Allowing for missing outcome data and incomplete uptake of randomised interventions, with application to an Internet-based alcohol trial

Missing outcome data and incomplete uptake of randomised interventions are common problems, which complicate the analysis and interpretation of randomised controlled trials, and are rarely addressed well in practice. To promote the implementation of recent methodological developments, we describe sequences of randomisation-based analyses that can be used to explore both issues. We illustrate these in an Internet-based trial evaluating the use of a new interactive website for those seeking help to reduce their alcohol consumption, in which the primary outcome was available for less than half of the participants and uptake of the intervention was limited. For missing outcome data, we first employ data on intermediate outcomes and intervention use to make a missing at random assumption more plausible, with analyses based on general estimating equations, mixed models and multiple imputation. We then use data on the ease of obtaining outcome data and sensitivity analyses to explore departures from the missing at random assumption. For incomplete uptake of randomised interventions, we estimate structural mean models by using instrumental variable methods. In the alcohol trial, there is no evidence of benefit unless rather extreme assumptions are made about the missing data nor an important benefit in more extensive users of the intervention. These findings considerably aid the interpretation of the trial's results. More generally, the analyses proposed are applicable to many trials with missing outcome data or incomplete intervention uptake. To facilitate use by others, Stata code is provided for all methods.