Teaching Math

Wobbly Math: Department of Cost-Effectiveness

Who pays and who benefits from a national sugar-sweetened beverage tax? A new paper in AJPH asked this question and demands our attention. Unfortunately, instead of offering objective answers, we find only wobbly math used to make a point about the hypothetical cost-effectiveness of an SSB tax.

A Complex Model to Make a Simple Point

Park Wilde and colleagues constructed a complex model to address questions about the cost-effectiveness of a national tax on SSBs in the U.S. They looked at this question from the perspective of nine distinct groups of stakeholders. What will the benefits be? What will the cost be to achieve the benefits?

But there’s just one problem. A cost effectiveness analysis doesn’t mean much when you have nothing but assumptions about effectiveness. It means even less when assumptions are not explicit. A model is only as strong as the assumptions that support it. This is a core principle defined by a landmark paper on good research practices for modeling studies in health economics:

A good study based on a model makes all of these assumptions explicit and transparent and states its conclusions conditionally upon them.

However, in the present paper, you won’t even find the word assumption – let alone an explicit list of the assumptions that drive this model. Needless to say, the conclusions in this paper are hardly conditional. “From health care and societal perspectives, the SSB tax was highly cost-saving,” say the authors.

The Critical Assumption: A Population Health Benefit

Deep within this paper, you can find some critical assumptions. The authors “did not model specific replacement scenarios” because they expected the effects to be small. In other words, they assumed that it would not matter what people drank instead of sugar-sweetened beverages.

The other big, implicit assumption is related. The authors take it as a given that less consumption of SSBs will cause reductions in heart disease, stroke, and diabetes. Again, they don’t call this an assumption. They treat it as a fact.

SSBs Alone Drive Cardiometabolic Disease?

Certainly, this is a common assumption. Thinking that excessive consumption of SSBs is driving some portion of cardiometabolic disease is a hypothesis that is reasonable.

But it’s equally reasonable to think that individual dietary macronutrients – in isolation – are not driving the prevalence of obesity and cardiometabolic disease. Kevin Hall and others have made this point in a way that we find compelling.

At the end of the day, one has to make assumptions to solve problems. Nothing wrong with that. The problem comes when assumptions are submerged. When that happens, the line gets blurred between speculation, scientific theories, and well-established facts.

What Do We Really Know?

Unless we distinguish facts from speculation, we cannot hope to solve such a complex problem as obesity.

What this model is really telling us is that if an SSB tax can reduce the prevalence of heart disease, stroke, and diabetes, then it would be cost-effective. “If” is a tiny word. But it makes a big difference.

Click here for the study in AJPH and here for more on good modeling practices.

Teaching Math, photograph © Don Harder / flickr

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January 4, 2019

One Response to “Wobbly Math: Department of Cost-Effectiveness”

  1. January 04, 2019 at 10:04 am, Allen Browne said: