Investigation of maternal effects, maternal-fetal interactions and parent-of-origin effects (imprinting), using mothers and their offspring

Abstract

Many complex genetic effects, including epigenetic effects, may be expected to operate via mechanisms in the inter-uterine environment. A popular design for the investigation of such effects, including effects of parent-of-origin (imprinting), maternal genotype, and maternal-fetal genotype interactions, is to collect DNA from affected offspring and their mothers (case/mother duos) and to compare with an appropriate control sample. An alternative design uses data from cases and both parents (case/parent trios) but does not require controls. In this study, we describe a novel implementation of a multinomial modeling approach that allows the estimation of such genetic effects using either case/mother duos or case/parent trios. We investigate the performance of our approach using computer simulations and explore the sample sizes and data structures required to provide high power for detection of effects and accurate estimation of the relative risks conferred. Through the incorporation of additional assumptions (such as Hardy-Weinberg equilibrium, random mating and known allele frequencies) and/or the incorporation of additional types of control sample (such as unrelated controls, controls and their mothers, or both parents of controls), we show that the (relative risk) parameters of interest are identifiable and well estimated. Nevertheless, parameter interpretation can be complex, as we illustrate by demonstrating the mathematical equivalence between various different parameterizations. Our approach scales up easily to allow the analysis of large-scale genome-wide association data, provided both mothers and affected offspring have been genotyped at all variants of interest.

Fig. 3

Results from simulation scenario F. See figure legend to Figure 1 for detailed description of plots. The different methods are denoted m₀–m₉. Method 2 is not shown as the allele frequency A₂ was found to be unidentifiable using Method 2 when fitting scenarios F, G, H, I, and J. The left hand panels show boxplots of the relevant parameter estimates (logs of the given relative risk parameter) with a line indicating the true value, while the top three right panels show the power of likelihood ratio tests of various hypotheses (specifically of whether the given parameter(s) are zero, when allowing for the effects of the other parameters). The lowest right panel shows a boxplot of the total estimated standard error (SE) over the 500 simulation replicates.

Fig. 1

Results from simulation scenario C. The different methods are denoted m₀–m₉. Five hundred case/mother duos were simulated, together with various control samples (500 unrelated controls, 500 units each consisting of the two parents (mother and father) of a control, or 500 control/mother duos) for use in Methods 3–9. The left panels show boxplots of the parameter estimates (logs of the given relative risk parameter) over 500 simulation replicates. A horizontal line is drawn at the true value of the log of the given parameter. The top three right panels show the power of likelihood ratio tests of various hypotheses. Power to achieve significance levels (P values) of 0.05, 0.01, and 0.001 are shown in white, gray, and black, respectively. The top panel shows the power for testing the full model (R₁, R₂, S₁, and S₂) against a null model where all parameters equal 1. The second panel shows the power for testing the full model (R₁, R₂, S₁, and S₂) against a null model that includes R₁ and R₂ only (i.e. the power for detecting the maternal genotype effects S₁ and S₂ while allowing for child genotype effects). The third panel shows the power for testing the full model (R₁, R₂, S₁, and S₂) against a null model that includes S₁ and S₂ only (i.e. the power for detecting the child genotype effects R₁ and R₂ while allowing for maternal genotype effects). The bottom right panel shows a boxplot of the total estimated standard error (SE) (i.e. the sum of the estimated standard errors of all four estimated parameters) over the 500 simulation replicates.

Fig. 2

Results from simulation scenario E. See figure legend to Figure 1 for detailed description of plots. Here the top three left hand panels show boxplots of the relevant parameter estimates (logs of the given relative risk parameter) with a line indicating the true value, and the top three right hand panels show the power of likelihood ratio tests of various hypotheses (specifically of whether the given parameter(s) are zero, when allowing for the effects of the other parameters). The lowest left panel shows a boxplot of the total estimated standard error (SE) over the 500 simulation replicates.

Fig. 4

Sensitivity to misspecification of minor allele frequency A₂. See figure legend to Figure 1 for detailed description of plots. Results are shown for method 1 with minor allele frequency A₂ assumed to be either 0.2, 0.225, 0.25. 0.3, 0.325, 0.35, 0.375 or 0.4. The true value of A₂ used in the simulation was 0.3. Three parameters (R₁, R₂, and I_m) were fitted according to scenario E (similar results were found for other scenarios). Data were simulated under the global null, i.e. the true value of each of these parameters was 1. The top left panels show boxplots of the parameter estimates (logs of the given relative risk parameter) with a line indicating the true value, the lowest left panel shows a boxplot of the total estimated standard error (SE) and the three right panels show the type 1 error for likelihood ratio tests of whether the given parameter or parameters are equal to 1. Type 1 errors for nominal significance levels (P values) of 0.05, 0.01, and 0.001 are shown in white, gray, and black, respectively.

Fig. 5

Results from simulation scenario C, case/parent trios. See figure legend to Figure 1 for detailed description of plots. Method 1 was not considered, but two different versions of Method 2 (2a and 2b) were considered, as described in the text.

Fig. 6

Results from simulation scenario E, case/parent trios. See figure legend to Figures 1 and 2 for detailed description of plots. Method 1 was not considered, but two different versions of Method 2 (2a and 2b) were considered, as described in the text.

Fig. 7

Results from simulation scenario F, case/parent trios. See figure legend to Figures 1 and 3 for detailed description of plots. Method 1 was not considered, but two different versions of Method 2 (2a and 2b) were considered, as described in the text.

Fig. 8

Results from simulation scenario C, case/parent trios with population stratification. Results are from 5,000 simulation replicates. See figure legend to Figures 1,5 and Supplementary Figure 8 for detailed description of plots. Data were simulated under the null hypothesis of no genetic effects, but in the presence of population stratification (two different sub-populations with differing disease rates and marker allele frequencies).

Fig. 9

Results from simulation scenario C, case/mother duos with population stratification. Results are from 5,000 simulation replicates. See figure legend to Figure 1 and Supplementary Figure 8 for detailed description of plots. Data were simulated under the null hypothesis of no genetic effects, but in the presence of population stratification (two different sub-populations with differing disease rates and marker allele frequencies).

Fig. 10

Results from data generated under simulation scenario B but analyzed assuming scenario A. See figure legend to Figure 1 for detailed description of plots. A horizontal line is drawn at the expected value of the log of the given parameter using logistic regression, as calculated in Tables VI and VII.