US CDC COVID-19 message
Posted in COVID19publichealthresearch Paradoxes

US COVID-19 pandemic: Cases vs deaths paradox

The US CDC data reveals an interesting age-specific case versus deaths paradox.

Look at the following graph. I created the graph using data available at the US CDC website.

US COVID-19 cases versus deaths paradox
(Data source: US CDC)
  • Of all the COVID-19 cases, 85.6 percent occurred among those aged equal and below 64 years.
  • In contrast, of all the COVID-19 deaths, 80.6 percent occurred among those aged 65 and above.

Now, my message is clear and straightforward based on this graph: Minimize the contact between these two age groups.

How can we minimize the contacts between these two age groups?

My suggestions are;

  • Provide financial and other incentives to those aged 65 and above to stay at home.
  • Mobilize all regional and local community organizations and all faith groups to create supportive environments to separate the two groups.
Simpson's paradox
Posted in Paradoxes

Simpson’s paradox: A trap in data interpretation

In 1934, two researchers – Morris Cohen and Ernst Nagel – tabulated death rates due to pulmonary tuberculosis in two cities – New York and Richmond. They found higher death rates in Richmond City than in New York City; 226 per 100,000 population versus 187 per 100,000 population.

However, they disaggregated the rates by ethnic groups; Caucasians versus African Americans. Interestingly, their previous finding was reversed. It was the complete opposite: for each ethnic group, the death rates became higher in New York than in Richmond (Look at the table below).

Death rates due to pulmonary tuberculosis

EthnicityNew YorkRichmond
African American560/100,000332/100,000
The detailed data set is available through this source:

This conundrum is known as “Simpson’s paradox”.

How did this happen?

When we disaggregate data into two different sub-groups, the real situation appears; in extreme instances, it becomes reverse.

Those situations are identified as “Simpson’s paradox” because Edward Simpson explained the phenomenon using hypothetical data as far back as 1951. However, prior to him, Yule demonstrated the bias again using hypothetical data set much earlier: in 1903.

According to statisticians, Simpson’s paradox, by definition, is not a true paradox; rather, it is a statistical illusion and could also be called aggregate bias. It is also a manifestation of confounding effects.

Its practical implications could well be devastating, particularly when we make decisions based on aggregate data.

In the above example, if the decision-makers were not aware of this, they would have allocated resources erroneously to Richmond instead of New York City to reduce the death rate due to pulmonary tuberculosis.

This bias seems to have been occurring much commoner than earlier thought.

Here are few more examples;

Hospital admissions of men with psychiatric illnesses over the years; gone up or down?

I created the following table using data that appeared in a short paper in the British Medical Journal.

According to the first table, the admission rates of men with psychiatric illnesses out of all admissions with such illnesses have declined slightly from 1970 to 1975.

Admission rate46.4% (343/739)46.2% (238/515)

Now, look at the following disaggregated data by age. The pattern reversed; the male admission rates have gone up.

Those aged <=6559.4% (255/429)60.5% (156/258)
Those >6528.4% (88/310)31.9% (82/257)
Overall46.4% (343/739)46.2% (238/515)

Another example from a hospital setting

The data that appears below is from a paper published based on a study about the use of prophylactic antibiotics in eight hospitals in the Netherlands. According to the first table, it seems better prophylactic use of antibiotics because the urinary tract infection rate is lower when using it rather than not using it.

Prophylactic antibioticsNo prophylactic antibiotics
Urinary tract infection rate (UTI)3.3% (42/1279)4.6% (104/2240)

Since the researchers were skeptical about the finding, they dis-aggregated data by grouping hospitals based on UTI infection rates; low-incident and high-incident hospitals using 2.5% as the artificial cut-off rate. Now, the first observation was reversed; the rates were higher when prophylactic antibiotics were used.

UTI ratesProphylactic antibioticsNo prophylactic antibiotics
Low incident (<=2.5%) hospitals1.8% (20/1113)0.7% (5/720)
High-incidence (>2.5%) hospitals 13.2% (22/166)6.5% (99/1520)
Overall UTI rate3.3% (42/1279)4.6% (104/2240)

The above study appeared on the Royal Statistical Society website when it discusses Simpson’s paradox.

Posted in Paradoxes

Prevention paradox in alcohol-related problems

Researchers have examined the applicability of the prevention paradox in alcohol-related problems: One year after Rose’s paper, in 1986, Norman Kreitman did jus that. He published his findings in the British Journal of Addiction.

As Rose did, Kreitman also used others’ data in his endeavor.

Kreitman’s paper

I chose two studies from his paper and created graphs for each to highlight the critical points.

1986 British study

Kreitman discussed a British study conducted by Wilson involving 2000 adults. The following graph summarises their key findings.

Alcohol consumption and problem impact paradox: based on data available in the 1986 Kreitman’s paper (created by Prasantha De Silva)

In the above graph, the dark brown area represents alcohol-related problems relevant to alcohol consumption limits; at the left corner, you find that among those who consumed alcohol below the limit three percent reported problems and those who consumed above the limit 31 percent reported such problems.

On the other hand, the light brown area refers to the proportions of alcohol-related problems out of all problems; as you can see that those who consumed below the limit reported 66 percent of all such problems. However, those who consumed above the limit reported less than half – 43 percent – of all problems.

Three Areas study

Kreitman uses data from another study to highlight the prevention paradox. In this study, the researchers used three consumption levels – a more detailed assessment than the previous one.

alcohol consumption and problem impact paradox: based on data available in Kreitman’s paper (created by Prasantha De Silva)

As you can see, this study too follows a similar pattern; although only 8 percent of light drinkers reported alcohol-related problems, they contribute 54 percent of all alcohol-related problems. It reverses among heavy drinkers; 20 percent of heavy drinkers reported alcohol-related problems although they contribute to only 12 percent of all alcohol-related problems.

2007 Finnish study

The previous studies I mentioned suffered quite a formidable limitation; all were based on self-reports. Kari Poikilonein addressed this limitation to a certain extent by looking at alcohol-related hospital admissions. Based on their data available in their published paper, I created the following graph which resembled the alcohol-related hospital admissions.

In 2007, Kari Poikilonein and her study team examined the prevention paradox in terms of alcohol-related hospital admissions and deaths. I created the following graph based on their data published in their paper in the Addiction journal in 2007.

Prevention paradox in alcohol-related hospital admissions

In the following graph, the brown and blue colors represent the proportion of women and men hospitalized out of all alcohol-related ones due to alcohol-related problems respectively.

alcohol intake and hospitalization paradox:
based on data available in the Kari Poikilonein et al. paper appeared in the Addiction journal
(created by Prasantha De Silva)

As you can see, of those who were hospitalized as a result of alcohol-related problems, if you look at the left end of the graph, an overwhelming majority – 71 percent of men’s and 64 percent of women – claimed to have light drinking habits as defined by the study, constituted the alcohol-related hospital admissions. The researchers further found a sub-group among light drinkers: those who drank five or more standard drinks in one session – they were called “heavy episodic drinkers”.

In contrast, if you shift your eyes from the left end to the right end of the above graph, you will find that only 34 percent of men and 29 percent of women claimed to have heavy drinking habits: less than half of light drinkers.

Preventive paradox in alcohol-related deaths

They further looked at alcohol-related deaths and found out a similar pattern; the majority who died reported to have light drinking habits earlier – the researchers linked previous survey data to hospital records.

Prevention paradox in alcohol-related deaths The graph was created by Prasantha De Silva based on data available in the Kari Poikilonein et al. paper appeared in the Addiction journal

Preventive paradox in 23 European countries

Much later, another group of researchers analyzed 38,370 alcohol-consuming 16 -year old student data from 23 European countries. Again, they also found similar results with regard to mean levels of alcohol consumption and heavy episodic drinking measure although the countries varied with drinking levels – a very robust, impressive finding. However, they emphasized a limitation of the concept: a minority – frequent heavy episodic drinkers – three or more heavy episodic drinkers a month – were the majority.

In other words, the existence of the prevention paradox in alcohol-related problems depends on the indicator used to measure consumption.

Posted in Paradoxes

What is Prevention Paradox?

Geoffrey Rose, an epidemiologist from the London School of Hygiene and Tropical Medicine coined the term “prevention paradox”.

In 1985 he popularized the concept through his paper under the title of “sick individuals and sick populations” and published in the International Journal of Epidemiology. In 2001, The World Health Organization’s bulletin reproduced this paper under its classic papers series.

This paper created an interesting and sustained debate about prevention strategies in the public health sector. To date, the paper has been cited by 4166 articles in the world according to Google search.

What is the prevention paradox?

To discuss the prevention paradox, I am using two examples that appeared in the Rose’s paper.

Example 1: More heart attacks from those with lower risk

Look at the following graph that I created using data published in Rose’s paper. He had obtained this data from the UK Heart Disease Prevention Project.

“Prevention paradox in heart health”
Created by Prasantha De Silva using data published in the
Rose paper, p.37.

The brown color represents the proportions of those who suffered a heart attack (myocardial infarction) out of all attacks reported during a 5-year period at 3 different increasing risk severity situations: the presence of risk factors, the presence of ischemia, and the presence of both risk factors and ischemia.

The blue color (including its shadow under the brown color) refers to the distribution of increasing risk severity. 7%, 11%, and 22%. For example,7 percent denotes that only 7 percent of those with risk factors suffered an attack. This percentage increases with ischemia to 11 percent. When both factors exist together, the risk reaches its highest: 22 percent.

What do you notice in the graph?

Contrary to our normal expectations, the majority of events occurred not among those with the highest risk, but among those with the lowest risk; This is the paradox.

Rose called it prevention paradox because, although we can certainly prevent attacks by screening the highest risk group and treating them, we can yield maximum benefit only by preventing events among those with the lowest risk.

Example 2: Down syndrome and its risk severity

Now, look at this graph, again, created by myself using data published in the same paper.

“Prevention paradox in Downs syndrome”: created by Prasantha De Silva using data published in the Rose paper, p. 37

As in the case of the previous graph, the brown color represents the proportions of cases of Down syndrome out of all reported and the blue color denotes the risk percentages of having such a baby relevant to maternal age. We all know that the risk rises with maternal age; the risk is lowest among those younger than 34 years and highest among those aged 45 and above. However, more than half the cases originate not among the highest risk but the lowest risk because of the relatively higher number of young women.

In another post, I discussed how another researcher demonstrated the existence of prevention paradox in alcohol-related problems. You can read that through this link: