One common statement used in anti-vaccination literature is that when outbreaks of vaccine-preventable diseases occur, the majority of those infected turn out to be vaccinated children. 1 According to the anti-vaccination advocates, this shows that vaccines are not at all effective at preventing the disease. The problem is that the statistic quoted actually demonstrates exactly the opposite. You see, the problem with the statistic as quoted by the anti-vaccination advocates is that the vast majority of children are vaccinated. Thus, even if only a tiny percentage of vaccinated children get the disease, their numbers will be larger than the number of unvaccinated children who get the disease.
The best way to illustrate this is to think of an example. Suppose a measles outbreak occurs in a school that has a population of 1,000. About 98% of those students (980) will be vaccinated. That leaves 20 that are not vaccinated. Now, suppose that only 2% of the vaccinated population contracts measles. That means about 20 vaccinated students will get the disease. Next, suppose that 90% of the unvaccinated children contract measles. That means 18 of the unvaccinated students will get the disease. Thus, of those who got the disease, 53% were vaccinated, and 47% were not. Does this mean that the vaccines did not work? Quite the opposite! While only a tiny minority of the vaccinated students got the disease, the vast majority of the unvaccinated students got the disease. Being vaccinated made you only 2% likely to get the disease, while not being vaccinated made you 90% likely to get the disease! Clearly, then, the vaccine was quite effective, as vaccinated students were 45 times less likely to be infected than unvaccinated students.
When comparing one group to another, then, you must make sure to take into account that one population might be greater in number than the other. Anyone with a modicum of training in research or statistics know this. Thus, in the medical literature, statistics are always reported in this way. If you look at studies that have been done on measles outbreaks, for example, you will find that the research indicates that vaccinated children are up to 35 times less likely to catch measles than unvaccinated children.2 This is the proper way to report such a statistic.
The question is, since the statistics are always discussed properly in the medical journals, why do anti-vaccination advocates misquote them in their literature? They must look at the studies, or they could not get the numbers. Why, then, do they ignore the proper way to quote the statistic and instead use a deceptive way? I think that the answer is obvious: quoting the statistic the proper way will hurt their cause, while quoting them in a deceptive manner will help fool the general public into accepting their ideas.
References
1. Neil Z. Miller, Vaccines: Are They Safe And Effective, New Atlantean Press, 2002, p. 29
2. Salmon DA, et al. “Health Consequences of Religious and Philosophical Exemptions From Immunization Laws: Individual and Societal Risk of Measles” JAMA, 1999; 282:47-53
Dr. Wile is not a medical doctor. He is a nuclear chemist. As a result, he does not dispense medical advice. He simply educates the public about scientific issues. Please consult a board-certified medical doctor before making any medical decisions for yourself or your family.