Although transmission disequilibrium tests (TDT) and the FBAT statistic are robust against population substructure, they have reduced statistical power, as compared with fully efficient tests that are not guarded against confounding because of population substructure. This has often limited the application of transmission disequilibrium tests/FBATs to candidate gene analysis, because, in a genome-wide association study, population substructure can be adjusted by approaches such as genomic control and EIGENSTRAT. Here, we provide new statistical methods for the analysis of quantitative and dichotomous phenotypes in extended families. Although the approach utilizes the polygenic model to maximize the efficiency, it still preserves the robustness to non-normality and misspecified covariance structures. In addition, the proposed method performs better than the existing methods for dichotomous phenotype, and the new transmission disequilibrium test for candidate gene analysis is more efficient than FBAT statistics. Copyright © 2013 John Wiley & Sons, Ltd.