Table 3.

Properties of different regression models in the presence of the eight analytical challenges, as detailed in Table 1

Model, $g\left(E\left(Y\right)\right)=$	Testing $H_0:$	C3/C4	C5/C6	C7/C8
$M_1:{\beta }_0+{\beta }_{S}S+{\beta }_A{G}_A$	${\beta }_A=0$	$\surd$	$\times$	$\times$
$M_2:{\beta }_0+{\beta }_{S}S+{\beta }_A{G}_A+{\beta }_D{G}_D$	${\beta }_A={\beta }_D=0$	$\surd$	$\times$	$\surd$
$M_3:{\beta }_0+{\beta }_{S}S+{\beta }_A{G}_A+{\beta }_{GS}GS$	${\beta }_A={\beta }_{GS}=0$	$\surd$	$\surd$	$\times$
$M_4:{\beta }_0+{\beta }_{S}S+{\beta }_A{G}_A+{\beta }_D{G}_D+{\beta }_{GS}GS$	${\beta }_A={\beta }_D={\beta }_{GS}=0$	$\surd$	$\surd$	$\surd$

Note: Whole‐genome considerations such as C1 (continuous vs. binary traits) and C2 (Hardy–Weinberg equilibrium vs. disequilibrium) are naturally dealt with by the genotype‐based regression approach. X‐chromosome‐specific considerations include C3 (choice of the baseline allele), C4 (sex as a confounder and type I error control), C5 (gene‐sex interaction), C6 (X‐chromosome inactivation (XCI) vs. no XCI), C7 (random vs. skewed XCI), and C8 (the dominance effect). In the table, $\times$ indicates a problem for the corresponding model and test, and $\surd$ means no problem. Relevant covariates $E$'s should be included in the model but omitted here for notation simplicity. Joint testing of $H_0:{\beta }_A={\beta }_D={\beta }_{GS}=0$ based on $M_4$ is the recommended, most robust approach; see Figures 2 and S5 for power comparisons among $M_1$–$M_4$.