Say we want to know the impact of smoking on lung cancer. We take two groups of 20 year olds who do and don't smoke and follow them up for 5 years Say, 1,000 smokers and 1,000 non-smokers
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At the end of the study, 10 non-smokers and 11 smokers have developed lung cancer The difference is non significant statistically Does this mean that smoking isn't associated with lung cancer?
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Think about it - how many 30 years olds develop cancer by the age of 35? Might this make our study's results biased towards a conclusion?
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The answer is...this study is probably wrong! If we extend the timeline, and look at the LIFETIME risk of smoking for 30 year olds, suddenly there's a HUGE increase in the risk of lung cancerpic.twitter.com/f0bZz5SfXq
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The problem is that initially, we stopped the clock BEFORE PEOPLE HAD THE OUTCOME WE ARE INTERESTED IN This meant that the difference - even though it was there! - was impossible to see in our data
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That's right-censoring in a nutshell If you stop counting results too early, suddenly your study has a significant bias (often towards low/no difference)
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What does this mean to antibody results for COVID-19? Well, think about how these studies are conducted. We test a bunch of people randomly on day x to get an idea of how many people are immune to COVID-19 on that day
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Then, to calculate mortality, most people take the number of deaths on day x and divide by the denominator implied by the results
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So, if we think 4% of 100,000 people have had COVID-19, and 10 of them have died on day x, we'd say that the infection-fatality rate is 10/4000 = 0.025%
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BUT there's an issue here People don't die from COVID-19 immediately. It usually takes somewhere between 15-20 days from when they get infected The data is right-censored!
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There are probably a bunch of people who HAVE the disease on day x who are counted in our sample and will die but haven't yet!
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So, what we SHOULD do in cases like these is either: a) use a statistical model to account for this issue b) wait a few weeks and use different death estimates to correct for potential right-censoring
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Instead, most people just take the proportion immune on day x and divide by deaths on the same day This will almost certainly underestimate the 'true' infection-fatality rate, and is a big worry
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