Mapping between measurement scales in meta-analysis, with application to measures of body mass index in children

Quantitative evidence synthesis methods aim to combine data from multiple medical trials to infer relative effects of different interventions. A challenge arises when trials report continuous outcomes on different measurement scales. To include all evidence in one coherent analysis, we require methods to `map' the outcomes onto a single scale. This is particularly challenging when trials report aggregate rather than individual data. We are motivated by a meta-analysis of interventions to prevent obesity in children. Trials report aggregate measurements of body mass index (BMI) either expressed as raw values or standardised for age and sex. We develop three methods for mapping between aggregate BMI data using known relationships between individual measurements on different scales. The first is an analytical method based on the mathematical definitions of z-scores and percentiles. The other two approaches involve sampling individual participant data on which to perform the conversions. One method is a straightforward sampling routine, while the other involves optimization with respect to the reported outcomes. In contrast to the analytical approach, these methods also have wider applicability for mapping between any pair of measurement scales with known or estimable individual-level relationships. We verify and contrast our methods using trials from our data set which report outcomes on multiple scales. We find that all methods recreate mean values with reasonable accuracy, but for standard deviations, optimization outperforms the other methods. However, the optimization method is more likely to underestimate standard deviations and is vulnerable to non-convergence.