Advice regarding the analysis of observational studies of exposure effects usually is against adjustment for factors that occur after the exposure, as they may be caused by the exposure (or mediate... Show moreAdvice regarding the analysis of observational studies of exposure effects usually is against adjustment for factors that occur after the exposure, as they may be caused by the exposure (or mediate the effect of exposure on outcome), so potentially leading to collider stratification bias. However, such factors could also be caused by unmeasured confounding factors, in which case adjusting for them will also remove some of the bias due to confounding. We derive expressions for collider stratification bias when conditioning and confounding bias when not conditioning on the mediator, in the presence of unmeasured confounding (assuming that all associations are linear and there are no interactions). Using simulations, we show that generally neither the conditioned nor the unconditioned estimate is unbiased, and the trade-off between them depends on the magnitude of the effect of the exposure that is mediated relative to the effect of the unmeasured confounders and their relations with the mediator. We illustrate the use of the bias expressions via three examples: neuroticism and mortality (adjusting for the mediator appears the least biased option), glycated hemoglobin levels and systolic blood pressure (adjusting gives smaller bias), and literacy in primary school pupils (not adjusting gives smaller bias). Our formulae and simulations can inform quantitative bias analysis as well as analysis strategies for observational studies in which there is a potential for unmeasured confounding. Show less
Nab, L.; Groenwold, R.H.H.; Smeden, M. van; Keogh, R.H. 2020
Observational data are increasingly used with the aim of estimating causal effects of treatments, through careful control for confounding. Marginal structural models estimated using inverse... Show moreObservational data are increasingly used with the aim of estimating causal effects of treatments, through careful control for confounding. Marginal structural models estimated using inverse probability weighting (MSMs-IPW), like other methods to control for confounding, assume that confounding variables are measured without error. The average treatment effect in an MSM-IPW may however be biased when a confounding variable is error prone. Using the potential outcome framework, we derive expressions for the bias due to confounder misclassification in analyses that aim to estimate the average treatment effect using an marginal structural model estimated using inverse probability weighting (MSM-IPW). We compare this bias with the bias due to confounder misclassification in analyses based on a conditional regression model. Focus is on a point-treatment study with a continuous outcome. Compared with bias in the average treatment effect in a conditional model, the bias in an MSM-IPW can be different in magnitude but is equal in sign. Also, we use a simulation study to investigate the finite sample performance of MSM-IPW and conditional models when a confounding variable is misclassified. Simulation results indicate that confidence intervals of the treatment effect obtained from MSM-IPW are generally wider, and coverage of the true treatment effect is higher compared with a conditional model, ranging from overcoverage if there is no confounder misclassification to undercoverage when there is confounder misclassification. Further, we illustrate in a study of blood pressure-lowering therapy, how the bias expressions can be used to inform a quantitative bias analysis to study the impact of confounder misclassification, supported by an online tool. Show less
Smit, R.A.J.; Trompet, S.; Dekkers, O.M.; Jukema, J.W.; Cessie, S. le 2019
