We seem to be having a little run of papers on Glasgow but no apologies because (a) Glasgow is an interesting place epidemiologically and (b) the papers are well written.
If you live in Glasgow the results have a personal significance; for the rest of us, there are some points of methodology to note.
Although the title implies an analysis of health, actually the outcome analysed is self-reported ill-health (e.g. anxiety, depression, doctor-diagnosed heart attack or stroke). We need to be clear whether we are talking about mortality, disease, ill-health, good health or something else.
The paper offers a nice worked example of multiple regression to take out known explanations and see what's left. Mostly, poor health in Glasgow relative to the rest of Scotland is fully explained by well known factors such as deprivation, smoking, and the age and sex structure of the population. You can see this by the way the odds of ill health in Glasgow dropped as more and more other factors are entered into the regression model.
For example psychological ill-health was reported by 18% of Glaswegians but by 14% in the rest of Scotland. This gives an unadjusted odds ratio of 1.40 for Glasgow vs the rest. Table 5 in the paper shows these odds dropping to 1.38, then 1.26 and so on, and finally into non-significance as more explanatory factors are added into the model. This means that the extra 40% in the crude odds ratio was in some sense being 'carried' by those other factors.
The odds for depression increase in Table 5 with the first adjustment (for age and sex) before dropping with the subsequent adjustments. SoGlasgow's age and sex structure predicts less depression than was actually found; hence the increase on adjustment.