Statistical Modelling 7 (2007), 125–153
Inference for the relative treatment effect with the density ratio model
Konstantinos Fokianos
Department of Mathematics & Statistics,
University of Cyprus
Cyprus
James F Troendle
Biometry and Mathematical Statistics Branch,
National Institute of Child Health and Human Development,
Bld 6100 Room 7B05
Bethesda, MD 20892
USA.
eMail:
jt3t@nih.gov
Abstract:
Consider the problem of estimating and testing the relative treatment
effect between two populations based on a random sample from each
distribution. Under the well-established normal theory,
inference is based on analysis of variance methods. However, there are
many examples of skewed data which show that normal theory is not
applicable. Then the problem of inference regarding the treatment
effect can be attacked by standard nonparametric methods. In this
paper, we propose a semiparametric model, the so-called density ratio
model, which specifies that the log-likelihood ratio of two densities is
linear in some parameters. For testing hypotheses regarding the relative
treatment effect, a robust test is obtained by employing the density
ratio model for a suitable Box-Cox transformation of the data. The
transformation, along with the density ratio model, are estimated by
maximum empirical likelihood. The new test procedure is studied
theoretically and it is applied to real and simulated data. It is
further compared with some nonparametric competitors, and it is
found to have relatively high power across a wide variety of
distributions, including those outside the density ratio family.
Keywords:
Box-Cox transformation; empirical likelihood;likelihood ratio test;
nonparametric Behrens-Fisher hypothesis; power; simulation
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