Table 5. 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 the FTO (rs1558902) genetic variant as an instrument.

Adiposity	Activity	N	Linear Regression			Instrumental Variable Regression (FTO rs1558902)
			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	35.0	0.01	−0.31 (−0.64, −0.03)	−54.5 (−114.3, 5.3)	0.07	0.28
	Moderate-to-vigorous activity (min/d)c		−0.17 (−0.20, −0.14)	−2.6 (−3.1, −2.1)	3.7×10−29			−0.16 (−0.49, 0.17)	−2.4 (−7.5, 2.6)	0.34	0.95
	Sedentary time (min/d)		0.05 (0.02, 0.08)	3.5 (1.5, 5.5)	5.0×10−4			0.50 (0.13, 0.86)	33.0 (8.9, 57.2)	0.007	0.01
FMI	Total physical activity (counts/min)	4,244	−0.18 (−0.21, −0.15)	−32.3 (−37.6, −27,1)	1.5×10−33	34.7	0.01	−0.31 (−0.64, 0.02)	−55.3 (−114.1, 3.4)	0.07	0.44
	Moderate-to-vigorous activity (min/d)c		−0.22 (−0.25, −0.19)	−3.4 (−3.8, −2.9)	2.4×10−48			−0.16 (−0.48, 0.17)	−2.4 (−7.4, 2.6)	0.35	0.71
	Sedentary time (min/d)		0.09 (0.06, 0.12)	5.8 (3.8, 7.7)	1.4×10−8			0.50 (0.14, 0.86)	33.4 (9.5, 57.3)	0.006	0.01

Regression results were adjusted for age.

^aCoefficients are displayed as sex-specific z-scores for both measures of adiposity and activity levels and have also 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.