Two methods of Bayesian model averaging (2D Monte Carlo type) to assess effects of covariate errors

Music City Center 

Measurement error alters exposure-response shape and hence extrapolated risk. Bayesian model averaging (BMA) methods of dealing with shared errors, common in many datasets, have received much attention. We test two types of BMA model, quasi-2DMC+BMA, similar to the BMA method proposed by Hoeting et al but distinct from the 2DMC+BMA method of Kwon et al (Stat Med 2016 35 399-423). The second (and newer type) we term marginal-quasi-2DMC+BMA, using a more complex marginal calculation, closer to 2DMC+BMA. Assuming a true linear exposure-response model, coverage probabilities for the linear coefficient are 90-95% for quasi-2DMC+BMA, but only 52-60% for marginal-quasi-2DMC+BMA. Assuming a true linear-quadratic model coverage probabilities of both linear and quadratic coefficients for quasi-2DMC+BMA are <5% when shared Berkson error is 50%. By comparison, coverage probabilities for both linear and quadratic coefficients for the marginal-quasi-2DMC+BMA method are generally too high, ~ 100%. The poor coverage results from substantial bias, both positive and negative. In summary the performance of both quasi-2DMC+BMA and marginal-quasi-2DMC+BMA methods are bad, with bias and poor coverage.

Covariate measurement error

Bayesian model averaging

Radiation

Classical error

Berkson error 

Section on Bayesian Statistical Science