Graduation Year

2009

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Epidemiology and Biostatistics

Major Professor

Charles Hendricks Brown, Ph.D.

Co-Major Professor

Getachew Dagne, Ph.D.

Committee Member

Yiliang Zhu, Ph.D.

Committee Member

Paul Greenbaum, Ph.D.

Committee Member

Wei Wang, Ph.D.

Keywords

Generalized Additive Model, EM algorithm, Monte Carlo EM, Markov Chain Monte Carlo, Metropolis-Hastings algorithm, nonlinear structural equation model

Abstract

In order to personalize or tailor treatments to maximize impact among different

subgroups, there is need to model not only the main effects of intervention but also the variation

in intervention impact by baseline individual level risk characteristics. To this end a suitable

statistical model will allow researchers to answer a major research question: who benefits or is

harmed by this intervention program? Commonly in social and psychological research, the

baseline risk may be unobservable and have to be estimated from observed indicators that are

measured with errors; also it may have nonlinear relationship with the outcome. Most of the

existing nonlinear structural equation models (SEM’s) developed to address such problems

employ polynomial or fully parametric nonlinear functions to define the structural equations.

These methods are limited because they require functional forms to be specified beforehand and

even if the models include higher order polynomials there may be problems when the focus of

interest relates to the function over its whole domain.

To develop a more flexible statistical modeling technique for assessing complex

relationships between a proximal/distal outcome and 1) baseline characteristics measured with

errors, and 2) baseline-treatment interaction; such that the shapes of these relationships are data

driven and there is no need for the shapes to be determined a priori.

In the ALV model structure

the nonlinear components of the regression equations are represented as generalized additive

model (GAM), or generalized additive mixed-effects model (GAMM).

Replication study results show that the ALV model estimates of underlying relationships

in the data are sufficiently close to the true pattern. The ALV modeling technique allows

researchers to assess how an intervention affects individuals differently as a function of baseline

risk that is itself measured with error, and uncover complex relationships in the data that might

otherwise be missed. Although the ALV approach is computationally intensive, it relieves its

users from the need to decide functional forms before the model is run. It can be extended to

examine complex nonlinearity between growth factors and distal outcomes in a longitudinal

study.

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