Methods to apply probabilistic bias analysis to summary estimates of association

Bias analysis methods are developed for application to 2 x 2 tables, which may be crude or stratified data. Methods for application to associations adjusted for multiple covariates, such as associations from regression modeling, are rarely seen. We have developed probabilistic methods to evaluate bias from disease misclassification or an unmeasured confounder that can be applied to adjusted estimates of association.

Rather than applying bias correction methods that rearrange data within 2 x 2 tables, we have applied them to bias factors directly. We illustrate the methods by application to two pharmacoepidemiology problems.

In example one, the adjusted odds ratio associating glucocorticoid use with the rate of basal cell carcinoma was 1.15 (95%CI 1.07, 1.25). With bias analysis to account for differential disease misclassification, the median odds ratio was 1.32 and the 95% simulation limits were 1.16 and 1.56. In example two, the adjusted odds ratio associating concomitant use of clopidogrel and proton pump inhibitors with recurrent myocardial infarction was 1.21 (95%CI 0.90, 1.61). With bias analysis to account for confounding by smoking, which was unmeasured, the median odds ratio was 1.15 with 95% simulation interval 0.85 to 1.55.

Methods to apply probabilistic bias analysis to adjusted estimates of association can be implemented if a bias factor can be calculated directly from the bias model. This strategy requires that the bias is independent of confounding by measured variables, or requires that the dependence be incorporated into the bias model, as illustrated in an extension of the second example.