I agree with most of this. The paper does need reworking. As you say, we need graphs of actual values (with separate charts for male/female, and adjustments for age if appropriate).A very precise reason.
In this particular case a group has reported some fascinating findings based on hard work and very timely and initiative-driven data gathering. But the data have been presented in the context of what look to me to be spurious arguments. And, importantly, that is linked to the presentation of the data being very difficult to follow and missing some key aspects. SOD3 and complement proteins look very interesting but we have almost no information about where the values lie in relation to normal scatter or whether they occur in the same people, and so on. There is very lengthy mathematical modelling in terms of 'mediation analysis' but if the diagnostic ascertainment problem is as big as we have been led to believe you cannot even begin to build a mediation model. Additionally the causal diagram looks to be back to front, again relating to a concept of a diagnostic 'disease' unity.
And, most important of all, we know that the people involved are headed up by first rate minds at least one of whom we know personally and I can only assume that the analysis reflects lack of familiarity with the practical complexities around diagnostic categories and the way we interpret biological measures in terms of process models. The introduction jumps off with stuff about physical activity, and then settles back into an account of ME/CFS, which presumably should come first, since the issue of physical activity's relevance to ME/CFS is very specific to the history of the disease and its models and management. It looks to me like an enthusiastic draft rather than a paper.
In many other cases there doesn't seem much point in going in to deep discussion because the science looks pretty scrappy in the first place. Nevertheless, I do tend to raise these issues whenever studies claim to be looking for diagnostic markers, and raising them repeatedly in the context of specific studies does seem necessary because people are still making the same mistakes.
I don't have a background in advanced statistics, so I say the following with much hesitation and willingness to be corrected, but, there are statistical techniques useful for identifying groups and subgroups based on clusters of attributes, things like PCA, random forest. If there are any promising clusters based on differences in individual molecule levels (and perhaps ratios of molecules), then it would be useful to see if a lack of activity can explain the differences. If physical activity does explain some attribute levels, those ones could be removed and classifying statistical techniques like PCA repeated, to see if any identified groups remain. I think we need that order of analysis - identify differences that are probably real differences in an identified group of individuals, and then consider if any of the differences are just the result lifestyle/medicine differences.
A family member did an analysis of a large collection of plants, looking to see if there were sufficient differences to divide the plants into two species, or just subspecies, or no division at all. I mention this, because I find it a useful, concrete way to think about how a differentiating analysis can be done. He had a whole lot of measured attributes including things like flower structure, leaf length and leaf width, as well as ratios of leaf length to leaf width. The classifying analyses showed that the plants divided neatly into two distinct groups. He then needed to consider if things like altitude or latitude could explain the differences, using regressions and spatial analysis, and found there was still a real difference. He then went on to speculate on the biological basis for the collection of attributes in each proposed species. I think the same sort of approach to the analysis, the same order of analysis, could be useful for studies like the one that is the subject of this thread, with physical activity being a possible confounder, like altitude might have been for the differences of my family member's plants.
Regarding the moved posts, we left enough to indicate that the problem had been raised in the context of this study and include some discussion of it. There were 27 posts that went into more detail or repeated points that were moved. I think SOD3 is another good example of where it is useful to split off the discussion. Personally, I would prefer that there is a separate thread for SOD3, rather than having a wide-ranging discussion of it on a study thread that covers many other things. That way, it is easier to go into much more detail and it is easier for people to find and follow the discussion. Threads on studies that have reported findings in ME/CFS cohorts can be linked.