the several existing states and the possible transitions among them into account. At the same time, covariate effects on each transition intensity may be investigated separately and, therefore, MSMs are more flexible than the standard Cox proportional hazards model. In this work, we use MSMs to investigate the impact of the quality of a transplanted kidney for a group of patients at the Hospital Universitario Central de Asturias. Specifically, we use an illness-death model to study the evolution of patients with kidney disease who received a renal transplant after a dialysis period. The intermediate state is defined as the failure of the received organ, while the terminating state is the death of the patient. In order to increase the potential number of organs available for transplant, the standards of quality for the transplanted kidneys were relaxed (the new criteria are labeled expanded criteria), and these ‘expanded kidneys’ were transplanted in appropriate candidates (older patients, with higher prevalence of diabetes mellitus). Results suggest that the expanded kidneys have a minor effect on survival, while both the kidney mortality and the risk of death increase with the patient's age and the serum creatinine and serum hemoglobin levels.     

Generalized Estimation of the BLUP in Mixed-Effects Models: A Comparison with ML and REML

The Best Linear Unbiased Predictor (BLUP) in mixed models is a function of the variance components and they are estimated using maximum likelihood (ML) or restricted ML methods. Nonconvergence of BLUP would occur due to a drawback of the standard likelihood-based approaches. In such situations, ML and REML either do not provide any BLUPs or all become equal. To overcome this drawback, we provide a generalized estimate (GE) of BLUP that does not suffer from the problem of negative or zero variance components, and compare its performance against the ML and REML estimates of BLUP. Simulated and published data are used to compare BLUP.     

A Comparison of the Performance of Phase II Simple Linear Profile Control Charts when Parameters are Estimated

The standard deviation of the average run length (SDARL) is an important performance metric in studying the performance of control charts with estimated in-control parameters. Only a few studies in the literature, however, have considered this measure when evaluating control chart performance. The current study aims at comparing the in-control performance of three phase II simple linear profile monitoring approaches; namely, those of Kang and Albin (2000), Kim et al. (2003), and Mahmoud et al. (2010). The comparison is performed under the assumption of estimated parameters using the SDARL metric. In general, the simulation results of the current study show that the method of Kim et al. (2003) has better overall statistical performance than the competing methods in terms of SDARL values. Some of the recommended approaches based solely on the usual average run length properties can have poor SDARL performance.