Table 3.

Empirical Size Results

Method	Size	Control-Only	Control + Affected (LOW)a	Control + Affected (MOD)a
min-adj p	10−2	1.32 × 10−2	1.32 × 10−2	1.31 × 10−2
	10−3	1.70 × 10−3	1.71 × 10−3	1.68 × 10−3
	10−4	2.58 × 10−4	2.61 × 10−4	2.47 × 10−4
	10−5	4.15 × 10−5	4.14 × 10−5	3.77 × 10−5
(weighted) traditional GEE	10−2	1.62 × 10−2	1.63 × 10−2	1.60 × 10−2
(4-DF; I/E/U)	10−3	2.59 × 10−3	2.61 × 10−3	2.51 × 10−3
	10−4	5.32 × 10−4	5.37 × 10−4	4.89 × 10−4
	10−5	1.09 × 10−4	1.10 × 10−4	9.29 × 10−5
(weighted) SMAT	10−2	1.17 × 10−2	1.17 × 10−2	1.16 × 10−2
(1-DF; I/E)	10−3	1.41 × 10−3	1.41 × 10−3	1.42 × 10−3
	10−4	1.89 × 10−4	1.90 × 10−4	1.94 × 10−4
	10−5	2.89 × 10−5	2.89 × 10−5	2.71 × 10−5
(weighted) SMAT	10−2	1.19 × 10−2	1.19 × 10−2	1.16 × 10−2
(1-DF; U)	10−3	1.44 × 10−3	1.42 × 10−3	1.41 × 10−3
	10−4	1.86 × 10−4	1.86 × 10−4	1.83 × 10−4
	10−5	3.09 × 10−5	3.10 × 10−5	2.81 × 10−5

Empirical size results for $B={10}^7$ simulated data sets and $n_0=n_1=700$ assuming the true correlation among the phenotypes is unstructured, as given in Table 1. For multiple phenotype analyses, independent (I), exchangeable (E), and unstructured (U) working correlation structures were considered. The results from the 4-DF GEE test with I, E, and U working correlation structures are nearly identical. The results from the 1-DF SMAT with the I and E working correlation structures are nearly identical.

^aLOW and MOD refer to disease prevalence $\pi =0.000745$ and $\pi =0.0745,$ respectively.