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Analysis of longitudinally observed irregularly timed multivariate outcomes: regression with focus on cross‐component correlation
Author(s) -
Carey Vincent J.,
Rosner Bernard A.
Publication year - 2000
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 - 10.1002/1097-0258(20010115)20:1<21::aid-sim639>3.0.co;2-5
Subject(s) - univariate , multivariate statistics , autocorrelation , statistics , exponential function , mathematics , component (thermodynamics) , regression , correlation , regression analysis , multivariate analysis , mathematical analysis , physics , geometry , thermodynamics
Components of repeatedly observed multivariate outcomes (for example, the two components of blood pressure measures (SBP it , DBP it ), obtained on subject i at arbitrarily spaced times t ) are often analysed separately. We present a unified approach to regression analysis of such irregularly timed multivariate longitudinal data, with particular attention to assessment of the magnitude and durability of cross‐component correlation. Maximum likelihood estimates are presented for component‐specific regression parameters and autocorrelation and cross‐correlation functions. The component‐specific autocorrelation function has the ‘damped exponential’ form $({\rm corr}(Y_{it},Y_{i,t+s})=\gamma^{|s|^{\theta}})$\nopagenumbers\end , which generalizes the AR(1), MA(1) and random intercept models for univariate longitudinal outcomes. The cross‐component correlation function (CCCF) has an analogous form, allowing damped‐exponential decay of cross‐component correlation as time between repeated measures elapses. Finite sample performance is assessed through simulation studies. The methods are illustrated through blood pressure modelling and construction of multivariate prediction regions. Copyright © 2001 John Wiley & Sons, Ltd.