Of the three anthropometric variables that were significantly inversely correlated with vitamin D3 only BMI and waist were further investigated as weight is considered too crude a measure of obesity. Vitamin D3 showed inverse relationships separately, but of the same magnitude, with both BMI and waist when corrected for confounders. Neither could be shown to be related to vitamin D3 given the level of the other. This may indicate either similar mechanisms, or that different metabolic processes are occurring, coincidentally producing similar outcomes.
Hypotheses from the literature are discussed in light of our findings
Whole body obesity, as defined by BMI, has been associated with or contributes to low vitamin D3 status [8, 12]. Wortsman et al., found lower vitamin D3 in the serum of obese participants after experimental UV irradiation, deducing that "obesity-associated vitamin D insufficiency is likely due to the decreased bioavailability of vitamin D3 from cutaneous and dietary sources because of its deposition in body fat compartments" . It was unclear from that trial which fat compartments were involved. In the current study MFBIA fat% did not correlate with vitamin D3, in contrast to that of Arunabh et al.,  where DEXA was performed in women, BMI<24 kg/m2. Total body fat includes both peripheral adipose at the hip and thigh, with beneficial metabolic effects in both women and men , as well as less healthy upper body and central fat depots . The opposing effects of these adipose depots could possibly weaken any correlation with vitamin D3. Furthermore, the lack of relationship of fat% with vitamin D3 may reflect influences of fat-free compartments of bone, muscle  and abdominal organs (liver, kidney, gut ).
The links between the metabolic syndrome and vitamin D3 are not clear. In the present study, apart from waist, none of MetSynM alone, MetSynMcount, nor the presence of MetSyn (defined by three of five positive markers ), was correlated with vitamin D3. This lack of relationship of vitamin D3 and MetSyn has been reported previously , and two studies of vitamin D3 in the morbidly obese report conflicting relationships [19, 20]. However, in the large USA NHANES dataset Ford et al., found that abdominal obesity as measured by waist alone, in addition to MetSyn, was related to low vitamin D3, notably affecting mixed-ethnicity participants equally .
Conversion of vitamin D3 to its derivative 1,25 vitamin D3 is complex and involves other hormones. 1,25 vitamin D3, via its receptor which is present in insulin-producing beta-islet cells, is known to be a potent regulator of cell proliferation and differentiation [22, 23]. However, there is evidence that low vitamin D3 itself is associated with TIIDM irrespective of 1,25 vitamin D3 . The inverse relationship of vitamin D3 with high to extreme HbA1c [24, 25] and/or FPG [7, 8] may indicate that it is the long-term, severely abnormal (carbohydrate) metabolism of TIIDM [7, 26, 27] and muscle insulin resistance , that is associated with hypovitaminosis D3. HbA1c, a glycated protein, is a predictor of 2-hour glucose in oral glucose tolerance testing,  an indicator of chronic hyperglycaemia, protein glycation damage  and oxidative stress . Many new, profound and interacting mechanisms link hypovitaminosis D with other correlates of the metabolic syndrome, including renin regulation . Vitamin D-upregulated protein-1 reportedly modulates endothelial oxidative stress, macrophage and smooth muscle function, depending on the stage of atherosclerosis [32, 33].
Limitations of the present study include the cross sectional design where cause cannot be attributed. Lifestyle, body shape sensitivity [34, 35] or cultural reasons  for precluding skin exposure to view, and ultraviolet light for efficient vitamin D3 synthesis, may selectively affect obese people but were not examined.
In the current study low serum vitamin D3 was inversely related to weight and BMI, but not fat mass, and to markers indicative of TIIDM (large waist and raised HbA1c), rather than MetSyn per se. The link between hypovitaminosis D3 and metabolic disorders, including obesity, MetSyn, TIIDM and CVD requires further investigation, particularly for those most at risk of these combined conditions.