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Family-based linkage tests are methods for detection of the genetic basis of a disease. For the case-parent triad data, it is known that tests of linkage interfere with the association parameter under recessive disease models. The purpose of the paper is to discuss the effects of nuisance parameters on the family-based linkage tests under general models. It is shown that the linkage tests do not only interfere with the association parameter, but also with the gene substitution effect in general models.