Abstract:
This thesis consists of three papers which investigate marginal models,
nonparametric approaches, generalized mixed effects models and variance
components estimation in longitudinal data analysis.
In the first paper, a new marginal approach is introduced for high-dimensional
cell-cycle microarray data with no replicates. There are two
kinds of correlation for cell-cycle microarray data. Measurements within a
gene are correlated and measurements between genes are also correlated since
some genes may be biologically related. The proposed procedure combines
a classifying method, quadratic inference function method and nonparametric
techniques for complex high dimensional cell cycle microarray data. The
gene classifying method is first applied to identify genes with similar cell cycle
patterns into the same class. Then we use genes within the same group
as pseudo-replicates to fit a nonparametric model. The quadratic inference
function is applied to incorporate within-gene correlations. An asymptotic
chi-squared test is also applied to test whether certain genes have cell cycles
phenomena. Simulations and an example of cell-cycle microarray data are
illustrated.
The second paper proposes a new approach for generalized linear mixed
models in longitudinal data analysis. This new approach is an extension of
the quadratic inference function (Qu et al., 2000) for generalized linear mixed
models. Two conditional extended scores are constructed for estimating fixed
effects and random effects. This new approach involves only the first and second
conditional moments. It does not require the specification of a likelihood
function and also takes serial correlations of errors into account. In addition,
the estimation of unknown variance components associated with random
effects or nuisance parameters associated with working correlations are not required.
Furthermore, it does not require the normality assumption for random
effects.
In the third paper, we develop a new approach to estimate variance
components using the second-order quadratic inference function. This is an
extension of the quadratic inference function for variance components estimation
in linear mixed models. The new approach does not require the specification
of a likelihood function. In addition, we propose a chi-squared test to test
whether the variance components of interest are significant. This chi-squared
test can also be used for testing whether the serial correlation is significant.
Simulations and a real data example are provided as illustration.
