Formulating tightest bounds on causal effects in studies with unmeasured confounders

This paper considers the problem of evaluating the causal effect of ail exposure on ail Outcome in observational studies with both measured and unmeasured confounders between the exposure and the Outcome. Under such a situation, MacLehose et al. (Epidemiology 2005; 16:548-555) applied linear programming optimization software to find the minimum and maximum possible Values Of file causal effect for specific numerical data. In this paper, we apply the symbolic Balke-Pearl linear programming method (Probabilistic counterfactuals: semantics, computation, and applications. Ph.D. Thesis, UCLA Cognitive Systems Laboratory, 1995; J. Amer Statist. Assoc. 1997; 92:1172-1176) to derive the simple closed-form expressions for the lower and upper bounds on causal effects under various assumptions of monotonicity. These universal bounds enable epidemiologists and medical researchers to assess causal effects from observed data with minimum computational effort, and they further shed light on the accuracy of the assessment. Copyright (C) 2008 John Wiley & Sons, Ltd.