Joint Dispersion Model with a Flexible Link

The objective is to model longitudinal and survival data jointly taking into account the dependence between the two responses in a real HIV/AIDS dataset using a shared parameter approach inside a Bayesian framework. We propose a linear mixed effects dispersion model to adjust the CD4 longitudinal biomarker data with a between-individual heterogeneity in the mean and variance. In doing so we are relaxing the usual assumption of a common variance for the longitudinal residuals. A hazard regression model is considered in addition to model the time since HIV/AIDS diagnostic until failure, being the coefficients, accounting for the linking between the longitudinal and survival processes, time-varying. This flexibility is specified using Penalized Splines and allows the relationship to vary in time. Because heteroscedasticity may be related with the survival, the standard deviation is considered as a covariate in the hazard model, thus enabling to study the effect of the CD4 counts' stability on the survival. The proposed framework outperforms the most used joint models, highlighting the importance in correctly taking account the individual heterogeneity for the measurement errors variance and the evolution of the disease over time in bringing new insights to better understand this biomarker-survival relation.Comment: 27 pages, 3 figures, 2 table

Semiparametric Point Process and Time Series Models for Series of Events

We are dealing with series of events occurring at random times tau_n and carrying further quantitive information xi_n . Examples are sequences of extrasystoles in ECG­records. We will present two approaches for analyzing such (typically long) sequences (tau_n, xi_n ), n = 1, 2, ... . (i) A point process model is based on an intensity of the form alpha(t) * b_t(theta), t >= 0, with b_t a stochastic intensity of the self­exciting type. (ii) A time series approach is based on a transitional GLM. The conditional expectation of the waiting time sigma_{n+1} = tau_{n+1} - tau_n is set to be v(tau_n) * h(eta_n(theta)), with h a response function and eta_n a regression term. The deterministic functions alpha and v, respectively, describe the long-term trend of the process

Variational Bayesian analysis of survival data using a log-logistic accelerated failure time model

The log-logistic regression model is one of the most commonly used accelerated failure time (AFT) models in survival analysis, for which statistical inference methods are mainly established under the frequentist framework. Recently, Bayesian inference for log-logistic AFT models using Markov chain Monte Carlo (MCMC) techniques has also been widely developed. In this work, we develop an alternative approach to MCMC methods and infer the parameters of the log-logistic AFT model via a mean-field variational Bayes (VB) algorithm. A piecewise approximation technique is embedded in deriving the VB algorithm to achieve conjugacy. The proposed VB algorithm is evaluated and compared with typical frequentist inferences and MCMC inference using simulated data under various scenarios. A publicly available dataset is employed for illustration. We demonstrate that the proposed VB algorithm can achieve good estimation accuracy and has a lower computational cost compared with MCMC methods

Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis