Bayesian Influence Measures for Joint Models for Longitudinal and Survival Data

Abstract

Summary This article develops a variety of influence measures for carrying out perturbation (or sensitivity) analysis to joint models of longitudinal and survival data (JMLS) in Bayesian analysis. A perturbation model is introduced to characterize individual and global perturbations to the three components of a Bayesian model, including the data points, the prior distribution, and the sampling distribution. Local influence measures are proposed to quantify the degree of these perturbations to the JMLS. The proposed methods allow the detection of outliers or influential observations and the assessment of the sensitivity of inferences to various unverifiable assumptions on the Bayesian analysis of JMLS. Simulation studies and a real data set are used to highlight the broad spectrum of applications for our Bayesian influence methods.

Semiparametric Bayesian inference on skew–normal joint modeling of multivariate longitudinal and survival data

“…We illustrated the proposed Bayesian semiparametric methods with a data set from a clinical trial study conducted by the IBCSG as described in the Introduction Section. The data set was analyzed by Zhu et al , for illustrating their proposed Bayesian influence measures under the JMLS framework with the multivariate normality assumption of the within‐individual measurement error and random effects. The data were obtained from 832 premenopausal women with node‐positive breast cancer in Switzerland, Sweden and New Zealand/Australia on items about the appetite ( y 1 ), perceived coping ( y 2 ), mood ( y 3 ) and physical well‐being ( y 4 ) assessed at the start of the study and randomly at months 3 and 18.…”

“…Four indicators of health‐related QOL, including physical well‐being (lousy–good), mood (miserable–happy), appetite (none–good) and perceived coping (‘How much effort does it cost you to cope with your illness?’ (a great deal–none)), were assessed at baseline and at months 3 and 18 after randomization. It is usual way to transform the corresponding observed values of QOL to , for the purpose of the normalization in proceeding papers . However, Figure S1 in Appendix C shows that the transformed data may not be normally distributed but has a considerable skewness along with possible thick tails; hence, it is relatively reasonable to fit the transformed data with a multivariate skew–normal distribution.…”

Bayesian variable selection and estimation in semiparametric joint models of multivariate longitudinal and survival data

“…(), Wang and Taylor (), Zhu et al. (), and references cited therein. Unlike the two‐stage model for longitudinal and survival data proposed by Tsiatis et al.…”

Bayesian Sensitivity Analysis of a Nonlinear Dynamic Factor Analysis Model with Nonparametric Prior and Possible Nonignorable Missingness

“…Such benchmark lines are, of course, arbitrary and are dependent on the perturbations pursued. Future studies should utilize approaches such as bootstrapping (Zhu et al, 2012) to construct empirical distribution for the local influence measures to identify components whose influence exceeds some critical thresholds determined using the bootstrap samples.…”