Adherence-corrected analyses of the effects of one additional VISIT
Estimates of the effect of one additional screening visit will use the method of Cuzick et al7 to allow for non-adherence, which avoids assuming similarity between those adherent and non-adherent to the random allocation. Adherence-corrected analyses estimate the effects of one additional screening visit among those women who would have had a screening visit if, and only if, randomly allocated to be invited for screening. (Screening does not include mammography after a breast cancer has been diagnosed.)
Some women, who may well be atypical in unknown but relevant ways, would not get screened, regardless of what their random allocation happened to be. Some other women, perhaps atypical in other relevant ways, would get screened anyway, again regardless of what their random allocation would be. All others would have a screening visit if, and only if, randomly allocated to be invited. *
Adherence-corrected analyses of the effects of actually having, vs not having, a screening visit involve comparing (A – B) vs (D – C), with groups A, B, C and D as defined in the table. For, subtraction of group B is equivalent to removing from group A those who would have been screened even if not invited, leaving those who would have a screening visit if, and only if, invited. Likewise, subtraction of C is equivalent to removing from D those who would not have been screened even if allocated to be invited, again leaving those who would have a screening visit if, and only if, allocated to be invited. *
This comparison of (A – B) vs (D – C) assesses unbiasedly the full effects among those who would have a screening visit if, and only if, allocated to be invited, without assuming that groups A, B, C and D are comparable with each other. This method of adjustment for adherence has little or no effect on the statistical power to detect any differences in breast cancer mortality between invitees and controls.
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* There might also, at least in theory, be a tiny group who, perversely, would all get exactly the opposite of whatever their random allocation happened to be. Ideally these non-adherent women would be excluded when analysing the results, but as they are not individually identifiable they cannot be. This does not, however, introduce any bias at all into the adherence-corrected estimates of the proportional effect of screening (as the adherence correction subtracts this tiny non-adherent group from both sides of the comparison).