A flexible Monte Carlo quantitative bias analysis for unmeasured confounding

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, $U$, 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) dependence between $C$ and $U$, and (iii) one or multiple binary or continuous $U$. To minimise 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, can virtually eliminate 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 and R package, qbaconfound.