AIMS: The analysis of randomized controlled trials with incomplete binary outcome data is challenging. We develop a general method for exploring the impact of missing data in such trials, with a focus on abstinence outcomes. DESIGN: We propose a sensitivity analysis where standard analyses, which could include 'missing = smoking' and 'last observation carried forward', are embedded in a wider class of models. SETTING: We apply our general method to data from two smoking cessation trials. PARTICIPANTS: A total of 489 and 1758 participants from two smoking cessation trials. MEASUREMENTS: The abstinence outcomes were obtained using telephone interviews. FINDINGS: The estimated intervention effects from both trials depend on the sensitivity parameters used. The findings differ considerably in magnitude and statistical significance under quite extreme assumptions about the missing data, but are reasonably consistent under more moderate assumptions. CONCLUSIONS: A new method for undertaking sensitivity analyses when handling missing data in trials with binary outcomes allows a wide range of assumptions about the missing data to be assessed. In two smoking cessation trials the results were insensitive to all but extreme assumptions.