Pairwise dependence diagnostics for clustered failure-time data

Frailty and copula models specify a parametric dependence structurefor multivariate failure-time data. Estimation of some jointquantities can be highly sensitive to the assumed parametricform, and hence model fit is an important issue. This paperlays out a general diagnostic framework for evaluating and selectingfrailty and copula models. The approach is based on the cumulativesum of residuals that are calculated in bivariate time. Theresiduals reflect the difference between the observed and expectedbivariate association structures. The proposed model-checkingprocess is interpretable with a limiting distribution whichcan be approximated using the bootstrap. Simulations and a dataexample illustrate the practical application of the method.     

On consistency of Kendall's tau under censoring

Necessary and sufficient conditions for consistency of a simpleestimator of Kendall's tau under bivariate censoring are presented.The results are extended to data subject to bivariate left truncationas well as right censoring.     

Analysis of clustered recurrent event data with application to hospitalization rates among renal failure patients

End-stage renal disease (commonly referred to as renal failure) is of increasing concern in the United States and many countries worldwide. Incidence rates have increased, while the supply of donor organs has not kept pace with the demand. Although renal transplantation has generally been shown to be superior to dialysis with respect to mortality, very little research has been directed towards comparing transplant and wait-list patients with respect to morbidity. Using national data from the Scientific Registry of Transplant Recipients, we compare transplant and wait-list hospitalization rates. Hospitalizations are subject to two levels of dependence. In addition to the dependence among within-patient events, patients are also clustered by listing center. We propose two marginal methods to analyze such clustered recurrent event data; the first model postulates a common baseline event rate, while the second features cluster-specific baseline rates. Our results indicate that kidney transplantation offers a significant decrease in hospitalization, but that the effect is negated by a waiting time (until transplant) of more than 2 years. Moreover, graft failure (GF) results in a significant increase in the hospitalization rate which is greatest in the first month post-GF, but remains significantly elevated up to 4 years later. We also compare results from the proposed models to those based on a frailty model, with the various methods compared and contrasted.     

A Monte Carlo EM algorithm for generalized linear mixed models with flexible random effects distribution

A popular way to represent clustered binary, count, or other data is via the generalized linear mixed model framework, which accommodates correlation through incorporation of random effects. A standard assumption is that the random effects follow a parametric family such as the normal distribution; however, this may be unrealistic or too restrictive to represent the data. We relax this assumption and require only that the distribution of random effects belong to a class of 'smooth' densities and approximate the density by the seminonparametric (SNP) approach of Gallant and Nychka (1987). This representation allows the density to be skewed, multi-modal, fat- or thin-tailed relative to the normal and includes the normal as a special case. Because an efficient algorithm to sample from an SNP density is available, we propose a Monte Carlo EM algorithm using a rejection sampling scheme to estimate the fixed parameters of the linear predictor, variance components and the SNP density. The approach is illustrated by application to a data set and via simulation.