Berkson’s Paradox

More broadly, however, we could only call it the Berkson effect because of the general application of unusual selection forces that are likely to create unexplored relationships. However, such a correlation clearly does not exist when we restrict our analysis of the NBA. [Sources: 11]

An obvious reading of Burkson’s paradox is that people who are good at basketball and short, and people who are bad and tall can compete in the NBA, but people who are short and poor at basketball were excluded from the champion. … intense competition. The significance of these rare attributes to the NBA can easily surpass the growth seen among the broader population. Growth is unrelated to playing in the NBA, because a short NBA player must have abnormally high skills to break into the tight circle known as the NBA. [Sources: 5, 11]

As a result of bias in our data collection, we end up seeing that 100% of the least educated are successful (Figure 3 – green), but only a fraction of the highly educated are successful (Figure 4 – green). This is the result of a compromise between the GPA and SAT scores of the people surveyed. [Sources: 4, 5]

It is tempting to see conflicting correlations and try to build a story about them, but they are often not surprising when we realize that a small circle is choosing between two dominant attributes. In general, if two factors influence the choice in the sample, we say that they “collide during the choice” (see Figure 2a). The lesson here is that we can see spurious correlations between variables as a result of sample bias. In the aggregate dataset, we come to the conclusion that if we divide this data into groups according to some criteria, we get results that are completely opposite to the results of previous observations. [Sources: 1, 5, 7, 9]

One of the most famous examples of the Simpsons paradox is the study of gender bias in the Graduate School of the University of California, Berkeley. This paradox is named after Joseph Berkson, who pointed out the selection bias in case-control studies to determine causal risk factors for the disease. Since the samples are taken from hospital patients rather than the general population, this may lead to negative and false associations between disease and risk factors. [Sources: 1, 7, 13]

This example is very similar to Berkson’s original 1946 work, in which the author noted a negative correlation between cholecystitis and diabetes in hospital patients, despite diabetes being a risk factor for cholecystitis. The paradox can also give the impression of a negative correlation, when in fact two variables are positively correlated or completely independent of each other. The Berkson paradox arises when this observation appears to be true, when in fact two properties do not correlate, or even positively correlate, because members of a population in which both are absent are observed unevenly. [Sources: 3, 5, 6]

According to Berkson’s paradox, cases in which two elements that appear to be related to people in general are not actually related. In other words, in the presence of two independent events, if we consider only the outcomes in which at least one occurs, they become negatively dependent, as shown above. This leads to the Berkson paradox, according to which, due to the presence of B in the subset, the conditional probability of A decreases, which explains the negative dependence of two independent events, provided that at least one of them occurs. The answer to any occurrence of Berkson’s error is to properly define or characterize the population and then statistically examine a significant portion of the population to test the relationship between A and B. [Sources: 0, 13]

In addition, a suitable procedure is proposed for generating inferences for a population based on a biased sample that has all the characteristics of the Burkson paradox. In particular, this occurs when there is an inherent estimation bias in the study design. Like other threats to causal inference, once you know about collider displacement, you will see it lurking everywhere: from introducing an association, when the two factors were effectively independent, to diminishing, exaggerating, or even altering the existing association in a way that is difficult to predict. … [Sources: 8, 9, 12]

In recent article 1, we summarize how collider displacement could play a role in Covid-19 research and identify hundreds of demographic, genetic, and health-related factors that influence the likelihood of a person being selected for Covid-19 testing. United Kingdom. Biobank participants. Observational errors and subgroup differences can easily lead to statistical paradoxes in any data analysis application. Hidden variables, variable collisions, and class imbalances can easily create statistical paradoxes in many data processing applications. In this article, we’ll look at 3 of the most common types of statistical paradoxes found in data science. [Sources: 3, 9]

A prime example is the observed negative association between the severity of COVID-19 and cigarette smoking (see, for example, Griffith 2020, recently published in the journal Nature, suggesting that this may be a case of a collider displacement, also called the Burkson paradox. The most common example of the Burkson paradox is is the false observation of a negative correlation between two positive traits, namely that members of the population who have some positive traits tend to miss a second. [Sources: 3, 5]

The Berkson paradox broadly refers to the tendency of subpopulations, caused by some selection effect, such as a cut estimate, to give the impression of correlations that do not exist or even exist in the opposite direction in a larger population. I have seen more general definitions of the Burkson paradox (sometimes Berkson bias) equate it with selection effects in general, but I think it is mainly used in situations where a portion of a population / dataset is excluded that will decrease or reverse the observed correlation if included. [Sources: 11]

In fact, this erroneous observation is based on erroneous assumptions related to “cause” and “effect” and bias in data collection. He is often described in the field of medical statistics or biostatistics, such as Joseph Berkson’s original description of the problem. He is often described in the field of medical statistics or biostatistics, such as Joseph Berkson’s original description of the problem. It is a probability statistical phenomenon in which trends appear in different data sets, but disappear or reverse when combined. [Sources: 1, 4, 8]

Because, looking at something from only one side, we will continue to see the same thing even on completely opposite data. If the observer only examines the stamps on display, he will discover a false negative relationship between beauty and rarity as a result of selection bias (i.e., lack of beauty clearly indicates rarity in an exhibition but not in a general collection). [Sources: 1, 13]

Burkson’s paradox states that two independent events become negatively dependent if we consider only the outcomes in which at least one of them occurs. The Berkson paradox is one of the results that can be obtained by mentally making conditional comparisons. The Burkson paradox, also known as Burkson bias, collider bias, or Burkson error, is the result of conditional and statistical probabilities that are often illogical and therefore a real paradox. [Sources: 0, 10, 13]

The Berkson paradox was originally discovered in the context of epidemiological studies that trace the relationship between disease and exposure to potential risk factors. Berkson’s original illustration includes a retrospective study examining the risk factor for disease in a statistical sample of the inpatient hospital population. [Sources: 2, 13]


— Slimane Zouggari


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