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Influence analysis for skew‐normal semiparametric joint models of multivariate longitudinal and multivariate survival data
Author(s) -
Tang AnMin,
Tang NianSheng,
Zhu Hongtu
Publication year - 2017
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.7211
Subject(s) - multivariate statistics , multivariate analysis , skew , semiparametric model , statistics , econometrics , multivariate normal distribution , longitudinal data , mathematics , computer science , parametric statistics , data mining , telecommunications
The normality assumption of measurement error is a widely used distribution in joint models of longitudinal and survival data, but it may lead to unreasonable or even misleading results when longitudinal data reveal skewness feature. This paper proposes a new joint model for multivariate longitudinal and multivariate survival data by incorporating a nonparametric function into the trajectory function and hazard function and assuming that measurement errors in longitudinal measurement models follow a skew‐normal distribution. A Monte Carlo Expectation‐Maximization (EM) algorithm together with the penalized‐splines technique and the Metropolis–Hastings algorithm within the Gibbs sampler is developed to estimate parameters and nonparametric functions in the considered joint models. Case deletion diagnostic measures are proposed to identify the potential influential observations, and an extended local influence method is presented to assess local influence of minor perturbations. Simulation studies and a real example from a clinical trial are presented to illustrate the proposed methodologies. Copyright © 2017 John Wiley & Sons, Ltd.