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Berkson’s Paradox also known as Berkson’s Bias or Collider Bias is a particular kind of selection bias that is caused by systematically observing some events more than the others. It seems to show case correlation between two independent events however in reality there is no such correlation that exists between those independent events. Here the correlation between two events let’s say A & B i.e. the probability of event A happening is higher in the presence of event B happens because cases where neither of the events occurs are excluded from the sample taken fro study. This principle was illustrated by Joseph Berkson in 1946 with a case study that linked diabetes with cholecystitis amongst the patients admitted in a hospital. There seemed to be no correlation amongst both the diseases based on the data collected from the overall population, however since the samples in this study were taken from the patients admitted in the hospital it indicated a misleading positive association between the two diseases. Let us see this example to understand why such association was observed:- Let’s say that the population of patients admitted in the hospital is 100 & the two diseases i.e. diabetes & cholecystitis are two independent events & we have even distribution of population amongst the four categories as shown below:- High cholecystitis & low diabetes : 25 High cholecystitis & high diabetes : 25 Low cholecystitis & low diabetes : 25 Low cholecystitis & high diabetes : 25 Now since the data was collected from the hospital hence the category with low cholecystitis & low diabetes would not appear in the study i.e. only the data for the other three categories would be reported. Let us calculate the probability that a patient with lower diabetes diagnosed with cholecystitis would be calculated as:- P(High cholecystitis | Low Diabetes) = 25/25 = 100% (since we have not considered the category with low cholecystitis & low diabetes in the study) Now let us calculate the probability that a patient with high diabetes would be diagnosed with cholecystitis:- P(High cholecystitis | High Diabetes) = 25/(25+25) = 50% (since we will be taking into considerations both the categories where patient has high diabetes) Thus there is a false conclusion now that the patients with high diabetes tend to have a lower risk of having cholecystitis. Let us now take another example in order to see the effect of Berkson’s Paradox:- Let us consider two seemingly dependent events i.e. Diligence & Academic Results. Now logically there should be a positive relationship between these two variables i.e. the more diligent you are the better your academic results would be. Thus there will be an uneven distribution of population as well as shown below:- Lazy & Good Results : 20 Hardworking & Good Results : 30 Lazy & Poor Results : 30 Hardworking & Poor Results : 20 Now let’s say the data is collected from a top school then we would not be considering lazy students with poor results. Here the probability of lazy students getting good results is given as :- P(Good Results | Lazy) = 20/20 = 100% (since we have not considered the category of lazy students having poor results in the study) Also the probability of hardworking students getting good results:- P(Good Results | Lazy) = 20/(30+20) = 60% (since we have not considered both the categories where students are having good results) Thus this study also gives us a wrong impression that the lazy students have better chances of getting good results which is not the case had we collected the data from the entire population of schools. Preventing Berkson’s Bias: Below are the common strategies should be adopted in order to prevent Berkson’s Bias:- Select the correct target population eg: if the target population is students then including locals who didn’t attend college will introduce bias. Select random samples from the target population eg: in order to study the effect of sleep on college student grades ensure that the right balance of students who have enrolled to early morning courses & night courses are included rather than taking students belonging to only one type of course. Perform a pilot study before going for a full blown study as this will give an idea quickly on the appropriateness of the selection design. Create a standard method of selecting samples from the population & measuring data so that everyone involved in the study is calibrated.

Berkson's paradox describes a situation where the conclusion on correlation between two variables from a sample study is found to be against our intuition. This happens because of wrong sample selection. For example, regular exercise keeps a person active. However, if the study is performed on hospitalized patients, the result can turn out to be counterintuitive. As another example, regular investments in mutual funds provides a positive return. But, if the the study is performed on poorly performing funds, the result might be negative returns. Sample selection needs to be done from a general population instead of a biased population to prevent occurrence of Berkson's paradox.