Linear Transformation Model With Parametric Covariate Transformations

• 成果类型: Article
• 署名作者: Fan, Chunpeng; Fine, Jason P.
• 署名单位: Sanofi-Aventis; Sanofi USA; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.770707
• 发表日期: 2013
• 页码: 701-712
• 关键词: partial likelihood; clustered data; regression; tests

摘要

The traditional linear transformation model assumes a linear relationship between the transformed response and the covariates. However, in real data, this linear relationship may be violated. We propose a linear transformation model that allows parametric covariate transformations to recover the linearity. Although the proposed generalization may seem rather simple, the inferential issues are quite challenging due to loss of identifiability under the null of no effects of transformed covariates. This article develops tests for such hypotheses. We establish rigorous inferences for parameters and the unspecified transformation function when the transformed covariates have nonzero effects. The estimates and tests perform well in simulation studies using a realistic sample size. We also develop goodness-of-fit tests for the transformation and R-2 for model comparison. GAGurine data are used to illustrate the practical utility of the proposed methods.