I'm more interested in how severity of symptoms, severity of disability, and cognitive/neurological symptoms are correlated to depression. Correlation of severity of symptoms with depression may well indicate that depression is a consequence of living with a severe chronic illness... Or looking at the correlation of cognitive symptoms with depression might indicate that severity of neurological issues in ME correlate with depression...
Still reading...
The abstract doesn't list all the main factors associated with depression - odds ratios from Table 2:
Fatigue (per 3-point increment on Chalder Fatigue Scale)†
1.75 (1.44 to 2.14), p<0.0001
Adjusted for other variables: 1.26 (1.02 to 1.57), p=0.04
Physical function (per 10-point increment on SF-36 physical function subscale)†
0.67 (0.60 to 0.75), p<0.0001
Adjusted for other variables: 0.77 (0.67 to 0.88), p<0.001
Pain (per 10 mm increment on Visual Analogue Pain Rating Scale)†
1.25 (1.15 to 1.36), p<0.0001
Adjusted for other variables:1.13 (1.03 to 1.25), p=0.01
(higher scores mean less problems with the SF-36 PF, hence the lower ORs)
So, as you say, the consequences of dealing with living with a severe chronic illness.
Female sex was borderline significant
Interestingly, when adjusting for other variables
School attendance of 40% or more 0.36 (0.23 to 0.56), p<0.0001 Adjusted for other variables: 0.75 (0.44 to 1.28), p=0.28
the protective value of school attendance of 40% or less decreased a lot and was no longer significant.
So forcing a child to school may not make if any benefit for their mental health (at least as measured by the HADS).