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Text of the page (random words):
far right it is rare 1 in 10 000 going down the rows the side effect rate from the treatment decreases so in the first row the side effect is very common the treatment causes it in 1 in 10 patients in addition to the background rate and by the last row it is rare only being caused in 1 in 1 000 000 patients within each panel we are seeing the percent of tests out of 500 where we were able to detect a correlation significant result on the y axis keeping in mind that there was a causal relationship in each test so anything less than 100 indicates a false negative an under powered test on the x axis we have increasing sample sizes on a log10 scale blue results are for randomize cohort trials and red indicates case control trials simulation results comparing the power of randomized controlled trials cohort studies and case control studies see text for details note that the x axis is on a log10 scale so each tick is 10 times the sample size of the previous tick there are several important and clear patterns here within each row the rate of positive results increases from left to right i e the lower the background rate the more powerful the test within each column the rate of positive results decreases from top to bottom i e the rarer the side effect the harder it is to detect within each panel the rate of positive results increases from left to right i e the larger the sample size the more power case control studies consistently have more power than randomized cohort studies with particularly pronounced differences for rare background and side effect rates before going any further i want to pause and stress that these are simulated results based on a simplistic scenario so the four trends described above apply to the real world but the exact numbers shown here don t necessarily apply and in the real world there would be confounding factors sex age medical history etc that would be built into the models interpreting the negative results now we get to a really important caveat about how to interpret negative results keeping in mind that in my simulation there was an effect of treatment in each simulation we just weren t always able to detect it technically speaking science never proves anything and it is particularly problematic to demonstrate a negative so when we fail to find a correlation technically we have not shown that there is no effect rather we have shown that if there is an effect it was too rare to detect with our sample size keep in mind that in real studies we know both the sample size and the background rate that s just the rate in the control group so the only unknown is the treatment effect side effect rate in our example therefore while we cannot conclusively with 100 certainty say that there is no relationship we can get a sense for how rare it would have to be if it occurred thus we can use the study design sample size and background rate to judge how concerned we need to be about the possibility of an undetectable effect if the study had low power then it may still be a legitimate concern but if the study had a high power then the concern is greatly reduced note that anti vaccers love to abuse this reality and play word games like demanding to see a study that proves that vaccines don t cause autism that s an impossible request it is never possible to prove that x does not cause y but we can show that if x causes y it would have to be doing so at such an incredibly low rate that it s not a big concern more on that in a sec applying this to vaccines finally let s bring this all back around to anti vaccers original argument that only placebo controlled trials are satisfactory for establishing vaccine safety as you can hopefully now see that is a really faulty claim and placebo controlled trials are actually badly under powered because of their low sample sizes if you showed me a randomized placebo controlled trial of 1 000 children a pretty big trial that failed to find a significant trend for autism i d actually agree with you that that study is weak evidence we know autism is fairly common it has a high background rate so that study would only eliminate the possibility of vaccines causing autism at a really high rate it would still be entirely possible for vaccines to be a substantial cause of autism that test was just under powered in contrast there have been several cohort studies of vaccines and autism with sample sizes of several hundred thousand children anders et al 2004 hviid et al 2019 madsen et al 2002 jain et al 2015 now we are talking about tests with some power tests that can confidently assert that if there is a relationship between vaccines and autism it is a very weak one and autism is a very rare side effect further we have case control studies on vaccines and autism with hundreds or even thousands of children destefano et al 2004 smeeth et al 2004 destefano et al 2013 uno et al 2015 again those are actually very powerful way more powerful than a randomized trial additionally there is even a meta analysis that combined the studies above into one uber study with some truly impressive power taylor et al 2014 guess what there was still no correlation so we can confidently state that there is no evidence of vaccines causing autism and if they do they are doing so at an incredibly low rate stated another way anti vaccers are technically correct that we cannot prove that vaccines don t cause autism but we can and have demonstrated that even if vaccines cause autism the rate is very very low thus the notion of vaccines causing an autism epidemic is completely falsified you almost certainly don t know anyone who has autism because of vaccines because even if that side effect ever occurs it is very rare conclusion i have been using autism as an example here but all of this applies generally to all vaccines and all medical research using these study designs when we are talking about safety and making claims about side effect rates randomized placebo controlled studies are often under powered and frequently aren t the best tool they are great during initial testing because they will detect common side effects and allow us to assign causation but once we are talking about side effects that only occur once in a few thousand people randomized trials are grossly under powered and cohort and case control trials are much better tools for detecting correlation associations randomization is important for assigning causation but it is not needed to detect correlation and while correlation does not indicate causation two things that are causally related will by definition be correlated though the correlation may be hard to detect as such anti vaccers are completely and totally wrong to insist that we don t know vaccines are safe without placebo controlled trials a lack of correlation association in large cohort and case controlled studies are great evidence that even if there was a side effect it would be extremely rare thus anti vaccers are fundamentally misunderstanding how study designs and statistical power work note on lack of correlation when i say that a lack of correlation indicates a lack of causation this is true in the strictest sense that if two things are causally related there will inherently be a relationship between them however that does not mean that failing to detect a correlation proves a lack of causation as seen in the post tests may simply have been under powered further there may be time lag effects or third causes that are also important so sample size and study design are important considerations i e did they correctly control for confounding factors nevertheless my fundamental point remains that a lack of correlation association in large cohort case control studies is good evidence that if there is a causal relationship it is a weak one with a small effect size model details this was a stochastic simulation meaning that there was chance variation in the results which accounts for some of the waviness in the figure for example if the background rate was 1 in 10 then each individual in the control population had a 1 in 10 chance of developing the outcome but this was determined stochastically so for runs with 100 individuals on average 10 would have the outcome but sometimes it would be 9 sometimes it would be 11 etc also note that the side effect rate was additive to the background rate so if background 1 in 10 and side effect rate 1 in 10 people who received the treatment had a 2 in 10 chance of developing the side effect also note that sample size i s per group so n 100 means 100 people in the control group and 100 people in the treatment case group for modeling simplicity for the case control trials it assumed that half of the total population received the treatment related posts how well do you understand placebo effects masks and covid vaccines were huge successes ivermectin and hydroxychloroquine were not the hierarchy of evidence is the study s design robust understanding the reported risks of medicines foods toxic chemicals etc vaccines and autism a thorough review of the evidence 2019 update vaccines are tested against placebos when can correlation equal causation litterateur cited anders et al 2004 thimerosal exposure in infants and developmental disorders a retrospective cohort study in the united kingdom does not support a causal association pediatrics 114 584 591 destefano et al 2004 age at first measles mumps rubella vaccination in children with autism and school matched control subjects a population based study in metropolitan atlanta pediatrics 113 259 266 destefano et al 2013 increasing exposure to antibody stimulating proteins and polysaccharides in vaccines is not associated with risk of autism j ped 163 561 567 hviid et al 2019 measles mumps rubella vaccination and autism a nationwide cohort study annals of internal medicine jain et al 2015 autism occurrence by mmr vaccine status among us children with older siblings with and without autism jama 313 1534 1540 madsen et al 2002 a population based study of measles mumps and rubella vaccination and autism new england journal of medicine 347 1477 1482 polack et al 2020 safety and efficacy of the bnt162b2 mrna covid 19 vaccine new england journal of medicine 383 2603 2615 smeeth et al 2004 mmr vaccination and pervasive developmental disorders a case control study lancet 364 963 969 taylor et al 2014 vaccines are not associated with autism and evidence based meta analysis of case control and cohort studies elsevier 32 3623 3629 uno et al 2015 early exposure to the combined measles mumps rubella vaccine and thimerosal containing vaccines and risk of autism spectrum disorder vaccine 33 2511 2516 share this share on x opens in new window x share on facebook opens in new window facebook like loading posted in nature of science vaccines alternative medicine tagged anti vaccine arguments bad arguments evaluating evidence peer reviewed studies placebos vaccines 5 comments understanding analogies in logical arguments posted on june 25 2026 by fallacy man yesterday on this blog s facebook page i posted the stick figure comic on the right lightly making fun of anti vaccers and using analogies to demonstrate why they are wrong that 100 effectiveness is needed for vaccines to be useful i love analogies they are a great way to get people past their biases and show underlying flaws in their reasoning but apparently many people don t understand how analogies work and the comments quickly filled with people saying that these were bad analogies false equivalencies because according to them unlike seat belts helmets birth control or air bags vaccines cause serious injury go inside you and are protected from lawsuits see examples below there is a lot wrong with these responses e g serious side effects from vaccines are extremely rare serious injuries can occur from the other things mentioned etc but i want to focus on the big one namely these responses totally misunderstand the nature of analogies and how to evaluate arguments this comic was about one specific argument the argument that vaccines aren t useful because they aren t 100 effective that s it effectiveness is the only thing being discussed as such all other considerations are 100 irrelevant even if vaccines were horribly dangerous they aren t that would not make this comic a bad analogy or a false equivalency because it is not about safety it is about the effectiveness argument the purpose of a good analogy is to get at the underlying logical structure of an argument and nothing outside of that structure matters to illustrate this let s break the argument down into its syllogism premise 1 vaccines aren t 100 effective conclusion therefore vaccines should not be used stated like that it is clear that the conclusion does not follow necessarily from the premises which is why there is actually a second unstated premise premise 1 vaccines aren t 100 effective premise 2 unstated things that aren t 100 effective should not be used conclusion therefore vaccines should not be used that is the argument being addressed by the comic and we can show that the argument clearly does not work by replacing vaccines with literally anything else that is useful despite not being 100 effective for example premise 1 seat belts aren t 100 effective premise 2 things that aren t 100 effective should not be used conclusion therefore seat belts should not be used do you see how that works all of those other considerations like safety are totally irrelevant for this analogy because they don t matter for this one particular argument to be completely clear things like safety are certainly important in a broader discussion of vaccines if i had said that this comic proves that we should be using vaccines then commenters would have been absolutely correct to point out that it doesn t address safety but no one ever claimed that this comic encompasses all considerations or proves that we should vaccinate it was about one specific argument about one specific aspect of vaccines and the examples used are completely analogous for that specific aspect thus it is in no way a false equivalency understanding this is really important because our brains are very resistant to information that is contrary to our beliefs and one of the tricks they play on us is to ignore an argument we are being presented with and shift to a different argument that is exactly what happened here rather than take the time to consider this one particular defect in anti vaccer reasoning people ignored the argument at hand and jumped to a different argument we all tend to do this frequently and it is a cognitive trap that we need to be aware of and train ourselves to avoid when presented with an argument train yourself to avoid the tendency to jump to what about stop take a deep breath and carefully consider the argument currently in front of you don t let your brain jump to other topics force yourself to focus on the specific argument you h...
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