A semiparametric efficient estimator in case-control studies

Details A semiparametric efficient estimator in case-control studies A semiparametric efficient estimator in case-control studies

2010-10-11

arxiv.org/abs/1010.2074v1

Bernoulli 2010, Vol. 16, No. 2, 585-603

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ210 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ210

We construct a semiparametric estimator in case-control studies where the gene and the environment are assumed to be independent. A discrete or continuous parametric distribution of the genes is assumed in the model. A discrete distribution of the genes can be used to model the mutation or presence of certain group of genes. A continuous distribution allows the distribution of the gene effects to be in a finite-dimensional parametric family and can hence be used to model the gene expression levels. We leave the distribution of the environment totally unspecified. The estimator is derived through calculating the efficiency score function in a hypothetical setting where a close approximation to the samples is random. The resulting estimator is proved to be efficient in the hypothetical situation. The efficiency of the estimator is further demonstrated to hold in the case-control setting as well.

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