Mapping between treatment effects: the role of RCT and non-RCT data

Abstract: The Mapping Problem is conceptualised as follows: for purposes of economic assessment we need to know the effect of treatments on Quality of Life. If this is not observed in RCTs, we "map" RCT-based estimates of treatment effects on Disease-Specific measures into treatment effects on, say, EQ-5D. The mapping coefficients are usually identified by regressing EQ-5D against the DSM in cohort studies on suitable patients.

However, mapping coefficients based on Ordinary Least Squares regression do not have the properties required for coherent mappings because they are neither invertible nor transitive.

We propose instead that mapping coefficients could be estimated from the ratios of treatment effects in placebo-controlled RCTs. This is illustrated in a set of 8 RCTs of biologics against placebo in Ankylosing Spondylitis, in which 6 different outcome measures were reported in different combinations (PAIN-VAS, BASFI, BASDAI, ASQOL, SF36-PCS, SF36-MCS). The advantage of this approach is that one can estimate the treatment effect on each outcome AND the between-outcome mappings at the same time. In this dataset it can be shown that mappings are not exactly constant across trials, but the degree of between-trial variation is pleasingly low, with a coefficient of variation (standard deviation / mean) around 12%.

This method can be explained in terms of the theory of "congeneric tests". Mappings can be seen as ratios of linear combinations of factor loadings, where the coefficients represent the relative size of the treatment effect on each factor.

Can cohort data be used to inform mappings? Not by itself. However, it should be possible to use the RCT-based mappings to identify (ie calibrate) the coefficients of the factor loadings derived from cohort data, and then apply these to estimate mappings between variables included in the RCTs and other variables in the cohort. We illustrate this with a factor analysis of a cohort with ankylosing spondylitis, based on a cross-sectional assessment of PAIN-VAS, BASFI, BASDAI, ASQOL, SF36-PCS, SF36-MCS, and EQ-5D. This generates a set of coherent trial-based mappings between all these scales.