Complex sentence: The studies were shown to be unreliable because of the "healthy user effect": reasonably healthy elderly people were more likely to be vaccinated, and those in poorer health were less likely to be vaccinated and more likely to die for any reason.
Split into simpler sentences: The studies were shown to be unreliable because of the "healthy user effect". Reasonably healthy elderly people were more likely to be vaccinated, and those in poorer health were less likely to be vaccinated and more likely to die for any reason.