Quantitative bias analysis (QBA) for unmeasured confounding is essential for observational studies. A probabilistic QBA incorporates external information about the unmeasured confounders via prior distributions for certain parameters (known as bias parameters) that specify the relationship between the unmeasured confounders,) for unmeasured confounding is essential for observational studies. A probabilistic QBA incorporates external information about the unmeasured confounders via prior distributions for certain parameters (known as bias parameters) that specify the relationship between the unmeasured confounders, U, and the study data. It can be implemented as a Bayesian or Monte Carlo QBA. Software implementations of probabilistic QBAs to unmeasured confounding are scarce and mainly limited to unadjusted analyses of binary variables. We propose a Monte Carlo QBA applicable to a generalised linear model or survival proportional hazards model that allows for: (i) binary, continuous, or categorical exposure and measured confounders C, (ii) correlation between C and U, and (iii) one or multiple binary or continuous U. To minimize the number of bias parameters, our proposed bias model does not model U directly but instead models the part of U not explained by C. Using a data example and simulation studies, we show that our Monte Carlo QBA, with informative priors, virtually eliminates the bias due to unmeasured confounding in a wide range of scenarios and performs as well as a Bayesian QBA. Our Monte Carlo QBA will be available as Stata command qbaconfound.
Authors: Rachel Hughes (Bristol), Emily Kawabata (Bristol), Chin Yang Shapland (Bristol) Tom Palmer (Bristol) David Carslake (Bristol) Kate Tilling (Bristol)
