title: Correction of the significance level when attempting multiple transformations of an explanatory variable in generalized linear models.
abstract: BACKGROUND
  In statistical modeling, finding the most favorable coding for an exploratory quantitative variable involves many tests. This process involves multiple testing problems and requires the correction of the significance level.
  
  
  METHODS
  For each coding, a test on the nullity of the coefficient associated with the new coded variable is computed. The selected coding corresponds to that associated with the largest statistical test (or equivalently the smallest pvalue). In the context of the Generalized Linear Model, Liquet and Commenges (Stat Probability Lett,71:33-38,2005) proposed an asymptotic correction of the significance level. This procedure, based on the score test, has been developed for dichotomous and Box-Cox transformations. In this paper, we suggest the use of resampling methods to estimate the significance level for categorical transformations with more than two levels and, by definition those that involve more than one parameter in the model. The categorical transformation is a more flexible way to explore the unknown shape of the effect between an explanatory and a dependent variable.
  
  
  RESULTS
  The simulations we ran in this study showed good performances of the proposed methods. These methods were illustrated using the data from a study of the relationship between cholesterol and dementia.
  
  
  CONCLUSIONS
  The algorithms were implemented using R, and the associated CPMCGLM R package is available on the CRAN.
authors.affiliation: University Bordeaux, ISPED, Centre INSERM U-897-Epidemiologie-Biostatistique, Bordeaux, France.
authors.forename: Benoit
authors.initials: B
authors.lastname: Liquet
authors.forename: Jérémie
authors.initials: J
authors.lastname: Riou
mesh_terms: D000368:Aged; D000465:Algorithms; D008076:Cholesterol, HDL / Q000097:blood; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D003704:Dementia / Q000097:blood; D015981:Epidemiologic Factors; D015340:Epidemiologic Research Design; D006801:Humans; D016014:Linear Models; D015999:Multivariate Analysis; D015203:Reproducibility of Results; D012307:Risk Factors; D018401:Sample Size
chemical_list: D008076:Cholesterol, HDL