This randomized controlled trial assessed the effects of supplementing with 800 vs. 1,800 IU of vitamin D per day for 12 months on serum vitamin D concentrations and losses in body fat among 41 participants following Roux-en-Y bariatric surgery. Before the surgery and 12 months after the surgery, the authors assessed between-group differences in the following outcomes:

Serum vitamin D (the primary outcome)
Weight
Waist circumference
Waist-hip ratio
Percentage of excess weight loss (excess weight loss was defined as current weight minus ideal weight)
Body adiposity index (a proxy for body fat percentage based on hip circumference and height)^[1]
Visceral adiposity index (a measure of visceral adipose tissue function, based on waist circumference, BMI, triglycerides, and HDL cholesterol)^[2]

Can supplementing with vitamin D improve bariatric surgery outcomes? Original paper