This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Salanti, G. Articles by Ulm, K. Search for Related Content PubMed PubMed Citation Articles by Salanti, G. Articles by Ulm, K. Social Bookmarking                         What's this?

A nonparametric changepoint model for stratifying continuous variables under order restrictions and binary outcome

Institute for Medical Statistics and Epidemiology, Munich, Germany, vorgia{at}web.de

Kurt Ulm

Institute for Medical Statistics and Epidemiology, Munich, Germany

Modelling using monotonic regression can be a useful alternative to parametric approaches when optimal stratification for continuous predictors is of interest. This method is described here in the context of binary response. Within this framework we aim to address two points. First, we propose a method to enhance the parsimony of the model, by applying a reducing procedure based on a sequence of Fisher exact tests and a bootstrap method to select between full monotonic and reduced model. Secondly, we discuss the case of multiple predictors: an iterative algorithm (an extension of the Pool Adjacent Violators Algorithm) can be applied when more than one predictor variable is taken into account. The resulting model is a monotonic surface and can be applied alternatively to the additive monotonic models as described by Morton-Jones and colleagues when the explanatory variables are assumed to interact. The monotonic-surface model provides also a multivariate extension of the monotonic likelihood ratio test. This test is discussed here and an approach based on permutations to assess the p-value is proposed. Finally, we combine both ideas (reduced monotonic regression and monotonic-surface estimation) to a simple and easy to interpret model, which leads to a combination of the predictors in a few constant risk groups. Despite the fact that the proposed approach becomes somewhat cumbersome due to the lack of asymptotic methods to infer, it is attractive because of its simplicity and stability. An application will outline the benefit of using bivariate step functions in modelling.

Statistical Methods in Medical Research, Vol. 12, No. 4, 351-367 (2003)
DOI: 10.1191/0962280203sm338ra


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?