Penalized spline joint models for longitudinal and time-to-event data

The joint models for longitudinal data and time-to-event data have recently received numerous attention in clinical and epidemiologic studies. Our interest is in modeling the relationship between event time outcomes and internal time-dependent covariates. In practice, the longitudinal responses often show non linear and fluctuated curves. Therefore, the main aim of this paper is to use penalized splines with a truncated polynomial basis to parameterize the non linear longitudinal process. Then, the linear mixed-effects model is applied to subject-specific curves and to control the smoothing. The association between the dropout process and longitudinal outcomes is modeled through a proportional hazard model. Two types of baseline risk functions are considered, namely a Gompertz distribution and a piecewise constant model. The resulting models are referred to as penalized spline joint models; an extension of the standard joint models. The expectation conditional maximization (ECM) algorithm is applied to estimate the parameters in the proposed models. To validate the proposed algorithm, extensive simulation studies were implemented followed by a case study. In summary, the penalized spline joint models provide a new approach for joint models that have improved the existing standard joint models.     

PHASE RANDOMIZATION: A CONVERGENCE DIAGNOSTIC TEST FOR MCMC

Most Markov chain Monte Carlo (MCMC) users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. Potentially useful diagnostics can be borrowed from diverse areas such as time series. One such method is phase randomization. This paper describes this method in the context of MCMC, summarizes its characteristics, and contrasts its performance with those of the more common diagnostic tests for MCMC. It is observed that the new tool contributes information about third‐ and higher‐order cumulant behaviour which is important in characterizing certain forms of nonlinearity and non‐stationarity.     

A modified two-stage approach for joint modelling of longitudinal and time-to-event data

Joint models for longitudinal and time-to-event data have been applied in many different fields of statistics and clinical studies. However, the main difficulty these models have to face with is the computational problem. The requirement for numerical integration becomes severe when the dimension of random effects increases. In this paper, a modified two-stage approach has been proposed to estimate the parameters in joint models. In particular, in the first stage, the linear mixed-effects models and best linear unbiased predictorsare applied to estimate parameters in the longitudinal submodel. In the second stage, an approximation of the fully joint log-likelihood is proposed using the estimated the values of these parameters from the longitudinal submodel. Survival parameters are estimated bymaximizing the approximation of the fully joint log-likelihood. Simulation studies show that the approach performs well, especially when the dimension of random effects increases. Finally, we implement this approach on AIDS data.     

A Bayesian approach for parameter estimation in multi-stage models

Multi-stage time evolving models are common statistical models for biological systems, especially insect populations. In stage-duration distribution models, parameter estimation for the models use the Laplace transform method. This method involves assumptions such as known constant shapes, known constant rates or the same overall hazard rate for all stages. These assumptions are strong and restrictive. The main aim of this paper is to weaken these assumptions by using a Bayesian approach. In particular, a Metropolis-Hastings algorithm based on deterministic transformations is used to estimate parameters. We will use two models, one which has no hazard rates, and the other has stage-wise constant hazard rates. These methods are validated in simulation studies followed by a case study of cattle parasites. The results show that the proposed methods are able to estimate the parameters comparably well, as opposed to using the Laplace transform methods.