Food and Health – Statistics and Lies

Is highly processed food bad for us?
Can we believe the statistics that are presented to us?

Shopping: a large range of ready-made meals

We live in an era of “dietism”. There are many books and articles on how various aspects of our food are responsible for all sorts of illnesses and threats to our longevity. I have pointed out previously that the past fifty years, since 1970, have seen a major and apparently spontaneous (that is "natural") decline in deaths from coronary heart disease, the end of the greatest epidemic of the 20th century. However this occurred at a time during which we have seen the emergence of “fast food”, that many people regard as “junk food”, and also our supermarkets have become stocked with  food that has been prepared in factories. The food is imaginative and it tastes good. But is it bad for us? Despite such allegations, how is it that the proportion of our population living beyond the 90th birthday continues to increase? Are we not in reality healthier than ever?

Statin trial

Shepherd J, Cobbe SM, Ford I, Isles CG, Lorimer AR, Macfarlane PW,

McKillop JH, Packard CJ, for the West of Scotland Coronary Prevention

Study Group. Prevention of coronary heart disease with pravastatin in
men with hypercholesterolemia. N Engl J Med. 1995;333:1301–1307.

We are also in an era of distorted statistics. I have illustrated previously that we are told from the WOSCOPS study (reference above) that pravastatin reduces the risk of death at eight years by 25%, but the reality is that the reduction was just 1%. The absolute reduction in death rates was from 4% to 3%. The 25-fold amplification of the result is manipulative, quoting proportionate reduction in death rate in place of absolute reduction. This means presenting the numerator without reference to the denominator. 

The absolute reduction of 1% tells us clearly that if 100 high-risk men take pravastatin daily for eight years, then the life of one of them will be prolonged. The proportionate reduction of 25% gives no useful information as the denominator is ignored. It is a manipulation to enable sales.

Let me illustrate this manipulation further.

Diet study from Paris

On May 30th 2019 there was a press release in the UK, appearing in many national newspapers and on radio transmissions. It stated that:

The press release indicted an increase of cardiovascular disease by 12% when the proportion of highly processed food in the diet of 105,000 individuals rose from 10% to 20%. Incidentally, is this an increase of 10% or of 100%? 

Read on for further understanding.

It is necessary to look at the original data, some of which was provided in an expansion of the press release in The Guardian, and it is of course found in the original paper in the British Medical Journal.

The study was of 105,000 adults age 18 or greater, and the follow-up was for five years. For the purpose of analysis the population studied was divided into four groups based on the proportion of highly processed food in the diet.

Results

The cardiovascular disease rate in the highest quartile of consumption of highly processed food was 277 per 100,000. This is the usual way of presenting health statistics.

For the lowest quartile of highly processed food consumption the disease rate was 242 per 100,000.

There was thus a higher disease rate in those consuming a diet relatively high in processed food. But how much higher?

Let us note the simple calculation:

277 - 242 = 35

This would appear to be non-controversial. It indicates that if 100,000 people consume a high processed food diet, then 35 more of them will develop cardiovascular disease compared to a similar group with a lower consumption of highly processed food. 

35 out of 100,000  = 0.035 out of 100  =  0.035%

If you are one of the 100,000 would an increased risk of 0.035% make you change your diet? The answer is probably “No”.

If this were the stated result of the study, it would almost certainly be ignored by the media. There would be no press release and the authors would remain in obscurity with no fame and little prospect of future research grants. The cost of the study was not stated but the paper had 13 authors and no doubt many unrecorded assistants and clerical staff employed over 10 years. This would suggest a cost of at least £/€/$ 1.5 million.

The Spin

Turning bad news into good news is a process called “spin”, frequently used by politicians. Enter statistical manipulation.

I have presented absolute proportions, and these enable us to understand the real world, how the results of the study affect "me" as an individual. We now need to look as to how the result is translated into “proportionate” changes.

The increase in disease rate is from 242 to 277, a difference of 35. This number is presented as proportion of 242.

35 / 242 = 0.145

and this represents an increase of 14.5% of cardiovascular disease by consuming a diet high in highly processed food.

0.035% represents a change. But using a proportionate result mean that we can use an increase from the lower number or a decrease from the higher number. 

And so alternatively:  35 / 277 = 0.127

which is a 12.7% decrease by having a diet low in highly processed food realise to a high level diet.

Using proportionate figures of 14.5% of 12.7% is much more dramatic than 0.035%, hence widespread newspaper headlines.

Expressing the result of this study as a proportionate rather than an absolute result amplified the diet effect from 0.035% to 12.7%. This is an amplification factor of about 350.

0.035% tells us about the real world, how the health of us as individuals is influenced by our diet. 25% tells us nothing.

This spin is common in medical papers and it ought to stop or be stopped.

Dubious mathematics - changing denominators

Disease incidence per 100,000
We encounter the mathematical effect of manipulating numerators with no reference to the denominator. In this case the numerators were 277 and 242, and the denominator was 100,000. You will see that the manipulation above took no account of the denominator.

Disease incidence per 1000

Let us assume that the denominator was different by a factor of 100:

High consumption group  277 per 1000

Low consumption group   242 per 1000.

The difference of 35 is now per 1000.

35 per 1000 = 3.5 per 100 = 3.5 %.

This is important, a hypothetical effect 100 times greater than the real study result.

But the proportionate calculation would remain just the same:

35 / 242 = 0.145 = 14.5%  or  35 / 277 = 0.127 = 12.7%

Disease incidence per 10,000,000

Let us suppose that the disease incidence is much lower, by a factor of 100. The numerators remain the same but are now found to be per 10,000,000, a much much lower incidence and a therefore a much larger denominator. The results would be:

277 per 10,000,000  and 242 per 10,000,000. 

The difference (numerator) would remain at 35, but now out of 10,000,000.

.

The absolute difference would be 0.00035%. This is a tiny population effect, but if the sample size is big enough it could achieve statistical significance, even though of no health significance.

However proportionate change manipulation still leaves us with 

35 / 242 = 0.145 = 14.5%  or 35 / 277 = 0.127 = 12.7%

Whatever the disease incidence, the answer is always 12.7% (or 14.5%). 

We can therefore see that proportionate results are meaningless in the real world and give no indication of real risk to the individual who is making a choice of what to eat.

Expressing the proportionate result implies a much higher risk than is really the case. It is intended to frighten the public (and their doctors) into taking tablets or altering their life-styles or to produce an impact much greater than it should be.

Is it acceptable to use numerators without reference to denominators?

This type of manipulation is completely outrageous. It should not be allowed in papers published by reputable journals, or any other form of publication. Numerators should not be separated from their denominators. 

I am no mathematician but I learned about numerators, denominators and percentages when I was in my primary school. I was taught that if the numerator is increased or reduced, then the denominator should be changed by the same proportion:

 3/4 = 6/8, not 6/4.  3/4 = 12/16, not 12/4.

The manipulations that we have seen would result in an examination "fail".

Are my salami sandwiches a form of suicide?

Reference:

Srour B, Fezeu LK, Kesse-Guyot E et al. Ultra-processed food intake and risk of cardiovascular disease: prospective cohort study (NutriNet-Santé). BMJ 2019;365:l1451