Categories
current events death mathematics numbers politics probability science statistics trust

Why Stories Circulate about Covid-19 Deaths

Share

I’ve seen several posts on Facebook claiming that deaths of relatives or friends have been falsely attributed to covid-19 when in fact they were due to some other cause. These anecdotes represent a misunderstanding of the way statistics work and how data for statistics is collected. Of course, researchers want as accurate a count as possible for the number of deaths caused by Covid-19. But that kind of accuracy is harder than it sounds.

At first researchers were counting only deaths where the person who died had tested positive for Covid-19. They soon realized however, that they were under-counting the number of Covid-19 deaths. How did they realize that? They knew what the death rate in a particular place was prior to the pandemic. For example, if a city typically had 1,000 deaths in 30 days, and suddenly the number jumps to 3,000 but only 1,500 of those were due to patients who tested positive for Covid-19, then that left 500 deaths unaccounted for. So researchers decided to broaden the criteria for recording deaths as attributable to Covid-19. They decided to included deaths where symptoms were similar to those caused by Covid-19. They also included deaths even when the patient tested negative.

Why would someone who tested negative for covid-19 still be listed as a victim of it? Testing is not 100% accurate. Data on accuracy of the most widely used Covid-19 test is not publicly available, but some estimates range as high as 30% for false negatives, meaning that 3 out of 10 people who test negative for the disease actually have it. Even with a test that is 100% accurate under ideal conditions, real-world conditions can skew results. Many conditions can affect the amount of virus in a specimen collected by a swab. The most widely used test has close to a 100% accuracy for positive results, the the accuracy for negative results is uncertain and can vary depending on many factors. This is why some people who have died after testing negative for covid-19 are nevertheless listed as victims of covid-19. As long as they had symptoms consistent with the infection, they might very well have covid-19 listed on their death certificate. Of course, casting a broader net for data also means that there will be instances of people being listed as having died from covid-19 who actually died of other causes. Researchers make every effort to ensure this does not happen, but no procedure is foolproof. However, if the number of deaths identified as having been caused by Covid-19 matches the uptick in deaths overall, then it’s a pretty safe assumption that the data is pretty clean.

Because many people are suspicious of our government or the media or liberal elites—none of which are actually sufficiently monolithic to carry off a genuine conspiracy—and of expert authority in general, these types of stories gain currency on social media. Some may be true, but they usually do not contain sufficient detail to validate them. Even if they are true, they are generally offered by people who are not experts in determining cause of death.

So before you share one of these anecdotes about a suspicious Covid-19 death, consider not just whether it is true, but also whether it undermines the very institutions we have put in place to help us deal with infectious disease epidemics. While there are plenty of politicians ready to make hay out of crisis events, the experts and researchers who do the actual work genuinely care about producing good quality studies that advance our understanding of the virus and how it spreads. They are not out to get you.

Share
Categories
culture death logic probability rant

Implausible Murder

Share

I’ve become a fan of NCIS. I watch an episode almost every night. I like it. (I’m currently on season 7, so don’t worry about reading any spoilers for a recent episode.) Every once in a while, however, they come up with a plot that is so full of holes, it should never have seen airtime.

Case in point, this episode, called Code of Conduct. At the end the episode it is revealed that the murder was committed by the victim’s step-daughter, a short, teen-aged girl. She planned the murder and intended to frame her step-mother. She bought duct tape and a garden hose using her step-mother’s credit card and used those items in a somewhat clumsy attempt to make the murder look like a suicide. All of that is fine as far as it goes, but there are lots of details that do not make sense.

If you are going to take the trouble to deliberately murder someone, you certainly aren’t going to leave anything to chance. Along with your planning and preparation—making sure you have an alibi, throwing suspicion on someone else—you certainly will not neglect to use a method that will guarantee your victim ends up dead.

Now, don’t get me wrong. I have nothing but admiration for the writers of crime dramas tasked with coming up with ever more innovative, even bizarre, ways of divorcing souls from bodies. Nevertheless, I can’t help thinking that one crucial criterion for a planned murder is this: Is the plan certain to succeed? Does it depend too much on chance?

In this episode we are asked to believe that this girl was smart enough to make a plan to make her step-father’s death look like a suicide. She bought the necessary supplies. Yet the means she actually used to kill him was to bring him a thermos of liquid nitrogen, telling him it was coffee. She apparently gave no thought to the possibility that he would pour it into a cup before drinking it or that he would simply look at it and wonder why it didn’t look like coffee or that he might take a tentative sip (thinking it was hot) instead of taking a fatal gulp. It’s not that I can’t imagine a Marine gulping down coffee without looking at it. It’s that I can’t imagine a murderer relying on that behavior to commit the murder.

But that’s not all.

The murderer was discovered because she drove her dad’s car and left the seat adjusted for her small body. She brought him the fatal drink, waited until he was dead, then manhandled his six-foot corpse into the car parked in the driveway, attached the garden hose to the exhaust pipe and threaded it through the window and plugged the holes with duct tape. She did all this in the driveway where everything she did would be visible from the street. In fact, there were kids next door throwing TP into a tree and laughing the way only teen boys laugh, and they were the ones who discovered the Marine’s body. Again, it’s not that I can’t imagine a teen girl having the chutzpah to put a corpse in a car where any passerby could see it. It’s that I can’t imagine that being part of a well-designed plan.

Share
Categories
probability

Probability

Share

I heard a caller on a local radio station this evening say something in praise of her 17-year-old son. The host said, “You must have a good relationship with your son.”

“Well, I have three sons,” said the caller. “So I have a 33% chance of having a good relationship.”

Of course, this was a flippant remark not meant as a serious estimate of the probability of having a good relationship. But it got me to wondering about the issue.

Suppose relationships can be unequivocally classified as either good or bad, and that both are equally likely. Then the probability of a good relationship with one son is 50%. With three sons, the probability of at least one good relationship out of the three is 87.5%, much better than 33%. In fact, for the probability to be only 33% for at least one good relationship with three sons, the probability of a good relationship with one son would have to be about 12.5%.

Probability can be tricky.

Suppose you are on a jury in a murder trial. A key piece of evidence comes from an eyewitness who claims that he saw the accused getting into a yellow cab. In tests the witness reliably identifies yellow cabs as yellow 95% of the time. The other 5% he mistakes them for white. He also correctly identifies white cabs 80% of the time, but 20% of the time mistakes them for yellow. However, 90% of the city cabs are white, and 10% are yellow. What is the probability that the witness actually saw a yellow cab?

Suppose there are 1000 cabs in the city. 900 are white, and 100 are yellow. Of the 900 white cabs, the witness would correctly identify 720 as white and misidentify 180 as yellow. Likewise, he would correctly identify 95 of the yellow cabs as yellow and misidentify 5 as white. Therefore, he would identify 275 cabs as yellow of which 180 are really white. The probability that the cab was yellow is 95/275 = 35%. Despite the reliability of the witness, the actual number of cabs of each color makes the probability of a mistaken identification 65%. It could easily be enough for reasonable doubt.

Share