Epidemiologic follow-up studies have become common in the last 5-10 years.
The aims of this proposal pertain to the evaluation of robustness, development of robust procedures, and detection of misspecification in regression models for the analysis of longitudinal data arising from such studies. Because of the recency of many multivariate regression methods used with unbalanced data these aspects of modelling, which are important for practical application, have not yet been fully explored. Two common examples of model misspecification are omitted covariates and incorrect assumptions on the mathematical form of the relationship. These problems are closely related since omitted covariates can lead to change in the form of regression equations. Conversely, for example quadratic terms in regression equations can be viewed as omitted covariates. Both forms of model violations may lead to differences in across and within individual regression coefficients, an often observed phenomenon. One example of such a situation has been modelled by letting the correlation between the covariate of interest x, and an omitted confounder z be different across than within individuals. Such situations are common (e.g. cohort and period effects in epidemiologic studies of the effect of aging). Extension of the results for this model form the basis for the proposed investigation. The data generating structure will be generalized in several directions, and the impact on longitudinal data analysis will be examined. The investigation of the sensitivity of various existing and novel analysis methods to specific model violations, will serve as a guide to choice and further development of robust methods. Since the impact of model misspecification differs by analysis approach, this will also be investigated as a potential method for detecting model violation. The methods developed in this proposal will be applied in the statistical analysis of data from several ongoing epidemiologic follow-up studies.
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