Thesis (Ph.D.)--University of Rochester. School of Medicine & Dentistry. Dept. of Biostatistics and Computational Biology, 2015.
This dissertation proposes a novel method to compare tumor growth patterns
and evaluates treatment effects using semiparametric linear mixed-effects (SLME)
model, which allows a flexible and smooth curve when modeling correlated data.
The regression function can be decomposed into a linear and a smooth nonparametric
component, giving the name \semiparametric linear." Correlation is taken
into account from a hierarchical mixed-effects perspective. Computation of the
SLME model is equivalent to some linear mixed-effects (LME) models, making it
easy to implement using existing software packages.
We also applied the SLME model to validating and testing the linearity assumption
in the linear mixed-e ects (LME) model against general forms of alternative
hypothesis. If linearity is violated, SLME is useful in suggesting proper
parametric models. Assumption of linearity can be checked via visual inspection
of the Bayesian confidence region of the smoothing component and p-value for
the nonlinear component. Further within-subject correlation structures not explained
by random effects, such as AR1 serial autocorrelation, can be naturally
accommodated by the corresponding LME model.
The SLME model is further generalized to model outcomes from the exponential
family, the generalized semiparametric linear mixed-e ects (GSLME) model.
We proposed an iterative re-weighted linear mixed-e ects (IWLME) algorithm
for fitting the GSLME. The IWLME procedure can also be used to estimate the
within-subject correlation structure for non-continuous outcomes with distributions
from the exponential family.
For hypothesis testing of linearity, we extended the existing generalized maximum
likelihood (GML) hypothesis testing method for independent data to generalized
correlated outcomes. Further within-subject correlation structures, such
as first-order autoregression (AR1), can be taken into account under the same
IWLME framework. This method can be used for validating and testing the
linearity assumption in generalized linear mixed-effects (GLMM) models against
general violations of linearity. The proposed IWLME fitting algorithm, GML
hypothesis testing method and effects of within-subject correlation structure on
estimation and hypothesis testing are evaluated via simulations and several realdata
examples.
The SLME and GSLME models provide us a way to explore, estimate and
compare exible patterns of curves, while taking into account correlation structures
in longitudinal data from an exponential family, including continuous Gaussian
and binomial outcomes. They are also capable of validating and suggesting
appropriate parametric mixed-effects models if linearity if violated.
The contributions of this thesis to existing literature can be summarized into
four parts:
First, we proposed a new way to compare treatment effects and tumor growth
curves using the SLME model, providing physicians and medical researchers a
useful tool to screen potentially effective anti-tumor agents in preclinical animal
studies and study the underlying biological intervention mechanisms between
treatments.
Second, we generalized the SLME model to allow outcomes from the exponential
family, and devised the IWLME fitting algorithm for estimation and calculation
of the Bayesian confidence region.
Third, we relaxed the within-subject independence assumption of the GML
hypothesis testing to allow within-subject covariance structures, and evaluated
the method in simulations and real-data examples. The algorithm is also made
ready for distributed and parallel computing in R.
Fourth, we proposed an IWLME procedure with continuous working dependent
variate to estimate the within-subject covariance structure of GSLME where
outcomes are not necessarily continuous. Specifically, we have evaluated the performance
of IWLME to estimate the within-subject autoregressive (AR1) correlation for
coefficient for binary outcomes. We have also studied the influence of mis-specification of the within-subject AR1 correlation structure on GSLME estimation and hypothesis testing via simulations.
