Supplementary Figure 1. Age-Specific Plot of Bmis for All Subjects in Both Sexes

Supplementary Figure 1. Age-specific plot of BMIs for all subjects in both sexes.

Supplementary Figure 2.BIC values under different orders of Legend orthogonal polynomials in two different sexes.

Supplementary Figure 3. Manhattan plot of p-values for association by genomic position for different sexes.

Supplementary Table 1.Structure of Sparse Longitudinal Data for GWAS for a Toy Example of 12 Subjects.

Note: Each subject is genotyped for m SNP markers and phenotyped for a complex trait at unevenspaced time points. At each marker, three genotypes are AA, Aa, and aa, symbolized by 1, 2, and 3, respectively.

Supplementary Table 2.Genes within 500kb of significant SNPs

Chr / Pos / Ss_ / Rs_ / ALLELE1 / ALLELE2 / Gene (within 500Kb)
1 / 180384945 / ss66267473 / rs4451518 / T / C / GLUL (Glutamate-ammonia ligase)
ZNF648 (Zinc finger protein 648)
10 / 133498454 / ss66164954 / rs7903156 / G / A / FLJ46300 (FLJ46300 protein)
PPP2R2D (protein phosphatase 2, regulatory subunit B, delta isoform)
BNIP3 (BCL2/adenovirus E1B 19 kDa protein-interacting protein 3)
12 / 96235821 / ss66059620 / rs7309679 / A / G / NEDD1** (Neural precursor cell expressed, developmentally down-regulated 1)
17 / 2688526 / ss66211622 / rs9915696 / C / G / PAFAH1B1 (Platelet-activating factor acetylhydrolase IB subunit alpha)
KIAA0664
GARNL4* (GTPase activating Rap/RanGAP domain-like 4)
OR1D4-5 (Olfactory receptor 1D4, 5)
18 / 73293243 / ss66442359 / rs948716 / C / T / GALR1 (Galanin receptor 1)
20 / 22580931 / ss66171460 / rs747911 / T / C / FOXA2 (Forkhead Box A2)
3 / 122054294 / ss66505757 / rs2171168 / C / T / HGD (Homogentisate oxygenase)
RABL3 (RAB, member of RAS oncogene family-like 3)
GTF2E1 (general transcription factor IIE, polypeptide 1)
4 / 125989067 / ss66397307 / rs13124340 / T / G / ANKRD50 (ankyrin repeat domain 50)
6 / 131562687 / ss66068448 / rs3903759 / C / A / EPB41L2 (Band 4.1-like protein 2)
AKAP7* (A-kinase anchor protein 7 isoform gamma)
8 / 11059516 / ss66288062 / rs17782554 / G / C / XKR6*(XK, Kell blood group complex subunit-related family, member )
MTMR9 (myotubularin related protein 9)
AMAC1L2 (acyl-malonyl condensing enzyme 1-like 2)
8 / 11093585 / ss66479137 / rs11783045 / A / G / XKR6*
MTMR9
AMAC1L2

* : SNP in the gene

** : SNP within 100Kb from the gene

Supplementary Table 3.Functions of genes

Shown in the excel table.

Supplementary Table 4. Simulation results by fGWAS.

Genotype Parameters true value estimated (MAF=0.1)

Sample size=1,000 sample size=2,000

AA u0 27.09 27.11(1.29) 27.19(1.26)

u1 2.85 3.39(0.48) 3.06(0.37)

u2 1.78 2.47(1.29) 1.98(1.12)

u3 0.58 1.35(0.47) 0.94(0.38)

Aa u0 26.07 26.52(1.57) 26.09(1.38)

u1 -0.40 -0.33(0.11) -0.37(0.10)

u2 -0.65 -0.61(0.12) -0.64(0.10)

u3 -1.02 -0.96(0.25) -0.99(0.19)

aa u0 26.37 26.42(1.65) 26.41(1.53)

u1 0.32 0.39(0.11) 0.34(0.11)

u2 -0.98 -0.94(0.09) -0.95(0.08)

u3 -0.14 -0.09(0.04) -0.10(0.04)

Genotype Parameters true value estimated (MAF=0.2)

Sample size=1,000 sample size=2,000

AA u0 27.09 27.57(1.28) 27.24(1.25)

u1 2.85 3.47(0.46) 2.97(0.36)

u2 1.78 2.33(1.28) 1.98(1.11)

u3 0.58 1.11(0.48) 0.72(0.35)

Aa u0 26.07 26.13(1.58) 26.08(1.38)

u1 -0.40 -0.33(0.10) -0.38(0.11)

u2 -0.65 -0.60(0.11) -0.62(0.10)

u3 -1.02 -0.97(0.25) -1.00(0.19)

aa u0 26.37 26.43(1.66) 26.39(1.52)

u1 0.32 0.39(0.09) 0.34(0.10)

u2 -0.98 -0.93(0.09) -0.97(0.08)

u3 -0.14 -0.08(0.05) -0.11(0.04)

Genotype Parameters true value estimated (MAF=0.3)

Sample size=1,000 sample size=2,000

AA u0 27.09 27.64(1.27) 27.19(1.26)

u1 2.85 3.29(0.49) 3.20(0.37)

u2 1.78 2.23(1.25) 1.97(1.10)

u3 0.58 0.99(0.48) 0.93(0.38)

Aa u0 26.07 26.12(1.56) 26.10(1.37)

u1 -0.40 -0.34(0.11) -0.38(0.10)

u2 -0.65 -0.60(0.12) -0.64(0.11)

u3 -1.02 -0.95(0.24) -0.99(0.18)

aa u0 26.37 26.42(1.65) 26.39(1.53)

u1 0.32 0.38(0.10) 0.35(0.11)

u2 -0.98 -0.93(0.09) -0.97(0.08)

u3 -0.14 -0.06(0.04) -0.11(0.04)

Genotype Parameters true value estimated (MAF=0.4)

Sample size=1,000 sample size=2,000

AA u0 27.09 27.51(1.29) 27.19(1.25)

u1 2.85 3.60(0.47) 3.14(0.37)

u2 1.78 2.55(1.27) 2.08(1.12)

u3 0.58 1.22(0.46) 0.95(0.38)

Aa u0 26.07 26.15(1.55) 26.08(1.38)

u1 -0.40 -0.35(0.12) -0.38(0.10)

u2 -0.65 -0.59(0.12) -0.63(0.11)

u3 -1.02 -0.96(0.24) -1.00(0.19)

aa u0 26.37 26.44(1.67) 26.39(1.53)

u1 0.32 0.39(0.09) 0.34(0.11)

u2 -0.98 -0.93(0.11) -0.96(0.08)

u3 -0.14 -0.08(0.05) -0.11(0.045)

Genotype Parameters true value estimated (MAF=0.5)

Sample size=1,000 sample size=2,000

AA u0 27.09 27.84(1.29) 27.45(1.26)

u1 2.85 3.57(0.46) 3.00(0.37)

u2 1.78 2.25(1.29) 1.93(1.11)

u3 0.58 1.26(0.46) 0.74(0.37)

Aa u0 26.07 26.13(1.55) 26.09(1.37)

u1 -0.40 -0.33(0.12) -0.37(0.09)

u2 -0.65 -0.60(0.11) -0.63(0.11)

u3 -1.02 -0.95(0.24) -1.00(0.19)

aa u0 26.37 26.43(1.67) 26.41(1.53)

u1 0.32 0.38(0.11) 0.33(0.10)

u2 -0.98 -0.91(0.10) -0.96(0.08)

u3 -0.14 -0.07(0.05) -0.10(0.04)

Covariance parameters estimate:

Sample size=1,000 Sample size=2,000

Parameters true value MAF MAF

0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5

σ 1.26 1.30 1.33 1.31 1.33 1.32 1.27 1.26 1.26 1.26 1.26

(0.95) (0.95) (0.96) (0.95) (0.95) (0.89) (0.88)(0.89)(0.88)(0.89)

ρ 0.45 0.51 0.52 0.49 0.50 0.50 0.45 0.45 0.44 0.45 0.44

(0.02) (0.02) (0.02) (0.025) (0.02) (0.02)(0.02)(0.02)(0.02)(0.02)