文档介绍：Regression Analysis when Co v ariates are
Regression P arameters of a Random E
ects
Mo del for Observ ed Longitudinal
Measuremen ts
C
Y
W ang
Naisyin W ang and Suo jin W ang
Division of Public Health Sciences
F red Hutc hinson Cancer Researc hCen ter
Seattle
W A
USA
email
cyw ang
Departmen t of Statistics
T exas A
M Univ ersit y
College Station
TX
Septem ber
SUMMAR Y
W e consider regression analysis when co v ariate v ariables are the underlying regression co ef
cien ts of another linear mixed mo del
A naiv e approac h is to use eac h sub ject
s rep eated
measuremen ts
whic h are assumed to follo w a linear mixed mo del
and obtain sub ject
sp eci
c
estimated co e
cien ts to replace the co v ariate v ariables
Ho w ev er
directly replacing the un
observ ed co v ariates in the primary regression b y these estimated co e
cien ts ma y result in
a signi
can tly biased estimator
The aforemen tioned problem can be ev aluated as a gen
eralization of the classical additiv e error mo del where rep eated measures are considered as
replicates
T o correct for these biases
w ein v estigate a pseudo exp ected estimating equation
EEE
estimator
a regression calibration
R C
estimator and a re
ned v ersion of the R Ces
timator
F or linear regression
the
rst t w o estimators are iden tical under certain conditions
Ho w ev er
when the primary regression mo del is a nonlinear mo del
the R C estimator is usu
ally biased
W e th us consider a re
ned regression calibration estimator whose p erformance
is close to that of the pseudo EEE estimator but do es not require n umerical in tegration
The
In addition to
R C estimator is also extended to the prop ortional hazards regression mo del
the distribution theory
w e ev aluate the metho ds through sim ulation studies
The metho ds
are applied to analyze a real dataset from a c hild gro wth study
Keywor