Here are some studies about vitamin D and obesity:

Vitamin D Treatment Improves Levels of Sexual Hormones, Metabolic Parameters and Erectile Function in Middle-Aged Vitamin D Deficient Men (2017)

Conclusion: In a 12-month study of 102 vitamin D-deficient middle-aged men, monthly high-dose vitamin D therapy raised their testosterone levels, improved erectile function, and reduced body fat.

Vitamin D Status, Body Composition, and Fitness Measures in College-Aged Students (2014)

Conclusion: A study of 39 young adults found that those with higher vitamin D levels also had a higher level of cardiovascular fitness (Vo2 Max) and less body fat.

Serum 25-Hydroxyvitamin D Concentrations are Associated with Prevalence of Metabolic Syndrome and Various Cardiometabolic Risk Factors in US Children and Adolescents Based on Assay-Adjusted Serum 25-Hydroxyvitamin D Data from NHANES 2001-2006 (2011)

Conclusion: In a study analyzing 5,867 adolescents, there was a higher prevalence of metabolic syndrome among those with lower vitamin D levels.

Vitamin D Status, Adiposity, and Lipids in Black American and Caucasian Children (2011)

Conclusion: 237 children had their BMI and vitamin D levels measured. 98% of the black and 90% of the white kids had low vitamin D levels.The study also found that the FATTER kids had lower vitamin D levels than leaner kids. Vitamin D-deficiency is known to be both a contributing factor TO and a symptom OF obesity. Vitamin D levels rose slightly in the summer.

A 16-Week Randomized Clinical Trial of 2000 International Units Daily Vitamin D3 Supplementation in Black Youth: 25-Hydroxyvitamin D, Adiposity, and Arterial Stiffness (2010)

Conclusion: A 4-month study of 44 black teenagers found that 95% had low vitamin D levels and that supplementing with 2,000 IU of vitamin D daily was effective for reducing arterial stiffness and increasing vitamin D levels. The study also found that the vitamin D levels of the obese subjects rose less than the leaner subjects. Although 2,000 IU daily was effective in raising levels, only 56% achieved sufficient levels after the four months.

Vitamin D, Adiposity, and Calcified Atherosclerotic Plaque in African-Americans (2010)

Conclusion: A study of 340 black adults with type-2 diabetes found that those with the highest percentage of body fat also had the lowest vitamin D levels and the highest amount of carotid artery and aorta plaque. There is a correlation between high body fat and low vitamin D levels and a correlation between low vitamin D levels and increased risk for atherosclerosis.

Prevalence and Associations of 25-Hydroxyvitamin D Deficiency in US Children: NHANES 2001-2004 (2009)

Conclusion: A 3-year study of 9,757 U.S. children and young people found that: 61% had low vitamin D levels, those who spent more time watching/using TVs and computers had lower vitamin D levels, obese children had lower vitamin D levels, and those with lower vitamin D levels had higher blood pressure.

Vitamin D Status and Parathyroid Hormone in Obese Children Before and After Weight Loss (2007)

Conclusion: Obese children were found to have lower vitamin D levels than non-obese children. In the obese children, losing weight resulted in an increase of their vitamin D levels.

Low Serum 25-Hydroxyvitamin D Concentrations are Associated with Insulin Resistance and Obesity in Women with Polycystic Ovary Syndrome (2006)

Conclusion: A study of 120 adult women found that those with the lowest vitamin D levels also had the highest body fat percentages and highest rates of insulin resistance.

Vitamin D Status and Glucose Homeostasis in the 1958 British Birth Cohort (2006)

Conclusion: 7,189 caucasian subjects from the 45-year 1958 British Birth Cohort were analyzed to find a possible correlation between amount of body fat, blood sugar levels, and vitamin D levels. The rate of vitamin D insufficiency was higher in the obese subjects (80%) compared to the others (68%) and those with lower vitamin D levels also had higher blood sugar. These results are in line much of the rest of the research that has been done showing that: vitamin D-deficiency promotes obesity, obesity also causes vitamin D-deficiency, and vitamin D-deficiency reduces glucose metabolism.

Concentrations of Serum Vitamin D and the Metabolic Syndrome Among U.S. Adults (2005)

Conclusion: People with higher vitamin D levels are less likely to be diagnosed with having metabolic syndrome.

Hypovitaminosis D is Associated with Insulin Resistance and Beta Cell Dysfunction (2004)

Conclusion: “The data show a positive correlation of 25(OH)D concentration with insulin sensitivity”

The Relationship between Obesity and Serum 1,25-Dihydroxy Vitamin D Concentrations in Healthy Adults (2004)

Conclusion: This study of 152 obese people and 148 non-obese people found that the obese people had lower vitamin D levels.

Body Fat Content and 25-Hydroxyvitamin D Levels in Healthy Women (2003)

Conclusion: In a study involving 410 women, women with higher total body fat percentages had lower vitamin D levels.

Intakes of Calcium and Vitamin D Predict Body Mass Index in the Population of Northern Norway (2003)

Conclusion: A study of 12,866 men and women in Norway found that those with lower vitamin D levels had higher body fat percentages.

Decreased Bioavailability of Vitamin D in Obesity (2000)

Conclusion: In vitamin D experiments carried out on a group of 19 obese people and a group of 19 normal weight people, the obese group experienced 57% lower vitamin D level increases following UVB irradiation compared to the non-obese group.

Evidence for Alteration of the Vitamin D-Endocrine System in Obese Subjects (1985)

Conclusion: The study compared the serum pre-vitamin D levels of a group of obese individuals to the levels of a group of normal weight individuals and found the obese group to have significantly lower pre-vitamin D levels.

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