## Bias-correction of relative risks by robustly incorporating validation studies that include multiple methods of physical activity assessment and related biomarkers

In cancer epidemiologic studies, exposure variables, for example, physical activity are often difficult to measure, and surrogates that are inexpensive to administer to a large number of participants are often used in the place of the true exposures. However, measurement error in surrogates can lead to substantial bias in estimating the relationship between exposures and cancer outcomes. A simple adjustment for bias due to measurement error is the regression calibration method, in which the naive estimate based on surrogates is scaled by the inverse of the estimated attenuation factor. The attenuation factor is estimated by the slope of true exposures on surrogates. In many cases, the gold standard for the true exposure does not exist, and an alloyed gold standard is available. If the alloyed gold standard is used instead of the actual gold standard, the regression of the alloyed gold standard on the surrogate will provide a consistent estimate of the attenuation factor when the errors in the alloyed gold standard and the surrogate are uncorrelated with each other. However, if the errors are correlated, the standard regression calibration method no longer produces consistent estimates of the attenuation factor. In IDATA, the scenario is much more complicated. There are multiple methods of assessments of the exposures, and a variable number of replicates within subjects. The replicated biomarker design includes, in addition to the alloyed gold standard and the surrogate, a biomarker, which is correlated with the true exposure and uncorrelated with the errors in both the alloyed gold standard and the surrogate. In this project we will apply semi-parametric techniques combined with generalized methods of moments or generalized estimating equations approaches to estimate the attenuation factors and other parameters of interest. Full utilization of all of the multiple assessment measures can improved the efficiency of estimation of the attenuation factor.

1. Apply generalized methods of moments (GMM) to efficiently estimate the attenuation factors.

2. Apply the second order generalized estimating equations (GEE2) instead for estimation.

3. User-friendly, public, computationally efficient software will be developed to support all methods arising from the previous aims.

Donna Spiegelman, Yale University