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By now, we've all seen them - studies that purport to show equivalent effects of LCHF and HCLF diets once diet quality is addressed and people are Eating Whole Unprocessed Foods.
The latter is a good thing, the default to go for in terms of population health; macronutrient tweaking is next-level.
But here's a question - why were almost all the original studies that validated the efficacy of LCHF diets to a skeptical medical world comparisons of ad lib low carb vs energy-restricted low fat?
To make a really low carb high fat diet (unless you want to pretend a high-protein diet is that) you're going to be using some isolated fats (cream) or refined ones (coconut oil, olive oil). There may not be sugar in your chocolate bar, but there will be cocoa butter.
This only works if in some way those isolated fats are NOT equivalent to sugar and flour.
What is the evidence for a difference?
One of the more lasting concepts in carb nutrition is the glycemic index, the average speed at which a food appears as glucose in the system. It's not perfect because sugar is only half glucose so is lower GI, but you get the idea.
High GI is worse for you.
The PURE study is good for producing null results, which makes whatever it does throw up seem a bit more reliable than most nutritional epidemiology.
"In the study population, 8780 deaths and 8252 major cardiovascular events occurred during the follow-up period. After performing extensive adjustments comparing the lowest and highest glycemic-index quintiles, we found that a diet with a high glycemic index was associated with an increased risk of a major cardiovascular event or death, both among participants with preexisting cardiovascular disease (hazard ratio, 1.51; 95% confidence interval [CI], 1.25 to 1.82) and among those without such disease (hazard ratio, 1.21; 95% CI, 1.11 to 1.34). Among the components of the primary outcome, a high glycemic index was also associated with an increased risk of death from cardiovascular causes. The results with respect to glycemic load were similar to the findings regarding the glycemic index among the participants with cardiovascular disease at baseline, but the association was not significant among those without preexisting cardiovascular disease."
As I've said before, everything in plants that is supposed to be good for you but isn't actually a real nutrient is probably lowering GI in some way. It's the glucose (glycemic load above) but the way it arrives in your bloodstream (GI) is more pointed.
Is there equivalency for fats? Do fats that are rapidly absorbed correlate with disease?
That would be the medium chain fatty acids, MCFA.
"In comparison to triglycerides containing LCFAs, those containing MCFAs are more rapidly hydrolyzed in the intestinal tract and do not become incorporated into chylomicrons. SCFAs and MCFAs are transported by portal bloodstream to the liver, where they are readily metabolized."
And perhaps also the unsaturated fatty acids, UFA.
"Although pancreatic lipase hydrolyzes fat only in the 1 and 3 positions of the molecule, it is nevertheless possible for fatty acids in the 2 position of the triacylglycerol to be hydrolyzed. This apparent violation of the specificity of pancreatic lipase occurs because of the relative instability of both the 2-monoacylglycerol and the 1,2-diacylglycerol (Crossley et al., 1959). These molecules rearrange by migration of the fatty acid in the 2 position to the 1 or 3 position, which is readily hydrolyzed by lipase (Figure 18–3). This rearrangement is more rapid when the fatty acid is either a short-chain one or an unsaturated one, and a portion of the 2-position fatty acids may be absorbed as fatty acids rather than as monoacylglycerols (Benzonana et al., 1964)."
We'll call this the fat index, FI.
Are fatty acids with a high FI worse than low-FI fats?
In epidemiological studies of individual fatty acids and their associations with disease risk, the MCFAs, which are SFAs, are always more benign than the longer-chain SFAs (see table 2).
"Two recent studies from the Netherlands reported largely diverging findings. In the European Prospective Investigation into Cancer and Nutrition study, intakes of 4:0-10:0 and 12:0 were inversely associated with ischemic heart disease risk, but no associations were found for 14:0, 16:0, and 18:0. However, in the Rotterdam study, only 16:0 intake was associated with higher risk of coronary heart disease." [see also table 2]
In an overfeeding experiment, the benefits of MCFA were obvious.
"In conclusion, substitution of a small amount of dietary LCFAs with MCFAs rescues insulin action in conditions of lipid-induced energy excess."
This is because high-FI fatty acids are metabolized more rapidly, and, in the case of MCFAs, oxidized with less metabolic and hormonal effort than LCFA.[2,6]
In conclusion - if you eat carbs in bulk you will need to pay some attention to the speed at which your body absorbs them; this rules out eating purified carbohydrates.
If you eat fats in bulk, you need pay little attention to the speed your body absorbs them; you may want more fast-absorbing fatty acids in your food, but this does not rule out eating purified fats.
 Jenkins DJA, Dehghan M, Mente A, Bangdiwala SI, Rangarajan S, Srichaikul K, Mohan V, Avezum A, Díaz R, Rosengren A, Lanas F, Lopez-Jaramillo P, Li W, Oguz A, Khatib R, Poirier P, Mohammadifard N, Pepe A, Alhabib KF, Chifamba J, Yusufali AH, Iqbal R, Yeates K, Yusoff K, Ismail N, Teo K, Swaminathan S, Liu X, Zatońska K, Yusuf R, Yusuf S; PURE Study Investigators. Glycemic Index, Glycemic Load, and Cardiovascular Disease and Mortality. N Engl J Med. 2021 Apr 8;384(14):1312-1322. doi: 10.1056/NEJMoa2007123. Epub 2021 Feb 24. PMID: 33626252.
 Schönfeld P, Wojtczak L. Short- and medium-chain fatty acids in energy metabolism: the cellular perspective. J Lipid Res. 2016;57(6):943-954. doi:10.1194/jlr.R067629
 Institute of Medicine (US) Committee on Military Nutrition Research; Marriott BM, editor. Food Components to Enhance Performance: An Evaluation of Potential Performance-Enhancing Food Components for Operational Rations. Washington (DC): National Academies Press (US); 1994. 18, Structured Lipids: An Overview and Comments on Performance Enhancement Potential. Available from: https://www.ncbi.nlm.nih.gov/books/NBK209064/
 Zong G, Li Y, Wanders A J, Alssema M, Zock P L, Willett W C et al. Intake of individual saturated fatty acids and risk of coronary heart disease in US men and women: two prospective longitudinal cohort studies BMJ 2016; 355 :i5796 doi:10.1136/bmj.i5796
 Anne-Marie Lundsgaard, Andreas M. Fritzen, Kim A. Sjøberg, Maximilian Kleinert, Erik A. Richter, Bente Kiens. Small Amounts of Dietary Medium-Chain Fatty Acids Protect Against Insulin Resistance During Caloric Excess in Humans.
Diabetes Jan 2021, 70 (1) 91-98; DOI: 10.2337/db20-0582
 James P DeLany, Marlene M Windhauser, Catherine M Champagne, George A Bray, Differential oxidation of individual dietary fatty acids in humans, The American Journal of Clinical Nutrition, Volume 72, Issue 4, October 2000, Pages 905–911, https://doi.org/10.1093/ajcn/72.4.905