#### Network harmonisation of physical activity data using validation data

Harmonisation can be achieved using statistical models derived from validation studies which compare two or more methods of assessment. The following coefficients can be used to transform data from starting values to a target criterion. For more information, please see Pearce et al. (2019) [3].

Table 1 Coefficients for harmonisation of Recent Physical Activity Questionnaire (RPAQ) data.

Starting Point Value Target Criterion Value β(SE) α(SE) r2
RPAQ MVPA (minutes/day) Trunk acceleration (m/s2) 5.84⋅10−5 (7.9⋅10−6) .1199 (.0015) .02
RPAQ MVPA (minutes/day) Heart rate PAEE (kJ/day/kg) .0840 (.0061) 60.9 (1.2) .08
RPAQ MVPA (minutes/day) Combined sensing PAEE (kJ/day/kg) .0390 (.0030) 50.69 (.57) .07
RPAQ MVPA (minutes/day) DLW PAEE (kJ/day/kg) .036 (.011) 45.1 (2.1) .14
RPAQ PAEE (kJ/day/kg) Combined sensing PAEE (kJ/day/kg) .239 (.014) 45.63 (.69) .12
RPAQ PAEE (kJ/day/kg) DLW PAEE (kJ/day/kg) .176 (.054) 42.7 (2.7) .14
RPAQ Cambridge Index Combined sensing PAEE (kJ/day/kg) Inactive =0;
Moderately inactive = 5.6 (1.5);
Moderately active = 13.0 (1.6);
Active = 24.2 (1.7)
44.2 (1.3) .12
RPAQ Cambridge Index DLW PAEE (kJ/day/kg) Inactive =0;
Moderately inactive = -7.9 (6.3);
Moderately active = -4.8 (6.4);
Active = 6.9 (6.5)
52.3 (5.8) .12

DLW=doubly labelled water; MVPA=moderate to vigorous physical activity; PAEE=physical activity energy expenditure; SE=standard error.

Table 2 Coefficients for harmonisation of Actiheart data.

Starting Point Value Target Criterion Value β(SE) α(SE) r2
RPAQ MVPA (minutes/day) DLW PAEE (kJ/day/kg) .66 (.11) 20.0 (8.1) .45
Trunk acceleration (m/s2) DLW PAEE (kJ/day/kg) 165 (32) 26.7 (8.2) .37
Heart rate PAEE (kJ/day/kg) DLW PAEE (kJ/day/kg) .34 (.07) 42.7 (5.8) .34

DLW=doubly labelled water; PAEE=physical activity energy expenditure; SE=standard error.

Table 3 Coefficients for harmonisation of wrist acceleration data.

Starting Point Value Target Criterion Value β(SE) α(SE) r2
Wrist acceleration (milli-g) DLW PAEE (kJ/day/kg) 1.05 (.12) 4.2 (5.3) .48
Wrist acceleration (milli-g) Trunk acceleration (m/s2) 4.78⋅10−3 (9.0⋅10−5) -.097 (.0036) .53
Wrist acceleration (milli-g) Combined sensing PAEE (kJ/day/kg) 1.232 (.012) -6.90 (.45) .67

DLW=doubly labelled water; PAEE=physical activity energy expenditure; SE=standard error.

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