When patients withdraw, Shih and Quan(1997) advocate an ITT analysis based on a joint test of (i) whether patients who complete, benefit from the intervention and (ii) whether those who withdraw have excessive adverse effects. As an illustration, consider a trial to reduce blood pressure. Suppose some patients withdraw from the trial, and subsequently some of these die of a heart attack. This approach divides patients into two groups (i) those who complete and (ii) those who do not. Amongst group (i) we compare the effect of the intervention on blood pressure, as originally intended. Amongst group (ii) we compare the effect of the intervention (or intending to give the intervention) on the risk of death.
This approach is attractive as it hard to conceive of a patient’s ITT blood pressure after they have died. However, it entails a unified definition of ‘intervention benefit’ across groups (i) and (ii) so a null hypothesis can be specified and tested. This means explicitly weighing the benefits of, for example, blood pressure reductions and heart attacks. When faced with multiple interventions, factorial designs, and/or unexpected adverse events, we anticipate such defini- tions of ‘intervention benefit’ are increasingly intricate, difficult to define in advance, difficult to communicate to non-statisticians and difficult to defend.
It is impossible to give completely general guidance, as, clearly, a lot depends on the interplay between the treatment and the adverse event. However, we feel that usually greater clarity emerges by keeping the analysis of the primary response separate from the adverse event rate. Nevertheless, the relevance of the ITT hypothesis becomes questionable.
Returning to the blood pressure reduction trial illustration, heart attack is not wholly attributable to blood pressure. If the predominant reason for withdrawal is a heart attack, a per-protocol analysis together with a comparison of the heart attack rate may provide a clear basis to interpret the trial. Here the per-protocol analysis estimates the effect of treatment if no heart attack occurs.
When the heart attack occurs after withdrawal, there is no substitute for post-protocol adherence follow-up data. With this, we can make progress towards evaluating the ITT hypothesis. Again, the ITT analysis estimates the effect of treatment if no adverse event occurs.
On the other hand, if heart attack might be directly linked to the treatment, by whatever mecha- nism, the primary focus switches to the end point of heart attack and composite hypotheses are of secondary interest.
In summary, without ruling out this approach, we believe that a trial can usually be more clearly interpreted by separating, rather than combining, the response of interest and adverse events. Composite hypotheses sidestep, rather than address, the ITT hypothesis. We therefore do not consider composite hypotheses further here.
1.9 A critique of CPMP guidelines
The Committee for Proprietary Medicinal Products (CPMP) (2001) adopted some ‘points to
consider on missing data’ (henceforth referred to as the CPMP-PTC), which aim to put flesh on the ICH E9 bones. We now review these in the light of the principles discussed in this Chapter.
First, this Chapter reinforces the important points made in CPMP-PTC that it is necessary (i) to take care, in both design and implementation, to try to minimise the number of missing
observations;
(ii) to consider how to cope with missing data when drawing up the analysis plan; (iii) where possible, to agree in advance the nature and scope of sensitivity analysis, and (iv) to look closely at the data, especially the proportion of missing data by time of withdrawal
and treatment arm.
The CPMP-PTC is also surely right to make the point that there can be no universal analysis when data are missing. However, unfortunately, it overlooks the fact that there are general principles to follow in the analysis of missing data, and these principles can and should inform specific analyses. It is these principles that we have aimed to set out in this Chapter. Without clear principles to inform the document, the motivation of various statements is unclear, and the application of the guidelines to specific problems unnecessarily difficult.
Perhaps this goes some way to explain a key misunderstanding on the effect of a relationship between treatment and missing outcome data. On page 4, at the top, the guidelines say
“mixed effects models ... assume that there is no relationship between treatment and missing outcome, and this generally cannot be assumed”
This is incorrect. Mixed models are a form of multivariate regression models; these do not rely on there being no association between missing outcome and treatment. Instead, the MAR principle described above applies directly: if outcome data are MCAR given treatment alone (i.e. MAR), then including treatment in the model (i.e. conditioning on it) gives a valid treatment estimate. Almost all primary analyses include treatment in this way.
In addition, the above statement implicitly contradicts page 2 of the guidelines, where it states: “In principle missing values will not be expected to lead to bias if they are only related to the treatment...”
However, the principles described in this Chapter show this is only true if data are MAR. We can never know if this is the case; indeed often, as discussed above, it will not be. As it stands, therefore, this statement is of very limited usefulness for informing the analysis of a trial with missing data.
A further point of concern is the discussion of the need to impute missing data to perform an analysis. Yet, we have seen that under MAR this is not necessary. In Chapter6we also see that this is not necessary for MNAR analyses. Of course, one way to do MAR and MNAR analyses is via imputation, but that is a separate issue.
Considerable space is also given to the discussion of Last Observation Carried Forward (see Chapter2), and imputing the best or worst values for missing data. Again, this is unhelpful. The principled approach set out here clearly shows that if data are missing, extra assumptions are
1.10 Inferential approach 27