## Noncompliers and dropouts

It can be useful and important to take account of the fact that some patients may either fail to receive their allocated treatment (non-compliers) or become unassessable for the outcome measure of interest (drop-outs). The impact of these two factors can be very different.

Drop-outs (best avoided by careful choice of outcome measure - see Section 5.2) do not contribute to the outcome assessment, and need to be replaced by an equal number of patients who will contribute, in order for the final analysis to retain the power of the original design. If a drop-out rate R is anticipated, and sample size calculations, assuming no drop-out, suggest a total of N patients, the required sample size is simply N* = N/(1 — R). Thus for example if a 10 per cent drop-out rate is assumed in a trial of 200 patients, you would aim to enter 200/(1 — 0.1) = 222 patients. Strictly, this is an approximation, as it assumes that drop-out is unrelated to prognosis. A patient at above average risk of the event of interest is more 'informative' than a patient with a below average risk of the event. Thus if higher risk patients are more likely to drop-out this will slightly underestimate the required sample size, if lower risk patients are more likely to drop-out, it will slightly overestimate the required sample size.

A very different issue arises when patients withdraw from treatment but remain assessable for the primary outcome measure. It will generally be appropriate to analyse patients according to their allocated treatment group, whether or not they received their allocated treatment (i.e. intention to treat analysis - see Section 9.4.1). In this situation, simply 'replacing' the non-compliers does not suffice, and the sample size actually needs to be increased by a similar means to that described in Section 4.3.2. The exact form of the calculation will depend on the treatment actually received by non-compliers (the calculation in Section 4.3.2 assumes cross over to the 'other' treatment), the likely response to that treatment and, as above, on assumptions about the prognosis of the non-compliant patients. Because of the unpredictable nature of many of these assumptions, it is rare to see the impact of non-compliance formally assessed in trial sample size calculations, but common to see sample sizes adjusted as for drop-out. This is at least tending in the right direction, but as demonstrated in Section 4.3.2, a 10 per cent withdrawal rate may require a compensatory increase in sample size of over 50 per cent. Therefore where non-compliance rates are likely to be non-negligible, it can be important to consider, and attempt to take account of, the potential impact on sample size.

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