Meta - Analysis , Measurement Error and Corrections for Attenuation

MacMahon, et al. (1990) present a meta-analysis of the effect of blood pressure on coronary heart disease, as well as new methods for estimation in measurement error models for the case when a replicate or second measurement is made of the fallible predictor. The correction for attenuation used by these authors is compared to others already existing in the literature, as well as to a new instrumental variable method. The assumptions justifying the various methods are examined and their efficiencies are studied via simulation. Compared to the methods we discuss, that of MacMahon, et al. (1990) may have substantial bias in some circumstances because it does not take into account: (i) possible correlations among the predictors within a study; (ii) possible bias in the second measurement; or (iii) possibly differing marginal distributions of the predictors across studies.