Down Syndrome and Mistakes of Reasoning

We have debunked the mystery of covid infection among the vaccinated population in one of the earlier posts. Today we will see something similar but perhaps far easier to understand.

It is well-known that the risk of Down Syndrome increases with maternal age. For example, women above 40 risk about 11 times higher than those younger than 35 to have babies with Down Syndrome.

Yet, 52% of the mothers who give birth to children with Down Syndrome are 35 years or younger? Based on the data collected from 10 US states and the department of defence between 2006-2010, of the total number of 5600 live births, mothers of 2935 children were women younger than 35.

How did that happen? The simple answer is there were more mothers younger than 35! In the same population set, a whopping 3.7 million out of a total of 4.4 million were mothers below 35!

Small Fractions of Large Numbers

When the number of individuals in the less-risky category becomes very large, the absolute numbers of events also go up, despite its small relative chances to occur. For the vaccination case, the more the percentage of people get vaccinated, the more the absolute number of infected people from the vaccinated category if the society has a high prevalence of infection, which, in turn, is driven by the unvaccinated! But that is temporary – more people getting into the vaccination pool eventually steers the incidence rates down, slowly but steadily.

Selected Birth Defects Data from Population-Based Birth Defects Surveillance Programs in the United States, 2006 to 2010

Epidemiology Visualized: The Prosecutor’s Fallacy