This paper considers a problem of evaluating the causal effect of a treatment X on a true endpoint Y using a surrogate endpoint S, in the presence of unmeasured confounders between S and Y. Such confounders render the causal effect of X on Y unidentifiable from the causal effect of X on S and the joint probability of S and Y. To evaluate the causal effect of X on Y in such a situation, this paper derives closed-form formulas for the sharp bounds on the causal effect of X on Y based on both the causal effect of X on S and the joint probability of S and Y under various assumptions. In addition, we show that it is not always necessary to observe Y to test the null causal effect of X on Y under the monotonicity assumption between X and S. These bounds enable clinical practitioners and researchers to assess the causal effect of a treatment on a true endpoint using a surrogate endpoint with minimum computational effort. Copyright © 2013 John Wiley & Sons, Ltd.
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