THESIS
2019
xv, 155 pages : illustrations ; 30 cm
Abstract
In Statistics, most theories are developed to deal with statistical modeling and
analysis when observations are assumed to have true values of covariates. However,
for the EPIC-InterAct Study, which is a large prospective case-cohort study
nested within the European Prospective Investigation into Cancer and Nutrition
(EPIC), covariate measured with error is an inevitable problem since dietary intake
assessed with a food frequency questionnaire is prone to measurement error.
Ignoring measurement error in covariates will cause biases of estimates as well as
loss of power, and sometimes leads to misleading results of data analysis. Thus,
to obtain more reliable results, data analysis of incorporating measurement error
model in the EPIC-InterAct Study is necessary.
In this thesis,...[
Read more ]
In Statistics, most theories are developed to deal with statistical modeling and
analysis when observations are assumed to have true values of covariates. However,
for the EPIC-InterAct Study, which is a large prospective case-cohort study
nested within the European Prospective Investigation into Cancer and Nutrition
(EPIC), covariate measured with error is an inevitable problem since dietary intake
assessed with a food frequency questionnaire is prone to measurement error.
Ignoring measurement error in covariates will cause biases of estimates as well as
loss of power, and sometimes leads to misleading results of data analysis. Thus,
to obtain more reliable results, data analysis of incorporating measurement error
model in the EPIC-InterAct Study is necessary.
In this thesis, we consider an additive error model according to the characteristics
of the EPIC-InterAct Study data, that is, 24HR intake measurements are
biased and errors in FFQ and 24HR measurements are highly correlated. Using
method of moments, we show how to estimate all unknown parameters of the
error model as well as other useful statistics under three reasonable assumptions.
By calculating skewness and kurtosis, we find out best transformation for interested nutrients in the EPIC-InterAct Study, to make them close to normal
distribution.
Based on our proposed additive error model, an approximate maximum likelihood
estimation (AMLE) for covariate with measurement error under the logistic
regression model is developed. This method can be regarded as the adjustment
of the regression calibration method and can provide approximate consistent estimator.
Asymptotic normality of this estimator is established under regularity
conditions. Furthermore, we explore the estimator for the interaction term between
one continuous variable and one categorical variable. Similarly, under the
Cox regression model, we propose an approximate profile likelihood estimation
(APLE) to deal with covariate measurement error in an additive form. Asymptotic
properties of this estimator and an extension of the proposed method to
the case with interaction between one continuous variable and one categorical
variable are also studied.
The logistic regression model and the Cox regression model are two widely used
models in applications, inferences under these two models are challenged if covariates
are measured with errors. We propose the AMLE and APLE to handle
measurement error under the logistic regression model and the Cox regression
model, respectively. Through simulation studies, the performances of our proposed
estimators are better than other corrected methods when errors are highly
correlated and regression coefficients of true covariates are relatively small. According
to real data analysis for the EPIC-InterAct Study, both results from
AMLE and APLE are much more reasonable than those from naive estimation.
Post a Comment