A documentary, Cholesterol, the Great Bluff (2016) - IMDb (depending upon location, available in Cholesterol: The Great Bluff), contains many examples of why statins are not only useless, but are actually harmful.
It claims that statins have severe side effects, the worst perhaps simply being that they do exactly what they are intended to do, reduce cholesterol. The problem is that a significant portion of the brain is composed of cholesterol, and the destruction of that cholesterol can cause dementia.
A (badly formatted) transcript, Transcript: Cholesterol: The Great Bluff | TVO.org, contains this anecdote, for instance:
[A woman in her forties with long brown hair speaks.]
[A caption reads "Doctor Beatrice Golomb, Professor of Medicine."]
[Doctor Golomb says]
We published a case series of 171 people with cognitive adverse effects on statins. And some of these are quite compelling and troubling cases. There was one individual who was a retired professor in multiple different departments with a reported IQ of over 180 who had actually been identified by two academic institutions as having the rapidly progressive form of Alzheimer's disease. And he actually went to a 50-year school reunion with a sign around his neck saying, "My name is [….] I have Alzheimer's", so that people would understand why he would repeat the same sentence again and again and wouldn't recognize people he'd known closely for decades. He also couldn't read more than a page of text because he couldn't remember what he'd read. And then his wife decided to stop his Simvastatin and he appeared to screen for an experimental drug trial for Alzheimer's at another university. And they reassessed him. And they said, not only do you not have Alzheimer's — you don't have dementia. And by his reckoning it was about two years before he was all the way back to normal. But by then he was back to reading three newspapers a day. The New York Times, the Wall Street Journal and Washington Post online.
Beatrice Golomb is Professor in Residence, Medicine, at UCSD.
The same source quotes Michel de Lorgeril — Wikipédia, doctor and researcher at CNRS, The European Society of Cardiology:
Statins, and anti-cholesterol drugs in general, cross over the blood-brain barrier, which means they enter the brain and disturb the production of cholesterol within the brain. This has an awful secondary effect because no one was aware of it until recently, and due to pressure from certain doctors and toxicologists, the health authorities finally admitted that statins could cause memory problems, sleep disorders and therefore neuro-toxicity. Unfortunately, despite being a major toxic factor, its effects are still underestimated. We must not forget that Alzheimer’s disease starts with memory problems, sleep disorders and therefore you can say that statins - although additional studies would obviously be required... almost push us towards Alzheimer’s disease, especially since statins are diabetogenics and diabetes is a major risk factor for developing Alzheimer’s, some people even say that Alzheimer’s is a type-3 diabetes.
This documentary finds many problems with current practices and beliefs related to cholesterol, but I'm not asking about the documentary itself, or about the significance of blood cholesterol.
Restricting the question to the very believable claim that statins cause brain damage and are responsible for recent increases in the incidence of dementia, something the pharmaceutical industry would obviously dispute, has there been any research to refute this specific claim?
In a comment, Dave Sherohman provides two references to small studies, one supporting (107 subjects) and one refuting (55 subjects) this claim. In both cases, the subjects all had type 1 diabetes. For the purposes of this question, I'll quote only the one supporting it:
… Propensity score analyses support that associations between poor cognitive outcomes and statin use were not due merely to confounding by indication.
Statin use was associated with cognitive impairment, particularly affecting memory, in these middle-aged adults with childhood-onset T1D, whom at this age, should not yet manifest age-related memory deficits.
Core tip: Animal and cell culture studies show that statins can damage cerebral gray and white matter, thereby affecting cognitive function. Findings from human studies remain controversial; early observational studies reported that statin use negatively affected cognition, especially memory, while more recent studies have not replicated these findings. Even though statins are widely prescribed for people with type 1 diabetes (T1D), only one study to date has examined whether statin use is related to cognitive impairment in this patient population. We propose that deleterious effects statins may exert on cognition may be more pronounced in people with T1D, as these individuals are already at an increased risk of cognitive impairment due to long-term exposure to metabolic dysregulation.