The debate over whether certain antihypertensive medications have benefits beyond what would be expected from their blood pressure lowering spurred the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial, which randomized 42,418 participants to chlorthalidone (15,255), amlodipine (9048), lisinopril (9054), or doxazosin (9061). We compared chlorthalidone, the active control, with each of the other three agents with respect to the primary outcome, fatal coronary heart disease or nonfatal myocardial infarction, and several other clinical endpoints. The arms were similar with respect to the primary endpoint, although some differences were found for other endpoints, most notably heart failure. Although the desire was to achieve similar blood pressure reductions in the four arms, we found some systolic blood pressure and diastolic blood pressure differences. A natural question is to what degree can observed treatment group differences in cardiovascular outcomes be attributed to these blood pressure differences. The purpose of this paper was to delineate the problems inherent in attempting to answer this question, and to present analyses intended to overcome these problems. Copyright © 2012 John Wiley & Sons, Ltd.