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Tests in a Case–control Design Including Relatives

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  • STEFANIE BIEDERMANN
  • EVA NAGEL
  • AXEL MUNK
  • HAJO HOLZMANN
  • ANSGAR STELAND

Abstract

. We present a new approach to handle dependencies within the general framework of case–control designs, illustrating our approach by a particular application from the field of genetic epidemiology. The method is derived for parent–offspring trios, which will later be relaxed to more general family structures. For applications in genetic epidemiology we consider tests on equality of allele frequencies among cases and controls utilizing well‐known risk measures to test for independence of phenotype and genotype at the observed locus. These test statistics are derived as functions of the entries in the associated contingency table containing the numbers of the alleles under consideration in the case and the control group. We find the joint asymptotic distribution of these entries, which enables us to derive critical values for any test constructed on this basis. A simulation study reveals the finite sample behaviour of our test statistics.

Suggested Citation

  • Stefanie Biedermann & Eva Nagel & Axel Munk & Hajo Holzmann & Ansgar Steland, 2006. "Tests in a Case–control Design Including Relatives," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 621-635, December.
  • Handle: RePEc:bla:scjsta:v:33:y:2006:i:4:p:621-635
    DOI: 10.1111/j.1467-9469.2006.00500.x
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