That is the question. In answer to the question — “Are vaccines safe?” — the Children’s Hospital of Philadelphia website states the following:
“But in truth, few things meet the definition of ‘harmless.’ Even everyday activities contain hidden dangers. For example, every year in the United States, 350 people are killed in bath- or shower-related accidents, 200 people are killed when food lodges in their windpipe, and 100 people are struck and killed by lightning. However, few of us consider eating solid food, taking a bath, or walking outside on a rainy day as unsafe activities. We just figure that the benefits of the activity clearly outweigh the risks.”
I would agree. I don’t worry about dying from a lightning strike, eating solid food, or taking a shower. To recap, the given numbers are as follows:
Let’s compare the numbers above to the average number of people who died from certain infectious diseases, before vaccines for them were in routine use.
In order to give some perspective, compare the number of deaths from the infectious diseases above, to the number of deaths for the causes listed below.
Comparing the numbers, we can see that the odds of dying from lightning are greater than the odds of dying from rubella, mumps, and rotavirus. “Food in the windpipe” is a greater cause of death than either the chickenpox or hepatitis A. The measles, on the other hand, is more deadly than bathing.
If we are not afraid of eating solid food, taking a bath, or walking outside on a rainy day, then why are we afraid of these infectious diseases? If my odds of dying from the chickenpox are about the same as my odds of dying from a lightning strike, then that is a risk I’m willing to take (I have had the chickenpox, by the way. I survived). I’m also willing to take that risk with rubella, mumps, rotavirus, and hepatitis A. Call me crazy, but I don’t mind playing those odds. Especially when there are things that I can do pro-actively to boost my immune system naturally and reduce my risk of dying from any infectious disease — not just the ones for which there is a vaccine.
In the USA, if the measles killed as many people today as it did before the measles vaccine was introduced in 1963, then about 820 people would die from the measles this year (population-adjusted figure). Today, thanks to the measles vaccine, no one dies from the measles. So that’s literally hundreds of lives that have been saved every year since 1963 thanks to the measles vaccine. It all sounds pretty good. At this point, it would be easy to conclude that anyone opposed to the measles vaccine is completely out of their mind. After all, the measles vaccine is obviously effective. And, it has saved many thousands of lives in the U.S. alone [440 deaths/year x 55 years = 24,200 lives saved] (figure not adjusted for population growth).
The problem is that an unknown number of people have also been harmed by the measles vaccine. While we have done a very good job of quantifying the benefits of vaccines, we have done a comparatively poor job of accurately quantifying the harm caused by vaccines (MMR or otherwise).
According to the non-profit National Vaccine Information Center (NVIC), as of March 31, 2018, there have been more than 89,355 reports of measles vaccine adverse reactions made to the federal Vaccine Adverse Events Reporting System (VAERS), including 445 related deaths, 1,657 related disabilities, and 6,196 hospitalizations. We cannot prove that the measles vaccine necessarily caused these adverse events; we can only say that these adverse events happened soon after receiving the vaccine. If we do the math and compare the numbers, it is easy to conclude that the benefits of the measles vaccine clearly outweigh the risks. That is, until we are confronted with this most unfortunate fact:
“Adverse events from vaccines are common but underreported, with less than one percent reported to the Food and Drug Administration (FDA).” 
This throws a monkey wrench into our calculations. Now we need to multiply by 100 to estimate the actual number of adverse events associated with the measles vaccine. This would give us an estimated 9 million adverse reactions, over the years, with potentially 44,500 deaths and 165,700 cases of disability associated with the measles vaccine (again, these are temporal associations, so not all these adverse events will actually have been caused by the vaccine).
Suddenly, the risk-benefit ratio is less clear. The problem is that we do not know the true extent of harm caused by the measles vaccine (or any vaccine for that matter), so it is impossible to make this calculation with confidence. Sure, it would be easy to simply assume that the benefits outweigh the risks, but that is not scientific. Science demands something more concrete than mere assumptions.
I want to be able to make this calculation confidently. And right now, I cannot. In fact, no one can. The Physicians for Informed Consent (a group of doctors and scientists) state that:
“the level of accuracy of the research studies available is insufficient to prove that the MMR vaccine causes less death or permanent injury than measles.”
Even a study conducted by the Cochrane organization concluded that:
“The design and reporting of safety outcomes in MMR vaccine studies, both pre- and post-marketing, are largely inadequate.”
I think this is one reason why public confidence in vaccines is declining, and more people are choosing not to vaccinate. When the known risk of dying from the measles is not that much greater than the risk of death from bathing, does it make sense to take on the unknown risk of the MMR vaccine? I reckon, for some people it will make sense to take that risk, and for others it will not. Let’s just say, to each their own.