Harmonisation of data for pooled analysis relies on the principle of inferential equivalence between variables from different sources. Ideally, this is achieved using models of the direct relationship with gold standard criterion measures, but the necessary validation data are often unavailable. This study examines an alternative method of harmonisation by indirect validation. Starting methods were self-report or accelerometry, from which we derived indirect models of relationships with doubly labelled water (DLW)-measured physical activity energy expenditure (PAEE) using sets of two bridge equations via one of three intermediate measures. Coefficients and performance of indirect models were compared to corresponding direct validation models (linear regression of DLW-measured PAEE on starting methods). Indirect model beta coefficients were attenuated compared to direct model betas (10-63%), narrowing the range of PAEE values; attenuation was greater when bridge equations were weak. Directly and indirectly harmonised models had similar error variance but most indirectly derived values were biased at group-level. Correlations with DLW-measured PAEE were identical after harmonisation using continuous linear but not categorical models. Wrist acceleration harmonised to DLW-measured PAEE via combined accelerometry and heart rate sensing had lowest error variance (24.5%) and non-significant mean bias 0.9 (95%CI: -1.6; 3.4) kJ·day-1·kg-1. Associations between PAEE and BMI were similar for directly and indirectly harmonised values, but most fell outside the confidence interval of the criterion PAEE-to-BMI association. Indirect models can be used for harmonisation. Performance depends on the measurement properties of original data, variance explained by available bridge equations, and similarity of population characteristics.
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