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1 Supplementary Online Content Ludwig DS, Ebbeling CB. The carbohydrate-insulin model of obesity: beyond calories in, calories out [published online July 2, 2018]. JAMA Intern Med. doi: /jamainternmed eappendix. Feeding Studies Included in the Meta-analysis of Hall and Guo ereferences This supplementary material has been provided by the authors to give readers additional information about their work.

2 Feeding Studies Included in the Meta-analysis of Hall & Guo 1 Only 4 of the 25* unique studies of energy expenditure had durations of 2.5 weeks, allowing at least minimally adequate time for physiological adaptation to high dietary fat intake. These studies are considered below. Abbott et al. 2 studied 20 Pima Indians after 18 days on test diets differing in carbohydrate (43% vs 65% of total energy intake). Energy expenditure was 66 kcal/day greater on the low-carbohydrate diet by whole room calorimetry, a method that may underestimate adaptive thermogenesis compared to measurement with stable isotopes (doubly-labeled water) in an unconfined setting 3 ). Rumpler et al. 4 studied 8 men for 4 weeks at 50% energy restriction with diets differing in carbohydrate (46% vs 66%). Energy expenditure by whole room calorimetry was 198 kcal/day greater on the low-carbohydrate diet. Hall et al. 5 treated 17 men with a standard diet for 4 weeks followed by a lowcarbohydrate diet for 4 weeks (5% vs. 50% carbohydrate). They reported significantly greater energy expenditure by both whole room calorimetry (57 kcal/day) and stable isotopes (151 kcal/day). However, this study is limited by the small observational design and confounding by time-varying covariates. Due to miscalculation energy requirements and greater physical activity level on days outside vs inside the metabolic chamber, participants progressively lost weight throughout the study, which would have biased results against the low-carbohydrate diet (which always followed the standard diet). Additional sources of bias in the same direction include probable loss of muscle mass and function with prolonged physical confinement; failure to measure energy from ketones and fat lost in breath, urine and feces; and the exclusion of one

3 outlier with exceptionally high energy expenditure on the low-carbohydrate diet. With reasonable adjustments for these effects, energy expenditure may have actually been at least 250 kcal/day greater on the low-carbohydrate diet. This estimate is comparable to results from our group, summarized below. Ebbeling et al. 6 conducted a 3-arm randomized cross-over study in 21 young adults. Compared to the 60% carbohydrate diet, energy expenditure by stable isotopes was 125 kcal/day greater on the 40% carbohydrate diet and 325 kcal/day greater on the 10% carbohydrate diet. Thus, for studies in the range of 2.5 to 4 weeks, total energy expenditure appears to increase by about 50 kcal/day per 10% decrease in dietary carbohydrate as a proportion of total energy intake a potentially major effect. For body composition, an outcome reflecting cumulative effects throughout the intervention, adequately powered studies of at least 10 weeks would be needed to disentangle transitory versus chronic effects. No studies in the meta-analysis approached that minimally adequate duration. Interestingly, among the three longest studies (Bogardus 1981, 7 Golay 1996, 8 Kahlhöfer all 6 weeks in duration), each show numerically though non-significantly greater fat loss on the low-carbohydrate diet. *Two studies had at least some of the same data as other included studies, and were therefore excluded: Verboeket-van de Venne (overlap with Verboeket-van de Venne ) and Shepard (overlap with Eckel ). Cooper was excluded because the 4 comparison diets had the same proportion of dietary fat. ereferences 1. Hall KD, Guo J. Obesity Energetics: Body Weight Regulation and the Effects of Diet Composition. Gastroenterology 2017;152(7): e3.

4 2. Abbott WG, Howard BV, Ruotolo G, et al. Energy expenditure in humans: effects of dietary fat and carbohydrate. Am J Physiol 1990;258(2 Pt 1):E Rosenbaum M, Ravussin E, Matthews DE, et al. A comparative study of different means of assessing long-term energy expenditure in humans. Am J Physiol 1996;270(3 Pt 2):R Rumpler WV, Seale JL, Miles CW, et al. Energy-intake restriction and diet-composition effects on energy expenditure in men. Am J Clin Nutr 1991;53(2): Hall KD, Chen KY, Guo J, et al. Energy expenditure and body composition changes after an isocaloric ketogenic diet in overweight and obese men. Am J Clin Nutr 2016;104(2): Ebbeling CB, Swain JF, Feldman HA, et al. Effects of dietary composition on energy expenditure during weight-loss maintenance. Jama 2012;307(24): Bogardus C, LaGrange BM, Horton ES, et al. Comparison of carbohydrate-containing and carbohydrate-restricted hypocaloric diets in the treatment of obesity. Endurance and metabolic fuel homeostasis during strenuous exercise. J Clin Invest 1981;68(2): Golay A, Allaz AF, Morel Y, et al. Similar weight loss with low- or high-carbohydrate diets. Am J Clin Nutr 1996;63(2): Kahlhofer J, Lagerpusch M, Enderle J, et al. Carbohydrate intake and glycemic index affect substrate oxidation during a controlled weight cycle in healthy men. Eur J Clin Nutr 2014;68(9): Verboeket-van de Venne WP, Westerterp KR, ten Hoor F. Substrate utilization in man: effects of dietary fat and carbohydrate. Metabolism 1994;43(2):152-6.

5 11. Verboeket-van de Venne WP, Westerterp KR. Effects of dietary fat and carbohydrate exchange on human energy metabolism. Appetite 1996;26(3): Shepard TY, Weil KM, Sharp TA, et al. Occasional physical inactivity combined with a high-fat diet may be important in the development and maintenance of obesity in human subjects. Am J Clin Nutr 2001;73(4): Eckel RH, Hernandez TL, Bell ML, et al. Carbohydrate balance predicts weight and fat gain in adults. Am J Clin Nutr 2006;83(4): Cooper JA, Watras AC, Adams AK, et al. Effects of dietary fatty acid composition on 24-h energy expenditure and chronic disease risk factors in men. Am J Clin Nutr 2009;89(5):