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Relative Risk vs Absolute Risk in Nutrition News

Quick answer: Relative risk tells you how much a risk changed compared with where it started. Absolute risk tells you how many people out of 100 or 1,000 were actually affected. "Lowers cancer risk 8%" is relative. If the starting risk is small, an 8% cut is a very small number of people. Before you change anything because of a headline, ask: 8% of what?

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The two numbers

Say a risk goes from 2 in 100 to 1 in 100.

Both are true. The first makes a better headline. The second tells you what it means for you.

Papers often report a hazard ratio (HR). An HR of 0.92 means the event happened at about 92% of the rate in the comparison group, which a headline turns into "8% lower risk". An HR of 1.06 becomes "6% higher risk".

A worked example: the multivitamin trial

The Physicians' Health Study II gave 14,641 male physicians aged 50 and up either a daily multivitamin or a placebo, for a median of 11.2 years. Total cancer came in with a hazard ratio of 0.92 (Gaziano et al., 2012). That's a real, randomized result, and it's where "multivitamins cut cancer risk 8%" comes from.

Now the arithmetic. The numbers below are made up to show the method, not taken from the trial:

  1. Suppose 100 men in every 1,000 got cancer over the study in the placebo group.
  2. An 8% relative cut takes that to about 92 in 1,000.
  3. That's 8 fewer cases per 1,000 men, or 0.8 percentage points.
  4. Flip it: about 125 men take the pill for the whole period for one of them to avoid a cancer (1,000 ÷ 8).

If the starting risk were lower, say 20 in 1,000, the same 8% would be under 2 cases per 1,000. Same headline, very different meaning. That's why you need the starting rate, which is in the paper, not the press release.

Fiber: when relative numbers stack up

Fiber research is full of relative numbers, mostly from observational studies:

Two things to notice. First, these are associations, so people who eat more fiber may differ in other ways. Second, the "per 10 g" phrasing is a slope, and the absolute effect depends on your own starting risk, which depends on your age, family history and everything else.

It's still a consistent signal across many outcomes, which is a good reason not to let fiber disappear on a low-carb diet. It just isn't a promise that 10 g of fiber removes 10% of anything for you personally.

The same trick with weight loss

Relative framing isn't only for disease. In DIETFITS, the healthy low-carb group lost about 6.0 kg in a year and the healthy low-fat group about 5.3 kg, a difference that wasn't significant (Gardner et al., 2018).

Do the division and low-carb lost about 13% more. That sounds like a win. In absolute terms it's about 0.7 kg, or a pound and a half, over twelve months. That's the size of an ordinary swing in water weight.

So what you do is ask for the absolute difference every time, whether the claim flatters your diet or not.

How to convert a headline

  1. Find the relative number. "Cuts risk 8%", "HR 0.92", "doubles the risk".
  2. Find the starting rate. How many people per 100 or 1,000 had the outcome in the comparison group? It's in the paper's results or tables.
  3. Multiply. Starting rate × relative change = absolute change.
  4. Check who was studied. Older men? Women 30–60? People with diabetes?
  5. Check the design. Randomized trial or observational? Observational relative risks can't show cause on their own.

A "doubled" risk of something rare can still be rare. A "small" relative drop in something common can matter a lot.

What the research says

The papers above show both kinds of number at work:

KetoDick's take

He hasn't made a video about relative risk as such, but the habit this article asks for is his. Back-of-envelope arithmetic is a habit of his; he's worked out that a 100 lb person at 10% body fat still carries about 35,000 kcal of stored fat, to show where the energy comes from in the weight-loss phase (video NUJNFG6lLWw).

He's also said he'll find people actual studies when asked, so they can decide for themselves whether it was too few people or too old a study (video xyEZL0HuejI). And he's told viewers to use Google Scholar or add "PubMed" to a search, because a study has to state its protocol (video 1JbK1_ClDmY). Those are exactly the places to find the starting rates a headline leaves out.

Key takeaways