This paper presents a general approach for assessing the sensitivity of the point and interval estimates of the primary exposure effect in an observational study to the residual confounding effects of unmeasured variables after 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 confounder to make statistical inferences about the true exposure effect by specifying the distributions of the unmeasured confounder in the exposed and unexposed 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 apparent exposure effect in the reduced model. One can then estimate the true exposure effect by making a simple adjustment to the point and interval estimates of the apparent exposure effect obtained from standard software or published reports. The proposed method handles both binary response and censored survival time data, accommodates any study design, and allows the unmeasured confounder to be discrete or normally distributed. We describe applications to two major medical studies.