I know you place a great deal of weight on these quotes from the abstract. And you know I don't. I would advise everyone who is interested, for an improved understanding, to read and understand the detailed discussion freely available in the Appendix. I will provide the link at the bottom. The reasons I don't blindly accept the authors suggestion of unlikelihood of over-estimation are, in part, the lack of real data presented by the very same authors to support such a suggestion, and in part, the other words of the authors themselves. Let's put the abstract aside. It seems to be a summary of these last two paragraphs, in the Appendix, interpreting "Table 14":
In the Appendix, Section 4, the authors identified and modeled 8 or 9 scenarios of non-compliance. It would seem they are suggesting "unlikely", based, at least in part, on Table 14 containing many "-" entries, and only 1 "+" entry.
First, nothing in the study gives the authors any special indication of the likelihood of compliance in any of these scenarios. Intuitively, some scenarios (e.g. non-dopers admitting doping) are less likely than others (e.g. dopers lying about doping), but the authors have no way to estimate or measure true compliance or non-compliance in any scenario that they've identified.
Rather, when looking at how Table 14 was produced, we find that the "various assumptions" and "numerous hypothetical scenarios" they spoke of are quite simply blanket assumptions of 30% non-compliance for every scenario. This looks like a useful assumption for discarding several scenarios of non-compliance as having a small effect, even for large non-compliance. But such a blanket assumption, with no supporting data or rationale or other basis, cannot support an overall suggestion of "unlikely to have overestimated".
The other thing about Table 14 is that these various scenarios are not independent, but rather there is a fair amount of overlap. For example, the "Underreporting Doping", with a small modification, would be a superset of all these other scenarios: "Switch from B to A", "Responding to Question A", "Automatic no Responding" and "Cheating with no Responding".
Another issue found in the closing paragraphs is factual. They say "none of the various assumptions would have caused us to overestimate the true prevalence within our sample by more than 3%". This looks factually incorrect, contradicted by Table 12A "Automatic yes Responding". Assuming 30% non-compliance, as they did, the true prevalence becomes 8.9%, resulting in a signficant over-estimate of 34.7% -- way more than 3%. So either:
1) This statement (that helps form the basis for "unlikely to have overestimated") is a lie
2) The authors are now talking about another estimate where "Automatic yes Responding" was already eliminated (see Table 4): 31.4%
So assessing the authors suggesting the unlikelihood of overestimates requires:
- assessing the likelihood of dopers under-reporting doping -- something the authors don't know
- assessing the likelihood of non-dopers over-reporting non-doping -- something the authors don't know
- assessing the likelihood of automatic yes responses -- something the authors don't know
- assessing the likelihood of automatic no responses -- something the authors don't know
- assessing the likelihood of any non-compliance -- something the authors don't know
Any opinion by the authors of the unlikelihood of overestimating, is not based on data that can be found in the study, but based on any preconceptions that they brought with them into the study.
Link to the Appendix:
https://static-content.springer.com/esm/art%3A10.1007%2Fs40279-017-0765-4/MediaObjects/40279_2017_765_MOESM1_ESM.pdf