Correcting for multivariate measurement error by regression calibration in meta-analyses of epidemiological studies

Abstract

Within-person variability in measured values of multiple risk factors can bias their associations with disease. The multivariate regression calibration (RC) approach can correct for such measurement error and has been applied to studies in which true values or independent repeat measurements of the risk factors are observed on a subsample. We extend the multivariate RC techniques to a meta-analysis framework where multiple studies provide independent repeat measurements and information on disease outcome. We consider the cases where some or all studies have repeat measurements, and compare study-specific, averaged and empirical Bayes estimates of RC parameters. Additionally, we allow for binary covariates (e.g. smoking status) and for uncertainty and time trends in the measurement error corrections. Our methods are illustrated using a subset of individual participant data from prospective long-term studies in the Fibrinogen Studies Collaboration to assess the relationship between usual levels of plasma fibrinogen and the risk of coronary heart disease, allowing for measurement error in plasma fibrinogen and several confounders.

Figure 1

Levels and timings of repeat measures of fibrinogen and systolic blood pressure* by study. *Each point represents the observed measurements per person-visit. Repeat measurements for smoking status not shown, but follow similar timings to systolic blood pressure.

Figure 2

Meta-analysis of the study-specific regression coefficients estimated from independent univariate RC models using a single repeat measure. *repeat_var and base_var represent the repeat and baseline measurements respectively for variables fibrinogen (fib), systolic blood pressure tenths (sbp) and smoking status (smok). The RC models are also adjusted for baseline age and sex. CHS = Cardiovascular Health Study, NPHSI = Northwick Heart Park Study 1, Procam = Prospective CV Munster Study, Strong=StrongHeart Study and WhiteII = Whitehall II Study.

Figure 3

Regression dilution ratios for a. Fibrinogen, b. Systolic Blood Pressure and c. Smoking Status with 95% CI, estimated independently for each study and repeat measurement time. C = Cardiovascular Health Study, N = Northwick Heart Park Study 1, P = Prospective CV Munster Study, S = StrongHeart Study and W = Whitehall II Study. Each block represents the estimated study- and time- specific RDR estimated from the model defined by equation (6), with baseline fibrinogen, systolic blood pressure, smoking, age and sex included in each model. Each repeat is represented by the mean time since baseline. The relative sizes of the blocks are proportional to the inverse of the RDR standard error.