Are latent variable models preferable to composite score approaches when assessing risk factors of change? Evaluation of type-I error and statistical power in longitudinal cognitive studies

As with many health constructs, cognition is difficult to measure accurately; it is assessed by multiple psychometric tests. Two approaches are commonly adopted to address this multivariate aspect in longitudinal analyses: the composite score approach summarizes the tests into a single outcome and subsequently analyzes its change; the multivariate approach relates the tests to the underlying cognitive level and simultaneously analyzes its change. We compared the quality of inference of these approaches in a simulation study based on three combinations of tests inspired by two population-based cohorts. In the absence of missing data and with relatively Gaussian psychometric tests, the composite score approach provided similar type-I error rates and statistical power as the multivariate latent process approach. In the more plausible scenario with departures from normality, transformations of each constituent test or of the composite score were required to avoid excess type-I error rates. When missing tests were more likely in cognitively impaired subjects, inference with the composite was not correct. In conclusion, composite scores can be used to assess risk factors for cognitive change provided they are correctly normalized, constituent tests are reliable and the amount of uninformative missing tests remains small. Otherwise, latent variable models are recommended.