Assessing the sensitivity of regression results to unmeasured confounders in observational studies

This paper presents a general approach for assessing the sensitivity of the point and interval estimates of the primary exposure effect in an observat ional study to the residual confounding effects of unmeasured variables aft er adjusting for measured covariates. The proposed method assumes that the true exposure effect can be represented in a regression model that includes the exposure indicator as well as the measured and unmeasured confounders. One can use the corresponding reduced model that omits the unmeasured conf ounder to make statistical inferences about the true exposure effect by spe cifying the distributions of the unmeasured confounder in the exposed and u nexposed groups along with the effects of the unmeasured confounder on the outcome variable. Under certain conditions, there exists a simple algebraic relationship between the true exposure effect in the full model and the ap parent exposure effect in the reduced model. One can then estimate the true exposure effect by making a simple adjustment to the point and interval es timates of the apparent exposure effect obtained from standard software or published reports. The proposed method handles both binary response and cen sored survival time data, accommodates any study design, and allows the unm easured confounder to be discrete or normally distributed. We describe appl ications to two major medical studies.