There is a clear reason why statins would promote Alzheimer's. They cripple the liver's ability to synthesize cholesterol, and as a consequence the level of LDL in the blood plummets. Cholesterol plays a crucial role in the brain, both in terms of enabling signal transport across the synapse  and in terms of encouraging the growth of neurons through healthy development of the myelin sheath . Nonetheless, the statin industry proudly boasts that statins are effective at interfering with cholesterol production in the brain  as well as in the liver.
Yeon-Kyun Shin is an expert on the physical mechanism of cholesterol in the synapse to promote transmission of neural messages, and one of the authors of  referenced earlier. In an interview by a Science Daily reporter, Shin said: "If you deprive cholesterol from the brain, then you directly affect the machinery that triggers the release of neurotransmitters. Neurotransmitters affect the data-processing and memory functions. In other words -- how smart you are and how well you remember things."
A recent review of two large population-based double-blind placebo-controlled studies of statin medications in individuals at risk for dementia and Alzheimer disease showed that statins are not protective against Alzheimer's . The lead author of the study, Bernadette McGuinness, was quoted by a reporter from Science Daily as saying, "From these trials, which contained very large numbers and were the gold standard -- it appears that statins given in late life to individuals at risk of vascular disease do not prevent against dementia." A researcher at UCLA, Beatrice Golomb, when asked to comment on the results, was even more negative, saying, "Regarding statins as preventive medicines, there are a number of individual cases in case reports and case series where cognition is clearly and reproducibly adversely affected by statins." In the interview, Golomb remarked that various randomized trials have shown that statins were either adverse or neutral towards cognition, but none have shown a favorable response.
A common side effect of statins is memory dysfunction. Dr. Duane Graveline, fondly known as "spacedoc" because he served as a doctor to the astronauts, has been a strong advocate against statins on his web page where he is collecting evidence of statin side effects directly from statin users around the world. He was led to this assault on statins as a consequence of his own personal experience of transient global amnesia, a frightening episode of total memory loss which he is convinced was caused by the statin drugs he was taking at the time. He has now completed three books describing a diverse collection of damning side effects of statins, the most famous of which is Lipitor: Thief of Memory .
A second way (besides their direct impact on cholesterol) in which statins likely impact Alzheimer's is in their indirect negative effect on the supply of fatty acids and antioxidants to the brain. It is a given that statins drastically reduce the level of LDL in the blood serum. This is their claim to fame. It is interesting, however, that they succeed in reducing not just the amount of cholesterol contained in the LDL particles, but rather the actual number of LDL particles altogether. This means that, in addition to depleting cholesterol, they reduce the available supply to the brain of both fatty acids and antixodiants, which are also carried in the LDL particles. As we've seen, all three of these substances are essential to proper brain functioning.
I conjecture that the reasons for this indirect effect are two-fold: (1) there is inadequate cholesterol in the bile to metabolize dietary fats, and (2) the rate-limiting effect on the production of LDL is the ability to provide adequate cholesterol in the shell to assure survival of the contents during transport in the blood stream; i.e., to protect the contents from oxidation and marauding bacteria and viruses. People who take the highest 80 mg/dl dosage of statins often end up with LDL levels as low as 40mg/dl, well below even the lowest numbers observed naturally. I shudder to think of the probable long-term consequences of such severe depletion in fats, cholesterol, and antioxidants.
A third way in which statins may promote Alzheimer's is by crippling the ability for cells to synthesize coenzyme Q10. Coenzyme Q10 has the misfortune of sharing the same metabolic pathway as cholesterol. Statins interfere with a crucial intermediate step on the pathway to the synthesis of both cholesterol and coenzyme Q10. Coenzyme Q10 is also known as "ubiquinone" because it seems to show up everywhere in cell metabolism. It is found both in the mitochondria and in the lysosomes, and its critical role in both places is as an antioxidant. The inert esters of both cholesterol and fatty acids are hydrolyzed and activated in the lysosomes , and then released into the cytoplasm. Coenzyme Q10 consumes excess oxygen to keep it from doing oxidative damage , while also generating energy in the form of ATP (adenosine triphosphate, the universal energy currency in biology).
The final way in which statins should increase Alzheimer's risk is through their indirect effect on vitamin D. Vitamin D is synthesized from cholesterol in the skin, upon exposure to UV rays from the sun. In fact, the chemical formula of vitamin D is almost indistinguishable from that of cholesterol, as shown in the two attached figures (cholesterol on the left, vitamin D on the right). If LDL levels are kept artificially low, then the body will be unable to resupply adequate amounts of cholesterol to replenish the stores in the skin once they have been depleted. This would lead to vitamin D deficiency, which is a widespread problem in America.
It is well known that vitamin D fights infection. To quote from , "Patients with severe infections as in sepsis have a high prevalence of vitamin D deficiency and high mortality rates." As will be elaborated on later, a large number of infective agents have been shown to be present in abnormally high amounts in the brains of Alzheimers patients .
Dr. Grant has recently argued  that there are many lines of evidence pointing to the idea that dementia is associated with vitamin D deficiency. An indirect argument is that vitamin D deficiency is associated with many conditions that in turn carry increased risk for dementia, such as diabetes, depression, osteoporosis, and cardiovascular disease. Vitamin D receptors are widespread in the brain, and it is likely that they play a role there in fighting off infection. Vitamin D surely plays other vital roles in the brain as well, as powerfully suggested by this quote taken from the abstract of : "We conclude there is ample biological evidence to suggest an important role for vitamin D in brain development and function."