Biology › Nutrition, digestion and health evidence › Diet, energy and how to read a health claim
Diet, energy and how to read a health claim
Two thirds of the energy you spend today goes on staying alive while doing nothing in particular. Most of what you have read about which foods to eat comes from studies that could not, even in principle, prove what the headline says they proved. Both statements are examinable, and the second is the more useful.
Before this Carbohydrates, lipids and proteins as molecules · Correlation and causation, confounding variables and randomisation · Mean, spread and what a statistical test does
Before you start
This study followed half a million people, so the result is reliable — a sample that large settles the question. Sample size is the most quoted number in health reporting and the least informative. A large sample buys precision: the confidence interval narrows and random error shrinks towards nothing. It cannot buy accuracy. If the people who eat more vegetables also smoke less, exercise more and earn more, recruiting half a million of them measures that bundle half a million times over, very precisely indeed. A large study can give you a tight interval around an answer to a question nobody asked.
What you should be able to do
- Define basal metabolic rate and state what a person's BMR mostly depends on.
- Calculate an energy balance and explain why a small daily surplus does not extrapolate.
- State what a diet must supply beyond energy, and give a named consequence of each shortfall.
- Distinguish a cohort study, a case-control study and a randomised controlled trial by what each starts with.
- Name the confounder, the reverse causation or the measurement problem in a given dietary study.
- Convert a relative risk into an absolute risk, and say which one a reader needs.
Energy in, energy out, and why the arithmetic misleads
Energy balance is the difference between the chemical energy absorbed from food and the energy the body expends. Expenditure has three parts, and the proportions surprise people who have spent time in a gym.
Basal metabolic rate is the rate at which energy is expended by a person at complete rest, awake, at a comfortable temperature, twelve hours or more after a meal. It pays for the sodium-potassium pumps in every cell, protein synthesis, the beating heart, the kidneys and the brain, which takes something like a fifth of it. What sets it, more than anything else, is lean body mass: muscle, liver, kidney and brain are expensive and adipose tissue is cheap.
BMR is measured by indirect calorimetry: oxygen consumption is measured and converted to an energy expenditure, because oxidising a known mass of substrate consumes a known volume of oxygen.
energy balance = energy absorbed − energy expendedpositive means storage, negative means mobilisation, and neither is a moral category
A small surplus, and what it does not do
A person's intake exceeds their expenditure by 0.4 MJ per day, about the energy in one biscuit. Adipose tissue stores about 29 MJ per kilogram. Calculate the mass they would gain in a year if nothing else changed, and explain why the real gain is much smaller. The figures are idealised.
Over a year the surplus is 0.4 × 365 = 146 MJ. At 29 MJ per kilogram of adipose tissue that is 146 ÷ 29 = 5.0 kg, and on this arithmetic the gain continues at 5 kg every year indefinitely.
It does not, and the reason is in the phrase 'if nothing else changed'. A heavier body has more tissue to maintain and costs more to move, so both the basal rate and the cost of any activity rise as mass is gained, and the surplus closes itself. Mass rises until expenditure matches the new intake and then stops: for a surplus of this size, modelling puts the eventual gain at around 4 to 5 kg in total, about half of it in the first year.
The examinable point is that a linear extrapolation of a physiological quantity is nearly always wrong, because the system responds to the change. Any answer that multiplies a daily surplus by 3650 and reports 50 kg has stopped doing biology.
What a diet has to supply
Energy is necessary and nowhere near sufficient. A diet has to provide specific molecules the body cannot make, in quantities that range over six orders of magnitude.
| Component | What it is needed for | What a shortfall causes |
|---|---|---|
| Carbohydrate | The main respiratory substrate | Protein and lipid broken down for energy instead |
| Protein | Amino acids for every protein you build | Loss of muscle mass; poor growth and repair |
| Lipid | Membrane phospholipid, steroid precursors, fat-soluble vitamin carriage | Essential fatty acid deficiency |
| Fibre | Bulk for the large intestine to work on | Constipation; associated with higher bowel disease risk |
| Vitamins | Coenzymes and regulators, in milligram amounts | Named deficiency diseases: scurvy, rickets, beriberi |
| Minerals | Iron in haemoglobin, calcium in bone, iodine in thyroxine | Anaemia, poor bone mineralisation, goitre |
| Water | The solvent everything else happens in | Rapid and total failure |
Nine of the twenty amino acids are essential in an adult: the body has no pathway to make them, so they have to arrive in food, while the rest can be made by transamination. Two fatty acids, linoleic and alpha-linolenic, are essential for the same kind of reason — human enzymes cannot introduce a double bond beyond a certain point in the chain. 'Essential' means 'we cannot synthesise it', not 'it matters more'.
The UK reference intake for protein is about 0.75 g per kilogram of body mass per day, so a 70 kg adult needs around 52 g. Vitamin C is needed at a few tens of milligrams a day, and its absence causes scurvy because vitamin C is required to hydroxylate proline in collagen, and unhydroxylated collagen cannot form a stable triple helix.
Malnutrition means any imbalance between what a diet supplies and what the body needs, and that includes excess. An adult who is obese and simultaneously deficient in iron and vitamin D is malnourished twice over, and this pattern is now common in high-income countries.
Body mass index, and what it does not know
A man has a mass of 82 kg and a height of 1.78 m. Calculate his body mass index, state which category it falls in, and give two reasons the figure might mislead a clinician.
BMI is mass divided by the square of height. Height squared is 1.78² = 3.1684 m², so BMI = 82 ÷ 3.1684 = 25.9 kg m⁻², which falls in the 25.0 to 29.9 band conventionally labelled overweight.
First reason: BMI cannot distinguish adipose tissue from muscle. A trained rower and a sedentary man of the same height and mass have the same BMI and very different bodies.
Second reason: it says nothing about where the tissue is. Adipose tissue around the abdominal organs is associated with much higher cardiovascular and metabolic risk than the same mass under the skin of the hips, and BMI is blind to the difference. Waist measurement, or the ratio of waist to height, captures some of what BMI misses.
The designs, and what each one can see
Almost every claim about food and health comes from one of four kinds of study, and knowing which one produced a finding tells you more than knowing the p value.
- Cohort study
- A group of people free of the disease is recruited, their exposure is recorded, and they are followed forward in time to see who develops it. Gives incidence and relative risk directly, and gets the time order right by construction.
- Case-control study
- People who already have the disease are compared with matched people who do not, and both groups are asked about past exposure. Fast and efficient for rare diseases; yields an odds ratio, not a risk.
- Randomised controlled trial
- Participants are allocated by chance, so the groups are balanced on every variable, including the ones nobody thought to measure.
- Relative risk
- The risk in the exposed group divided by the risk in the unexposed group; 1 means no association.
Randomisation is the only device that deals with confounders you have not thought of, which is why a trial outranks the rest. Dietary trials are nonetheless hard, and the difficulties are examinable in their own right: participants cannot usually be blinded to what they are eating, adherence drifts over years so the two groups' diets converge, cardiovascular outcomes take decades to accumulate, and nobody can assign a person to a lifetime of anything.
So most of what is known about diet comes from cohort studies, and the good ones are formidable. The British Doctors Study recruited over 34,000 male doctors in 1951 and followed them for fifty years, which is how smoking and lung cancer was settled without a single randomised trial. Confounding could not be ruled out by design; the findings were strong and consistent enough that the confounding explanation stopped being credible.
| Design | Starts with | Gives you | Its weakness |
|---|---|---|---|
| Randomised trial | Volunteers, allocated by chance | A causal answer for the people studied | Short, expensive, hard to blind for diet |
| Cohort | People without the disease | Incidence, relative risk, correct time order | Confounding; needs huge numbers and years |
| Case-control | People with the disease | An odds ratio, quickly, for rare diseases | Recall bias; choosing fair controls |
| Cross-sectional | A population at one moment | Prevalence and associations | Cannot tell which came first |
Confounding, recall and reverse causation
A confounding variable is one that is associated with the exposure and independently affects the outcome. In nutrition they are everywhere, because eating habits travel in packs with everything else about a life: people who eat more wholegrain also smoke less, exercise more, are richer and go to the doctor sooner. That bundle is the healthy-user effect, and it is large enough to manufacture a respectable-looking association out of nothing.
Statistical adjustment can subtract the effect of a confounder, but only one that was measured, and only as accurately as it was measured. Adjusting for 'smoking: yes or no' leaves behind all the difference between two a day and forty. What is left over is residual confounding, and it is the standard explanation for a relative risk close to 1 that appears and disappears between studies.
The measurement problem is worse than most readers realise. Dietary intake in large cohorts is usually recorded with a food frequency questionnaire asking how often someone ate around a hundred foods over the past year. Against objective methods, adults under-report their energy intake by something like a fifth to a third, and the size of the under-reporting is related to body mass — so the error is not noise that averages out, it is bias pointing one way.
Reverse causation is the third standard alternative. Undiagnosed disease changes appetite and diet years before a diagnosis, so a study can find that people who ate less of something went on to be diagnosed with the illness that was already quietly changing what they ate. Careful cohorts discard the first few years of follow-up and re-run the analysis; if the association survives, reverse causation is a weaker explanation.
TRY IT — Naming the alternative explanation
A cohort study of 90,000 adults reports that people in the highest quintile of coffee consumption had a 15% lower risk of death over 12 years than those in the lowest, after adjustment for age, sex and smoking status. A newspaper reports that coffee makes you live longer. Evaluate that conclusion.
Give three specific reasons for caution and say, for each, what would reduce it.
Check your answer
The study is observational: nobody assigned the coffee, so the groups differ in many ways at once and the comparison is between kinds of people, not between treatments.
First, confounding. Smoking was adjusted for as a yes-or-no variable, which leaves the whole difference between light and heavy smokers untouched, and heavy smokers drink more coffee. Adjusting for cigarettes per day, and repeating the analysis in people who have never smoked, would test it.
Second, reverse causation. People already unwell often give up coffee, loading the lowest-consumption group with people who were ill at the start. Excluding deaths in the first four years would test it.
Third, the size of the effect. A relative risk of 0.85 from observational data is small enough to be produced by residual confounding alone.
What would strengthen the claim: a dose-response across the quintiles, and the same result in populations where coffee drinking is not associated with smoking.
Relative risk, absolute risk, and the missing denominator
A headline that says a food raises your risk by 18% is quoting a relative risk, and a relative risk on its own is unreadable. Eighteen per cent of what?
Turning a relative risk into people
About 6 in every 100 people in the UK develop bowel cancer at some point in their lives. Eating 50 g of processed meat a day is associated with an 18% higher relative risk. Calculate the absolute risk for someone eating that much, the increase in absolute terms, and the number of people who would have to eat that way for one extra case to arise.
The baseline absolute risk is 6.0%. Raising it by 18% gives 6.0 × 1.18 = 7.08%, so about 7 people in every 100 rather than 6.
The increase in absolute risk is 7.08 − 6.00 = 1.08 percentage points, or about 11 extra cases per 1000 people.
The number who would have to be exposed for one extra case is 1 ÷ 0.0108 = 93 people. That is the figure a reader deciding what to have for breakfast actually needs.
Both numbers are honest and they are not interchangeable. Relative risk is the right measure for asking whether an exposure does anything; absolute risk is the right measure for asking whether it matters to you.
The same confusion runs through the way carcinogens are classified. When processed meat was placed in the highest group in 2015, alongside tobacco smoking, the classification was a statement about the strength of the evidence that it causes cancer in humans, not about the size of the risk. Both bodies of evidence are considered sufficient; the risks differ by more than a factor of ten. A scheme that sorts by confidence will always be misread as sorting by danger.
One more distinction, because papers use both words. A relative risk can only be calculated where the risk in each group is known, so it comes from cohorts and trials. A case-control study cannot know the risk, because the investigator chose how many cases and controls to recruit, so it reports an odds ratio. For a rare disease the two are close; for a common one the odds ratio sits further from 1, so quoting it as a risk overstates the finding.
Why a scare and a real finding look identical in print
Both arrive as the same sentence: eating X is linked to a Y% higher risk of Z. Everything that separates them sits below the headline, and most of it can be established in about two minutes.
| Ask | Reassuring answer | Warning sign |
|---|---|---|
| What design? | Randomised trial, or several cohorts agreeing | One cross-sectional survey |
| How big is the relative risk? | Well above 2, with a dose-response | 1.1 to 1.3, adjusted heavily |
| What is the absolute risk? | Stated, with a denominator | Not mentioned anywhere |
| How was the exposure measured? | Weighed, or biochemically | Recalled over the past year |
| Is there a mechanism? | Tested in cells or animals | Proposed afterwards to fit |
| Is it new? | Replicated in other populations | First report, single group |
| Who is speaking? | The paper itself | A press release, or a supplement company |
That last row carries more weight than it looks. Work published in 2014 compared health stories in the UK press with the university press releases they came from, and found that most of the exaggeration — turning correlation into causation, turning animal work into human advice — was already present in the press release. The journalists were largely reproducing what scientists' own institutions had sent them.
None of this is a reason to disbelieve nutritional science, and cynicism is not scepticism. Some dietary findings are as secure as anything in medicine: that vitamin C prevents scurvy, that folate before conception reduces neural tube defects, that iodine deficiency causes goitre. Each has a mechanism, a dose-response, an effect too large for confounding to explain, and evidence from more than one kind of study. Findings with none of those are not lies; they are hypotheses reported as conclusions.
The exam form of all this is short. Name the design, name the specific alternative explanation you are worried about, say what would settle it, and put a denominator under any risk you are given. Writing 'correlation does not imply causation' and stopping is worth almost nothing, because it is true of every observational study ever conducted and so says nothing about this one.
In the exam
- BMR has a definition with conditions in it: at rest, awake, warm, and well after a meal. An answer that says 'the energy you use doing nothing' will not score.
- When a question gives a relative risk, calculate the absolute risk if you are given the baseline, and say explicitly which one you are quoting. Marks are attached to that distinction more often than to the arithmetic.
- Name the confounder. 'There could be other factors' scores nothing; 'people who ate more oily fish were also wealthier, and income affects health independently' scores.
- For a study design question, the discriminator is what the investigators started with: healthy people (cohort), people with the disease (case-control), or volunteers allocated by chance (trial).
- Energy calculations: 1 kcal is 4.184 kJ, and a food label's 'calories' are kilocalories. Check the units before the arithmetic, because both appear on the same packet.
Check yourself
A case-control study of 600 people with type 2 diabetes and 600 matched controls finds that the cases drank sugar-sweetened drinks more often, with an odds ratio of 1.7. Explain what this study can and cannot establish, and describe the study you would want next.
Answer
It establishes an association between recalled consumption of sugar-sweetened drinks and having a diagnosis of type 2 diabetes, measured as an odds ratio of 1.7. Because the investigators chose how many cases and controls to recruit, this is not a risk and should not be reported as a 70% higher risk.
It cannot establish the time order. Both groups were asked after diagnosis, so the drinking may have preceded the disease or followed it, and people who have been told they have diabetes may also recall their past differently from people who have not — recall bias operates in the direction that inflates the finding.
It cannot rule out confounding. Sugary drink consumption is associated with total energy intake, body mass, income and physical activity, each of which affects diabetes risk independently, and matching controls on age and sex does nothing about any of them.
What comes next is a prospective cohort: recruit people without diabetes, measure consumption at the start and repeatedly afterwards, follow them for a decade or more, and record who is diagnosed. That fixes the time order, gives a genuine relative risk and allows a dose-response to be looked for. A randomised trial of an intermediate outcome, such as insulin sensitivity over a year, would test the mechanism directly even though it could not run long enough to count cases.
Questions
Question 15 marks
A cross-sectional survey of 40 000 adults reports that those taking a vitamin supplement have a 12 per cent lower rate of heart disease than those who do not. A newspaper concludes that the supplement protects the heart. Evaluate that conclusion.
Mark scheme
- B1 in support: the sample is large, so random error is small and the association is unlikely to have arisen by chance alone
- B1 in support: an association of this kind is a reasonable hypothesis to generate, and it can be tested directly by a design that settles the question
- B1 against: the design is cross-sectional, measuring a population at one moment, so it cannot say which came first — people already diagnosed may have started or stopped taking supplements because of the diagnosis
- B1 against: nobody allocated the supplement, so the two groups differ in many ways at once; people who take supplements tend to smoke less, exercise more and earn more, and a relative risk of 0.88 is close enough to 1 to be produced by residual confounding alone
- B1 judgement: the conclusion is not supported by this study, which reports an association as though it were a cause; what would settle it is a randomised controlled trial of the supplement against a placebo, since randomisation balances the confounders nobody measured
Question 24 marks
In a population, 4 people in every 100 develop a particular cancer during their lifetime. A cohort study reports a relative risk of 1.25 for that cancer in people with a high intake of one food. Calculate the absolute lifetime risk for those people, calculate the increase in absolute risk in percentage points, and calculate how many people would have to eat that way for one extra case to arise.
Mark scheme
- M1 the absolute risk in the exposed group is the baseline absolute risk multiplied by the relative risk
- A1 4.0 × 1.25 = 5.0 per cent, so about 5 people in every 100 rather than 4
- A1 the increase in absolute risk is 5.0 − 4.0 = 1.0 percentage point
- M1 the number needed for one extra case is 1 ÷ 0.010 = 100 people
Question 34 marks
Compare a cohort study with a case-control study, referring to who is recruited, what measure each produces, and the main weakness of each.
Mark scheme
- B1 a cohort recruits people who are free of the disease and follows them forward in time, whereas a case-control starts with people who already have the disease and compares them with matched people who do not
- B1 a cohort records exposure before the disease appears, so the time order is right by construction, whereas a case-control asks both groups about past exposure and cannot establish which came first
- B1 a cohort gives incidence and a relative risk, whereas a case-control gives an odds ratio, because the investigator chose how many cases and controls to recruit and so cannot know the risk in either group
- B1 a cohort needs very large numbers and many years and is still open to confounding, whereas a case-control is quick and efficient for a rare disease but is open to recall bias and to unfair choice of controls
Question 44 marks
A cohort study finds that adults who reported eating the least fruit were later diagnosed with cancer more often than those who reported eating the most. Suggest two explanations for this association other than a protective effect of fruit, and suggest for each what the investigators could do to test it.
Mark scheme
- B1 confounding: people who eat more fruit also tend to smoke less, exercise more and be wealthier, and each of those affects cancer risk independently
- B1 that could be tested by adjusting for cigarettes smoked per day rather than for smoking as a yes-or-no variable, and by repeating the analysis in people who have never smoked
- B1 reverse causation: undiagnosed disease changes appetite and diet years before a diagnosis, so people who were already ill may have eaten less fruit because of the illness rather than the other way round
- B1 that could be tested by discarding the first few years of follow-up and re-running the analysis; if the association survives, reverse causation is a weaker explanation
Question 52 marks
State the conditions under which basal metabolic rate is measured, and state what a person's basal metabolic rate mostly depends on.
Mark scheme
- B1 at complete rest, awake, at a comfortable temperature and twelve hours or more after a meal
- B1 lean body mass: muscle, liver, kidney and brain are metabolically expensive tissues while adipose tissue is cheap
Worth remembering
- Basal metabolism is roughly two thirds of a day's energy expenditure, and lean mass is what mostly sets it.
- A daily surplus does not extrapolate, because expenditure rises as mass rises until the two match again.
- Cohort starts with healthy people and looks forward; case-control starts with the disease and looks back; only randomisation balances the confounders nobody measured.
- A relative risk without an absolute risk is unreadable, and an odds ratio is not a risk at all.
- Sample size fixes precision, not bias. A bigger study of a badly measured exposure is a more precise wrong answer.