Table 6. Associations between body mass index/fat mass index and activity levels as tested both by conventional epidemiological approaches and through the application of instrumental variable analysis using a 31-SNP weighted allelic score (excluding FTO) as an instrument.

Adiposity	Activity	N	Linear Regression			Instrumental Variable Regression (Weighted Allelic Score with 31 SNPs)
			Z-Score Value Coefficient (95% CI)a	Difference in Activity, Raw Units (95% CI)a	p-Value	F-Statistic	Partial R 2	Z-Score Value Coefficient (95% CI)a	Difference in Activity, Raw Units (95% CI)a	p-Value	p-Value (DWH)b
BMI	Total physical activity (counts/min)	4,296	−0.12 (−0.15, −0.10)	−22.3 (−27.6, −17.0)	1.6×10−16	88.9	0.02	−0.13 (−0.34, 0.07)	−24.0 (−61.2, 13.1)	0.21	0.92
	Moderate-to-vigorous activity (min/d)c		−0.17 (−0.20, −0.14)	−2.6 (−3.1, −2.1)	3.7×10−29			−0.19 (−0.40, 0.02)	−2.9 (−6.1, 0.3)	0.07	0.85
	Sedentary time (min/d)		0.05 (0.02, 0.08)	3.5 (1.5, 5.5)	5.0×10−4			0.09 (−0.12, 0.30)	5.8 (−8.2, 19.7)	0.42	0.75
FMI	Total physical activity (counts/min)	4,244	−0.18 (−0.21, −0.15)	−32.3 (−37.6, −27,1)	1.5×10−33	73.3	0.02	−0.16 (−0.38, 0.07)	−28.1 (−68.4, 12.2)	0.17	0.84
	Moderate-to-vigorous activity (min/d)c		−0.22 (−0.25, −0.19)	−3.4 (−3.8, −2.9)	2.4×10−48			−0.22 (−0.44, 0.01)	−3.4 (−6.8, 0.8)	0.06	0.99
	Sedentary time (min/d)		0.09 (0.06, 0.12)	5.8 (3.8, 7.7)	1.4×10−8			0.10 (−0.13, 0.33)	6.8 (−8.4, 22.1)	0.38	0.89

Regression results were adjusted for age.

^aCoefficients are displayed as sex-specific z-scores for both measures of adiposity and activity levels and have been rescaled to give more meaningful outcomes relating to the raw units of these variables. The raw-unit difference was computed by multiplying the z-score value by the SD of the variable, taken from Table 1.

^b p(DWH) is the p-value of the Durbin form of the DWH test, which examines the difference between the estimates from linear regression and instrumental variable analysis.

^cModerate-to-vigorous activity was log transformed for analysis.