Testing in semiparametric models with interaction, with applications to gene-environment interactions

Arnab Maity, Raymond J. Carroll, Enno Mammen, Nilanjan Chatterjee

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Motivated from the problem of testing for genetic effects on complex traits in the presence of gene-environment interaction, we develop score tests in general semiparametric regression problems that involves Tukey style 1 degree-of-freedom form of interaction between parametrically and non-parametrically modelled covariates. We find that the score test in this type of model, as recently developed by Chatterjee and co-workers in the fully parametric setting, is biased and requires undersmoothing to be valid in the presence of non-parametric components. Moreover, in the presence of repeated outcomes, the asymptotic distribution of the score test depends on the estimation of functions which are defined as solutions of integral equations, making implementation difficult and computationally taxing. We develop profiled score statistics which are unbiased and asymptotically efficient and can be performed by using standard bandwidth selection methods. In addition, to overcome the difficulty of solving functional equations, we give easy interpretations of the target functions, which in turn allow us to develop estimation procedures that can be easily implemented by using standard computational methods. We present simulation studies to evaluate type I error and power of the method proposed compared with a naive test that does not consider interaction. Finally, we illustrate our methodology by analysing data from a case-control study of colorectal adenoma that was designed to investigate the association between colorectal adenoma and the candidate gene NAT2 in relation to smoking history.

Original languageEnglish (US)
Pages (from-to)75-96
Number of pages22
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number1
StatePublished - Jan 2009
Externally publishedYes


  • Additive models
  • Diplotypes
  • Function estimation
  • Non-parametric regression
  • Omnibus hypothesis testing
  • Partially linear model
  • Repeated measures
  • Score test
  • Semiparametric models
  • Smooth backfitting
  • Tukey's 1 degree-of-freedom model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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