# Adaptive Regression for Modeling Nonlinear RelationshipsAdaptive Poisson Regression Modeling of Multivariate Count Outcomes

Adaptive Regression for Modeling Nonlinear Relationships: Adaptive Poisson Regression Modeling of... [This chapter formulates and demonstrates adaptive fractional polynomial modeling of means and dispersions for repeatedly measured count outcomes, possibly converted to rates using offsets. Marginal modeling extends from the multivariate normal outcome context to the multivariate count/rate outcome context. However, due to the complexity in general of computing likelihoods and quasi-likelihoods (as needed to account for non-unit dispersions) for general multivariate marginal modeling, generalized estimating equations (GEE) techniques are often used instead, thereby avoiding computation of likelihoods and quasi-likelihoods. This complicates the extension of adaptive modeling to the GEE context since it is based on cross-validation (CV) scores computed from likelihoods or likelihood-like functions, but a readily computed extended likelihood is formulated for use in adaptive GEE-based modeling of multivariate count/rate outcomes. Conditional modeling also extends to the multivariate count/rate outcome context, both transition modeling and general conditional modeling. In contrast to marginal GEE-based modeling, conditional modeling of means for multivariate count/rate outcomes with unit dispersions is based on pseudolikelihoods that can be used to compute pseudolikelihood CV (PLCV) scores on which to base adaptive transition and general conditional modeling of multivariate count/rate outcomes. These marginal and conditional models can be extended to model dispersions as well as means. Example analyses of these kinds are presented of the post-baseline seizure rates per day over time for patients with epilepsy in terms of the baseline seizure rate, clinic visit, and treatment group (prescribed the drug progabide versus a placebo).] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

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Publisher
Springer International Publishing
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-33944-3
Pages
275 –285
DOI
10.1007/978-3-319-33946-7_14
Publisher site
See Chapter on Publisher Site

### Abstract

[This chapter formulates and demonstrates adaptive fractional polynomial modeling of means and dispersions for repeatedly measured count outcomes, possibly converted to rates using offsets. Marginal modeling extends from the multivariate normal outcome context to the multivariate count/rate outcome context. However, due to the complexity in general of computing likelihoods and quasi-likelihoods (as needed to account for non-unit dispersions) for general multivariate marginal modeling, generalized estimating equations (GEE) techniques are often used instead, thereby avoiding computation of likelihoods and quasi-likelihoods. This complicates the extension of adaptive modeling to the GEE context since it is based on cross-validation (CV) scores computed from likelihoods or likelihood-like functions, but a readily computed extended likelihood is formulated for use in adaptive GEE-based modeling of multivariate count/rate outcomes. Conditional modeling also extends to the multivariate count/rate outcome context, both transition modeling and general conditional modeling. In contrast to marginal GEE-based modeling, conditional modeling of means for multivariate count/rate outcomes with unit dispersions is based on pseudolikelihoods that can be used to compute pseudolikelihood CV (PLCV) scores on which to base adaptive transition and general conditional modeling of multivariate count/rate outcomes. These marginal and conditional models can be extended to model dispersions as well as means. Example analyses of these kinds are presented of the post-baseline seizure rates per day over time for patients with epilepsy in terms of the baseline seizure rate, clinic visit, and treatment group (prescribed the drug progabide versus a placebo).]

Published: Sep 21, 2016

Keywords: Transition Model; Generalize Estimate Equation; Marginal Model; Count Outcome; Seizure Rate