TABLE 3.

Estimated^* regression effects, with standard errors in brackets. Results are given for each model equation shown in Table 4

	Equation Number and Outcome Variable
	⁽¹⁾	⁽²⁾	⁽³⁾	⁽⁴⁾	⁽⁵⁾	⁽⁶⁾	⁽⁷⁾	⁽⁸⁾
Predictor	PASE	LH	TT	E2	FM	ALM	GRIP STRENGTH	PHYSICAL FUNCTION
LH			1.30
			[0.86, 1.75]
TT				0.22	−2.81	0.13
				[0.16, 0.27]	[−4.28, −1.33]	[−0.42, 0.68]
E2					2.24
					[1.06, 3.41]
Height					0.22	0.26
					[0.11, 0.33]	[0.21, 0.31]
PASE					−0.33	0.57	0.93	0.14
					[−1.13, 0.47]	[0.28, 0.85]	[−0.27, 2.11]	[−0.05, 0.34]
FM						0.15	−0.17	−0.04
						[0.11, 0.20]	[−0.35, 0.01]	[−0.06, −0.01]
ALM							1.34	0.02
							[0.97, 1.72]	[−0.03, 0.07]
Grip								0.03
								[0.003, 0.05]
Age	−0.19	0.07	−0.22		0.33	−0.55	−0.83	−0.38
	[−0.27, −0.10]	[0.03, 0.10]	[−0.40, −0.04]		[−0.42, 1.08]	[−0.82, −0.29]	[−1.81, 0.15]	[−0.56, −0.19]
Model R²	0.04	0.03	0.12	0.18	0.17	0.45	0.23	0.16

Estimates weighted according to sampling design (see Methods).

Abbreviations and units: luteinizing hormone (log-transformed LH, IU/L), total testosterone (TT, 100 ng/dL), total estradiol (E2, 10 pg/mL), Physical Activity Scale for the Elderly (PASE, 1 SD), fat and appendicular lean mass (FM and ALM, kg), grip (kg), age (10 y).

Listed below is the system of equations used to estimate the parameters in this table. Regression parameters α, λ, β, γ, and ζ quantify the association between upstream variables and downstream outcome measures including physical activity (PASE), hormones [testosterone (T), luteinizing hormone (LH), and estradiol (E2)], body composition [appendicular lean and total body fat mass (ALM and FM)], grip strength, and physical function, respectively, while ε indicates error terms.

⁽¹⁾

PASE = λ₀ + λ₁Age + ε₃

⁽²⁾

LH = α₀ + α₁Age + ε₁

⁽³⁾

T = α₂ + α₃Age + α₄LH + ε₄

⁽⁴⁾

E2 = α₅ + α₆T + ε₅

⁽⁵⁾

FM = β₀ + β₁Age + β₂T + β₃E2 + β₄Height + β₅PASE + ε₆

⁽⁶⁾

ALM = β₆ + β₇Age + β₈T + β₉Height + β₁₀PASE + β₁₁FM + ε₇

⁽⁷⁾

Grip Strength = γ₀ + γ₁Age + γ₂PASE + γ₃FM + γ₄ALM + ε₈

⁽⁸⁾

Phys. Function = ζ₀ + ζ₁Age + ζ₂PASE + ζ₃FM + ζ₄ALM + ζ₅Grip + ε₉