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The problem with these studies is that they measure people who chose to get the vaccine against people who don't. People who chose to get vaccinated are by definition concerned with their heath and more likely to take care of themselves. In the United States where vaccines are paid for by heath insurers, these studies are splitting the two groups into income brackets which naturally demarcate health. In other words, the studies compare healthy people to unhealthier people. You would think that any study worth its salt would eliminate this obvious problem by doing double blind experiments with vaccines versus placebos. But because the vaccine is presumed to work, it's considered unethical to give some a vaccine and others a placebo!
Some have challenged the results of this circular logic. In 2004, Lisa Jackson, a researcher with Group Heath Research Center in Seatle, studied medical histories of 72,000 people aged 65 and older. She found that outside of flu season, the baseline risk of death was 60 percent higher for the those that did not get flu shots.
This confirms the so-called "healthy user effect" demonstrating that healthier people tended to get the flu shot. In fact, the degree that they were healthier accounts for all of the supposed efficacy of the flu vaccine studies!
When Jackson presented these results to the Journal of the American Medical Association, they were rejected on the grounds that the results were akin to "suggesting the earth was flat." Other evidence is just as confounding. For example, just 30 years ago, few to none of people over 65 got a seasonal flu vaccine. Today nearly 75 percent get vaccinated, yet we don't see a decrease in influenza deaths to any degree that would indicate that the vaccine works. These obvious facts contravene sacred beliefs and are summarily ignored. It's possible that flu strains become have more infectious and lethal over that period and that lethality has exactly matched increasing rates of vaccinations but there is no evidence to support that claim. What seems most likely stems from the mechanics of the vaccine itself: those with good immune systems respond well to both the vaccine and the flu. Or more simply, the vaccine does nothing.
If a drug statistically appears to do nothing, then I will skip a step and not take it!
Important Post Script: I do not count myself among those who believe that certain vaccines cause autism or any number of other scientifically untenable claims.