Power calculations for likelihood ratio tests for offspring genotype risks, maternal effects, and parent-of-origin (POO) effects in the presence of missing parental genotypes when unaffected siblings are available

Abstract

Genotype-based likelihood-ratio tests (LRT) of association that examine maternal and parent-of-origin effects have been previously developed in the framework of log-linear and conditional logistic regression models. In the situation where parental genotypes are missing, the expectation-maximization (EM) algorithm has been incorporated in the log-linear approach to allow incomplete triads to contribute to the LRT. We present an extension to this model which we call the Combined_LRT that incorporates additional information from the genotypes of unaffected siblings to improve assignment of incompletely typed families to mating type categories, thereby improving inference of missing parental data. Using simulations involving a realistic array of family structures, we demonstrate the validity of the Combined_LRT under the null hypothesis of no association and provide power comparisons under varying levels of missing data and using sibling genotype data. We demonstrate the improved power of the Combined_LRT compared with the family-based association test (FBAT), another widely used association test. Lastly, we apply the Combined_LRT to a candidate gene analysis in Autism families, some of which have missing parental genotypes. We conclude that the proposed log-linear model will be an important tool for future candidate gene studies, for many complex diseases where unaffected siblings can often be ascertained and where epigenetic factors such as imprinting may play a role in disease etiology.

Figure 1

Simulation-based power calculations when effects of the child genotype on risk are simulated and modeled. Results for 2000 samples of 200 families with 1 missing parent simulated under additive, dominant and multiplicative models where R₁=1.8 and the allele frequency p=0.30. Triads are represented by □ , quads by , quints by ■ .

Figure 2

Plot of estimated power based on 2000 simulations where maternal effects are modeled, shown as a function of the percentage of families where the father is missing genotype data. The model was simulated so that R₁=1, R₂=1, S₁=1.8, S₂=2.5, and Im=1. A 2-df LRT was used to test maternal genotype effects. Dashed lines represent power for the fully typed dataset. The triangles are used to plot the results using only completely typed triads and circles are used for the LRT that incorporates the EM algorithm using triads with missing parents. The cross and square are used to plot the power results for the LRT that incorporates the EM algorithm when 1 or 2 unaffected siblings are used, respectively.

Figure 3

Plot of estimated power based on simulations where a POO effect is modeled and as a function of the percentage of families where 1 parent is missing genotype data. The model was simulated so that R₁=1.8, R₂=2.5, Im=2.5 and S₁=S₂=1. A 1-df LRT was used in the analysis. The power for the fully typed dataset is represented by dashed lines. The triangles are used to plot the results using only completely typed triads and circles are used for the LRT that incorporates the EM algorithm using only triads. The cross and square are used to plot the power results for the LRT that incorporates the EM algorithm when 1 or 2 unaffected siblings are used, respectively.

Figure 4

Plot of estimated power based on 2000 simulations where a POO effect is modeled and as a function of the percentage of families where both parents are missing genotype data. The model was simulated so that R₁=1.8, R₂=2.5, Im=2.5 and S₁=S₂=1. A 1-df LRT was used in the analysis. The power for the fully typed dataset is represented by dashed lines. The triangles are used to plot the results using only completely typed triads, circles are used for the LRT that incorporates the EM algorithm using only triads. The cross and square are used to plot the power results for the LRT that incorporates the EM algorithm when 1 or 2 unaffected siblings are used, respectively.