Flexible Modeling Tools for Continuous Longitudinal Data

Abstract

In this dissertation we have focussed on methods for modeling continuous, i.e., Gaussian, longitudinal data. We have shown that a flexible, rich set of tools is available for analyzing this type of data. In the repeated measures setting, each of the three model families, which were compared in detail in Chapter 4, model both the dependence of the response on the explanatory variables and the autocorrelation among the responses. Ignoring this correlation leads to incorrect inferences about the fixed-effect regression coefficients, and to a loss of efficiency, that is, less precise estimates. This point was illustrated in Chapter 5, where we were able to establish an additional treatment effect that had gone undetected in previous, simpler analyzes. By properly accounting for birdspecific effects, we gained power to assess the effect of treatment, underscoring the strength of the non-linear mixed modeling framework. In addition to a gain in efficiency, the modeling of within-subject correlation can also be of direct scientific interest. In Chapter 3, the correlation structure was examined to describe the persistence dimension of patients exhibiting persistent disturbing behavior (PDB). In Chapter 6, we focused on serial correlation and we proposed a spline-based approach to flexibly model the serial correlation function. Applying this method to data from a pre-clinical experiment in dementia, enabled us to show that a circadian pattern played a role in the mean structure, variance structure and the correlation structure simultaneously. However, as Davidian and Giltinan (1995, p. 330) mentioned, second moment behavior is inherently difficult to characterize, and this is especially true for correlation parameters. This also means that a substantial amount of information, i.e., a large dataset, is needed when drawing conclusions about the nature of the correlation structure. (Excerpt from Conclusion).