In un lungo articolo su towardsdatascience.com si illustra il processo statistico che consente di interpretare correttamente i risultati di un esame diagnostico e di come questo abbia delle implicazioni nell’attività di contenimento delle epidemie, come accade in queste settimane per il COVID-19. Fondamentale è l’applicazione della regola di Bayes in relazione all’affidabilità del test, a sua volta determinata da specificità e sensibilità.

A diagnostic test is performed by collecting samples from your body (eg. mucus in the back of the nose) and looking for presence of the virus in those samples. It seems simple enough, and people have a lot of faith in science. This may lead people into making this first mistake.

Incorrect interpretation: a positive result means a patient has novel coronavirus, while a negative result means that a patient does not.

This is not true, because the test is not always reliable. There are many reasons why a test may give a misleading result:

• A patient in the very early stages of an infection may not excrete a detectable amount of virus.
• The virus itself may only exist deeper inside the body, hence being inaccessible by a swab test.
• There may have been accidental contamination of the sample.

In general, the people who make the testing kits will specify the reliability of the test.

Suppose that a company now markets their test as “90% accurate”.

Ma cosa significa che un test è accurato al 90%? È assai probabile (no pun intended) rispondere in maniera errata a questa domanda. E purtroppo si tratta di un errore comune anche tra i medici, come spiegato in questo articolo di BBC News dedicato al quesito che tra il 2006 e 2007 lo psicologo tedesco Gerd Gigerenzer propose a più di mille praticanti ginecologi:

A 50-year-old woman, no symptoms, participates in routine mammography screening. She tests positive, is alarmed, and wants to know from you whether she has breast cancer for certain or what the chances are. Apart from the screening results, you know nothing else about this woman. How many women who test positive actually have breast cancer? What is the best answer?

• nine in 10
• eight in 10
• one in 10
• one in 100

Gigerenzer then supplied the assembled doctors with some data about Western women of this age to help them answer his question. ( …)

1. The probability that a woman has breast cancer is 1% (“prevalence”)
2. If a woman has breast cancer, the probability that she tests positive is 90% (“sensitivity”)
3. If a woman does not have breast cancer, the probability that she nevertheless tests positive is 9% (“false alarm rate”)

In one session, almost half the group of 160 gynaecologists responded that the woman’s chance of having cancer was nine in 10. Only 21% said that the figure was one in 10 – which is the correct answer. That’s a worse result than if the doctors had been answering at random.

 

Foto di mattbuck da Wikimedia Commons.