What to think of massive food recalls?

There's a lot I can say about the ongoing salmonella outbreak investigation and the massive recall of 36 million pounds of turkey, much of which you'll find in Chapter 2 of Numbers Rule Your World.

One question you might want to ask is: how big a risk is it for you?

It should be clear that the level of risk is different for different people. For example, I don't eat ground turkey so my risk is the risk of CDC identifying the wrong culprit (a false positive), meaning that I might eat something else that would get me sick. If you do consume ground turkey, your risk is that of buying a pack of ground turkey that happens to be contaminated -- plus the risk of a false positive.

According to the official press release, about 10% of Americans consume ground turkey in any given week. This means about 1/3 of Americans consume ground turkey in any given 4 weeks (1 - (0.9)^4 assuming independence from week to week), 6/10 in any 8 weeks.

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Because fresh food is perishable, the risk depends on time. Assuming a temporary source of contamination, the batches of bad food would make its way through the food cycle in a fixed amount of time. (Permanent sources would be much easier to identify because you can just test samples from each machine to find the culprit.)

The following time-line chart from CDC is instructive:

Notice a few features of this chart:

• the vertical scale has some very tiny numbers, we are talking about a few cases per week across the entire country
• there is a "background" level of so-called sporadic infections (maybe about 2 a week) that would be visible whether or not there is a specific outbreak
• the horizontal axis plots the time of reported illness which means that the actual times of infection would be shifted to the left
• it was on July 27 when CDC issued a public health warning: note that this is to the far right of the curve. Could it be that the contaminated food has mostly made it through the distribution system? That the outbreak is well past its prime?
• Cargill recalled batches dated all the way back to Feb 20. Could it be true that such meat is somewhere still on sale? I hope not.

In the book, I discuss the perils of statistical modeling with so few cases, the chance of false positives, the difficulty of establishing a cause-effect relationship, the incentives of health agencies, the logic of food recalls, and so on.

 

Comments

[Ken]

Hopefully they are using some sort of control chart methodology to handle the randomness. Looking at it as a process also suggests that the process has come back under control, so there is little point in recalling food.

[John]

I would be careful in extrapolating the percentages of affected Americans, as it's very likely that some people never eat ground turkey, and others eat it all the time. That is, in any given week, the same X% (<10%) of Americans eat ground turkey and Y% never do.