There is one study that looks bad for LCHF. It looks bad mostly based on the name of the study rather than the science (American Journal of Epidemiology, Volume 134, Issue 6, 15 September 1991, Pages 590–603. High-Fat, Low-Carbohydrate Diet and the Etiology of Non-Insulin-dependent Diabetes Mellitus: The San Luis Valley Diabetes Study. Julie A. Marshall Richard F. Hamman Judith Baxter).
The study (1990) suggests that High Fat diets are associated with onset of non-insulin dependent diabetes mellitus.
The findings support the hypothesis that high-fat, low-carbohydrate diets are associated with the onset of non-insulin-dependent diabetes mellitus in humans.
The problem is that, at least in the abstract, there’s no evidence that the people were on anything at all related to a Low Carbohydrate diet. That was inferred based on the High Fat. But you don’t need to go any farther than your local McD’s to know that french fries are both high in fat and high in carbs.
When you look close you can see that the study was an association study not a Randomized Control Trial. Association does not prove causation. Just because people who got diabetes at lower carb/higher fat diets doesn’t mean that the diet caused the diabetes.
This paper (Risk Factors for Non-Insulin Dependent Diabetes. Marian Rewers, MD, PhD, and Richard F. Hamman, MD, DrPH) lists quite a few studies on this subject (Table 9.6) and includes a helpful comment:
There are substantial methodological problems in measuring exposure to behavioral factors such as physical inactivity and diet pp 179-181. Most studies have used a single recording of activity or diet as a measure of exposure. While it is assumed that such point estimates are correlated with habitual exercise or intake, it is uncertain what period of time is necessary to obtain the most valid estimates