Data Patterns in the Mediterranean Diet Score

The original construction of the edifice known as the Mediterranean Diet began with a paper which used a scoring system to handle the mass of data that results when you give thousands of people food frequency questionnaires. The data manipulation is roughly like this: People say how often and how much they eat of typical dishes and foodstuffs; these quantities and frequencies are converted to daily food group consumption for which a score is given. RESULT massive amounts of data reduced to one number.

Let's recall the basics: the food groups were: vegetables, fruits & nuts, legumes, meat & poultry, fish, dairy products, cereals, monounsaturated to saturated fat intake ratio and alcohol intake. The bad score was 0 for eating more of the bad groups (meat & poultry, dairy, low mono to saturated fat ratio and alcohol) and not enough of the good groups (vegetables, fruit & nuts, legumes, fish, cereals) and the good score was 1 for doing the opposite. When these scores are added up, the lowest possible score (bad) is 0 and the highest (good) is 9.

Now, it turns out that the pattern of scores expected can be modeled by a mathematical probability distribution known as the binomial distribution. Strictly speaking, to adopt this model of the situation we need to make two assumptions about the behaviour of the participants. Firstly, we assume that each participant is operating (i.e. choosing foodstuffs and quantities of these to eat) independently of (i.e. not influenced by) each other participant (this is quite likely) and secondly, we need to assume that a participant's scoring on each food group is independent of (i.e. not influenced by) the score of other food groups. This second assumption is not entirely true, for example, it is clear that there would be some correlation between both dairy products and meat & poultry consumption and the monounsaturated/saturated fat ratio. However, for now, let's make this assumption and then we can check whether the actual data support this view.

With this model for the scoring process, it becomes possible, given the total number of participants, to calculate the expected numbers with different scores. It is quite easy to see that, given the way the scoring system has been constructed, there will be a full spread of scores, because on every food item, there is a 50-50 chance of scoring 0. Another point to consider is that, with the exception of scores 0 and 9, there are multiple ways of obtaining the other scores. For example, a score of 1 may be obtained by being above the median on one and only one of the 9 food groups - which means there are 9 different ways of getting this score. Whereas a score of 2 may be obtained by combining a score of 1 from 2 out of 9 groups: there are 36 ways of doing this. For the most likely scores of 4 and 5, it can be shown that there are 126 different ways to obtain each of these scores.

Table 2 (and you should look at this table while reading the next bit) in the paper shows the individual food group scores versus the Mediterranean diet score. This table is important because it gives some insight into the raw results of the scoring process which is otherwise obscured because score results for the individuals are grouped into three categories: low diet score (0-3), medium (4-5) and high (6-9). This is distinctly unhelpful and does not let us see how many got each individual score. However we can see – within each diet score category – how many people scored 0 or 1 for a particular food group (i.e. how many people ate more than the median amount and how many ate less than it - or vice versa).

Using the binomial distribution and the total number of individuals, it is possible to predict how many people should score 0 or 1 for each food group in the three diet score categories under our assumptions outlined above. (But note that we will get the same prediction for each and every food group because the model makes no distinction between these.) For example, for men in the category of low diet score (0-3), we would expect 2257 individuals and to see only 643 (28%) scoring 1 but 1616 (72%) scoring 0. In the category of medium diet score (4-5) 4378 individuals are expected, with equal numbers scoring 0 and 1 and in the category of high diet score (8-9), we would expect to see 643 of 2257 (28%) scoring 0 and 1616 (72%) scoring 1.

How does the prediction compare to the actual values? Quite well in fact for legumes and fruit & nuts (both 23%/77% and 50/50 in the medium score category) and dairy products (31%/69% in the low and high categories and 50/50 in the medium category) not quite so well for fish, vegetables and fat ratio where the ratios are actually 'more extreme' than predicted (18%/82% or 20%/80% in the low and high score categories). Cereals (36%/64%) and meat & poultry show the worst correspondence where the ratios are 'less extreme' than predicted. Overall we slightly overestimate the number in the medium score category (actual number 3808) and underestimate the numbers in the low and high categories.

There are some foodstuffs included in Table 2 which are not included in the calculation of the Mediterranean diet score: eggs, potatoes and sweets. As they are not used to calculate the score, it can be expected, that any participant in any diet score group would be equally likely to be above as below the median consumption of these items and so there would be approximately a 50%/50% split in the consumption in each diet score category. A sizeable departure from these figures would suggest that the participant's consumption of these non-scoring foodstuffs is in some way dependent on or linked to consumption of a scoring food group. However, this is clearly not the case, except possibly for potatoes, which show about 16% deviation from the expected 50-50 split in favour of (unsurprisingly) vegetables.

This leads to the most notable find in this table - a point which was completely unmentioned in the original article. The distribution of meat and poultry consumption appears to be essentially independent of the Mediterranean diet score. Within each scoring category, the distribution of above and below median consumption for meat and poultry is much more like that of eggs and potatoes and sweets than it is of the other items making up the diet score. Whatever the diet score group, there is close to a 50-50 split in the distribution of individuals' meat consumption. On a Chi-sqared test on the actual versus the expected values, the meat and poultry item shows the strongest result for independence in common with the foodstuffs which are independent of the diet score (e.g. eggs, potatoes, sweets) because they are not used in its calculation. It is interesting that this result is not remarked upon in the paper. In fact, to the contrary, when giving an example based on the link between a 2-point increment in the diet score and improved survival, it is mentioned that such an increment could be achieved by `making a substantial reduction in meat intake' despite the evidence that many high scorers score highly in spite of an above median meat intake!

When epidemiology works

Sometimes epidemiology produces a reasonable result. Take this recent story.

Researchers note that somewhere has a very high rate of a relatively rare condition. In this case a province of Iran with a high rate of oesophageal cancer. The first step in such a situation is often the case control study. This is a study done on the basis of matching people already diagnosed with the condition as closely as possible with controls who do not have the condition and then attempting to find significant ways in which the cases and the controls differ. Case control studies can be problematic because the results can be manipulated by choice of the controls. Also this type of study is purely observational and it is after the fact observation. You are relying on people's recall and what they recall may be influenced by their present condition - particularly when they have a serious disease. However in this study the results were quite striking:

Compared with drinking warm or lukewarm tea (65C or less), drinking hot tea (65-69C) was associated with twice the risk of oesophageal cancer, and drinking very hot tea (70C or more) was associated with an eight-fold increased risk.

The speed with which people drank their tea was also important.

Drinking a cup of tea in under two minutes straight after it was poured was associated with a five-fold higher risk of cancer compared with drinking tea four or more minutes after being poured.

There was no association between the amount of tea consumed and risk of cancer.

Compare this with the purported increase in risk of death from eating red meat (based on the responses to one labyrinthine food frequency questionnaire ten years earlier) of about 0.31 times (men) to 0.36 times (women).

And what was also nice was that having asked people to estimate how hot they drank their tea, they then went and measured the actual temperature.

Calorie Restriction and Memory - Low-Carb wins again, actually...

This study is the latest to make headlines around the world as it is claimed that modest calorie restriction in elderly people can result in an improvement in memory. From the abstract:

Animal studies suggest that diets low in calories and rich in unsaturated fatty acids (UFA) are beneficial for cognitive function in age. Here, we tested in a prospective interventional design whether the same effects can be induced in humans. ......We found a significant increase in verbal memory scores after caloric restriction .... which was correlated with decreases in fasting plasma levels of insulin....No significant memory changes were observed in the other 2 groups. This interventional trial demonstrates beneficial effects of caloric restriction on memory performance in healthy elderly subjects.

However, what caught my eye in reports of the study was this:

However, care was taken to make sure that the volunteers, despite eating a restricted diet in terms of calories, carried on eating the right amount of vitamins and other nutrients.

Now, this is an important point - it was even - implicitly - used as an objection to the approach by an anonymous dietician who said that:

....people, particularly those already at normal or low weight, should be "extremely careful" about attempting such a diet. She said: "There is other evidence that, far from enhancing memory, dieting or removing meals can interfere with memory and brain function.

presumably because it follows that if you just cut calories by 30% you cut nutrition by 30%.

But these people claim they didn't reduce the subjects intake of vital nutrients, how did they manage this?

The truth is revealed in the (rather limited) data in the Table S2 in the supplementary information package.

For individuals in the caloric restriction experimental group the mean calories fell from 1843 to 1630, the mean protein intake went from 77g to 71g (all numbers rounded to nearest whole number), the mean fat intake from 70g to 57g and the mean carbohydrate intake from 192g to 74g!! Converted to percent energy measures, this means the mean values went from 17% protein, 35% fat and 43% carbohydrate to 24% protein, 43% fat and 25% carbohydrate (the values don't add to 100% because alcohol intake was included). In other words caloric restriction was achieved, without compromising nutrition, by restricting carbohydrates (especially one imagines typical nutritionally empty carbohydrates like products made mainly of white flour and white sugar).

Interestingly, the individuals in the second experimental group which increased its unsaturated fat intake (to 68% of total fat intake on average - that's 36% mono-unsaturated fat which didn't actually increase (baseline for that group was 36%) and 32% polyunsaturates (from 15%)) didn't show the memory improvement, although they also appeared to have achieved a conversion to 'low-carb'. However, in their case the standard deviation for carbohydrate intake was bigger than the mean value (and much larger than the baseline value), which suggests a huge variation within the group.

Another caveat is that while taking the mean values of consumption and converting to calories reproduces (to within 40 calories or better) the reported mean caloric intake for the before case in all the groups, it is does not do so for the after case (the discrepancy is as much as 400 calories - and in all cases the mean nutrient data (in grams) result in an under-estimate of the mean calories). A better model - using a normal distribution for each parameter - might give an idea as to why this is so. Another interesting fact related to this is that - apart from the unsaturated to saturated fat ratio for the unsaturated fatty acid experimental group, none of the reported differences in before and after macronutrient mean intakes were reported as significant.

To sum up: the calorie restriction appears to have been mainly achieved by restricting carbohydrates. The researchers claimed that they had achieved calorie restriction without reducing nutrient content of the diet. The only way to do this is by removing or significantly reducing nutritionally empty carbs e.g. see here. Mean dietary data reported from the study lends support to this theory. The results observed in the subjects e.g. reduced insulin levels also support this theory.

Lark Rise - Discussion

The book Lark Rise documents the apparent good health and long lives of nineteenth century rural labourers despite a physically demanding lifestyle, a life of considerable material poverty relative to today and less medical support than is available today. The testimony of this book is backed up by my own observations of mortality and lifespans while doing family history research. What could be the explanation?

The first that springs to mind is that the author is simply mistaken; that her recollection is clouded by time, by the rosy glow of the good old days. However, the author herself seems aware of this possibility and her own seeking for an explanation suggests that, as far as she can tell, she is recalling fact and not invention.

It's likely that one of the reasons the doctor was seen so rarely was due to the cost. In those days there was no NHS. A doctor's services had to be paid for although it is claimed that wealthy doctors also treated patients who were unable to pay for free and many hospitals were charitable institutions and free to the poor (see for example, discussion in the following books: Sociology as applied to medicine by Graham Scrambler, Elsevier, 2008 and Social policy and welfare by Walsh, Stephens and Moore, Nelson Thornes, 2000, both available on Google books). However, it seems likely that the doctor was only called in when absolutely necessary. People might have treated less serious complaints themselves and put up with chronic conditions and pain such as arthritis.

Assuming then that this does show that serious disease - such as cancer - was largely absent what is the reason for this generally robust health and long life?

First and foremost, probably vitamin D: - children were sent outside to play every day, labourers worked outdoors. Pork meat and fat was a major component of the diet and the pigs were kept outside and fed a diet of scraps, milk and vegetable matter which would have been notably deficient in soy and corn (i.e. maize, because in nineteenth century England, corn meant wheat)! Thus, the lard obtained likely would have been as high in vitamin D as it is possible for lard to be and probably lower in omega-6 polyunsaturates than today's. Thus the diet would have been better balanced in the omega-6/omega-3 ratio.

Meat was eaten daily and, even if only once a day, because of the way nothing was wasted and everything cooked in one pot, the goodness (minerals, gelatine) from meat and bone juices would have been eaten up by the children, soaked into the bread or pudding. In addition, it appears that fish was eaten weekly (the fishmonger called weekly) and fish roe was prized and preferentially given to children.

Although many fruits and vegetables we habitually eat today (oranges, bananas, tomatoes) were absent. Other, native green plants (e.g. sorrel, nettle, dandelion, goose grass and many more are all edible) were taken from the wild and eaten. (It is in fact to this that the author herself attributes the good health of the hamlet.)

Finally, the bread was made from stoneground wheat. It is widely believed that this is more nutritious than today's refined white flours. But, it's not as clear cut as it seems.

On the one hand, white flour is very low in nutrients compared to wholemeal (see here for the effects of modern processing on flour). From Fitday, all-purpose white wheat flour unenriched has the following micronutrient profile (as a percentage of daily allowance)

Vitamin A	0	%
Calcium	2	%
Vitamin D	0	%
Thiamin	10	%
Niacin	8	%
Vitamin B6	3	%
Phosphorus	14	%
Selenium	61	%

Vitamin C	0	%
Iron	8	%
Vitamin E	0	%
Riboflavin	3	%
Vitamin B12	0	%
Manganese	43	%
Copper	9	%
Magnesium	7	%
Zinc	6	%

whereas whole wheat flour has much more Iron, B vitamins and other minerals.

Vitamin A	0	%
Calcium	4	%
Vitamin D	0	%
Thiamin	36	%
Niacin	38	%
Vitamin B6	20	%
Phosphorus	42	%
Selenium	121	%

Vitamin C	0	%
Iron	26	%
Vitamin E	5	%
Riboflavin	15	%
Vitamin B12	0	%
Manganese	228	%
Copper	23	%
Magnesium	41	%
Zinc	23	%

But without neutralization of the phytate content of the wholemeal flour, much of this nutritional content, particularly the minerals, cannot be absorbed [1] (see also the discussion of White Flour vs Whole Wheat here). There is also the question of its effect on teeth. There are also other 'anti-nutrients' in whole grains - see for example here.

However, it's possible that, as the bread was made at home, it was actually a sourdough bread. In this case the effects of anti-nutrients (lectins and leptins) and phytate would have been partially neutralized by the longer fermentation. (Stephan on Whole Health Source has many posts on this issue.)


[1] McGee, H. On Food and Cooking, London: Unwin Hyman Ltd, 1984.

Lard in Lark Rise

I'm very keen on researching my family history, and recently I've been working on the predecessors of one great-grandmother who were all East Anglian 'ag labs' (agricultural labourers). I noticed an interesting thing about them: in the nineteenth century particularly, very many of them lived to a ripe old age. Even going back to individuals born in the middle of the eighteenth century, I can find more than a few - across different families - who lived into their late 70s and 80s. Why is this so? They were poor, they didn't have access to modern medical care and they worked hard physically.

One book which sheds light on this is Lark Rise to Candleford*, the first part of which was published by Flora Thompson in 1939. It is a novel/memoir of her childhood in a rural England (Oxfordshire) which even then was passing out of existence. By the 1880s, when Flora and my great-grandmother (living a similar life in Cambridgeshire) were growing up, the industrial revolution in Britain was a hundred years old, but in the agricultural sector machine power was only just beginning to replace manpower and horse-power. Hamlets and small villages were populated still by agricultural labourers, living in cottages which came with the job, and working for the local farmer. The farms were mixed farms, in the area Thomson grew up, they were mostly arable with some livestock. The weekly wage would not normally have been enough for such large families not to starve, but they survived and even thrived in the rural setting as they had the opportunity to provide for themselves: an opportunity denied to poor families in town. Indeed, Thomson notes that the general opinion of those in her village of the nearest big town, Oxford, was that although a man might earn more there, as he'd be paying more rent and would

have nowhere to keep a pig or to grow many vegetables, he'd be a fool to go there. (p. 33)

Thomson refers to the adult generation of the 1880s as 'The Beseiged Generation'. The term seems to be meant in two ways: firstly, it was a period just before enormous change. Although the social structures of the time were to hold for at least another thirty years (until after the Great War) and to a lesser extent for sixty more, not collapsing completely until after the Second World War, the big change in agriculture and the start of the inexorable decline in manpower on the land was just around the corner. Maybe it is just a coincidence, maybe it is a consequence of the initial impact of small changes, innovations, where before, for so many years, there were none, but it was a time of decaying tradition and custom. For example, she says of the herb garden:

As well as the garden herbs, still in general use, some of the older women used wild ones, ..... But the knowledge and use of these was dying out; (p. 115).

Secondly, it was a tough time economically, the agricultural wage of the 1880s was 10 shillings per week (equivalent to £258 per week today) and every way possible had to be used to feed, shelter and clothe a large family (and they did have large families, my great-grandmother was the 1oth of 11 children).

So why were they apparently so healthy? Indeed, the author herself seems somewhat pushed to explain the robust good health of the hamlet she remembers. She says:

There were two epidemics of measles during the decade, ... but, for years together, the doctor was only seen there when one of the ancients was dying of old age, or [for] some difficult first confinement... There was .... except for a few months when a poor woman was dying of cancer, no invalid. (p.19)

What They Ate
The staples of the diet were bread, lard and bacon. Every household raised and killed one or two pigs each year. The importance of the pig was shown by the amount of effort lavished on their care and feeding. They were given not only household scraps (if there were any) but specially cooked up meals of potatoes mixed with leftover cooking liquor, milk and barley meal. Children gathered weeds and grass or even snails to supplement the pig's diet. Often half the pig had to be 'mortgaged' to the baker or publican as a way of buying on credit the necessary pig fattening food.

Only one meal a day would have any meat. As an agricultural labourer's house did not have an oven, nor even a range, cooking was done in the fireplace in an iron pot slung from a rack or chain built into the lower part of the front of the chimney piece. This arrangement meant everything was cooked (boiled) together: bacon, green vegetables kept together in a net, potatoes in another net and a roly-poly pudding greased and floured and wrapped in a pudding cloth. (This last is a peculiarly English creation being a flour and suet or lard dough adaptable to either sweet, if fruit, currants or jam are added, or savoury purposes, if meat.) All that was necessary was careful timing of when to put in and take out the various components. There were no leftovers for the pig, save the vegetable and potato peelings and the cooking water.

The other two meals (breakfast and lunch) were bread and butter (rarely) or bread and lard. According to Thomson, butter was expensive, although cheaper in the summer when a pound cost tenpence, and the cheaper imitation 'butterine', presumably an early form of margarine, was not liked. Instead they collected their own lard from their pigs and flavoured it with rosemary from the garden. Rosemary did not just improve the flavour. Herbs such as rosemary and sage have anti-oxidant properties and help to prevent the unsaturated fatty acids in the lard from going rancid ([1], p.606) as it had to last until the next pig killing, an important consideration in houses which had no refrigeration.

The pig killing was an important event and was followed by a celebratory 'pig feast' to which the extended familly was invited. The feast featured "joints of pork, potatoes, batter puddings, pork pies, and sometimes a cake or two" [to take advantage of the opportunity of using the baker's oven] (p. 27) plus three or four different kinds of vegetables and a meat pudding.

At the pig feast here would be no sweet pudding, for that could be had any day, and who wanted sweet things when there was plenty of meat to be had! (p. 27).

This statement is one of the most remarkable in the whole book: it would be hard for today's children to understand.

Nothing from the pig was wasted: home-cured bacons and hams kept the family provided throughout the winter and beyond (depending of course on the size of the family and whether half the pig was already spoken for!), 'hog puddings' were also made (from the pig's blood) and the chitterlings were made into sausages after they had been rinsed under running water for three days.

Throughout the year, the main meat to be had was the preserved, salted and dried bacon and ham. Once a week, there would be a small amount of meat bought ("six-pennyworth of pieces") made go further by making a meat pudding. Even less often a small joint would be roasted "on a string before the fire" or used as a pot-roast, cooked with lard in a saucepan over the same fire. A "toad", the meat wrapped in a suet [pastry] crust and boiled over the fire would again make a small joint go farther and make sure the precious meat juices were not wasted.

Bread was bought, but the women also needed flour - to make the puddings which were otherwise the way of eking out a meagre supply of meat. This flour was obtained by the right of the labourers to the leazings: the heads of grain left behind in the field from the less efficient time before mechanical harvesting. For two to three weeks once harvesting was over, the women and children went out to the stubbly fields each day, collecting by hand the leftover ears of wheat. Once threshed by hand at home, it was taken to the local mill and a large sack of flour returned:

one bushel, two bushels, or even more, in large, industrious families. (p.28)

It would have been stone ground flour too, at least at the beginning of the decade (of which more later).

Just as the pig was home-raised, vegetables and fruits were also home-grown. The men tended allotments (parcels of land granted to them, probably as part of the cottage rental to allow them to grow food crops) where they grew potatoes and wheat or barley. In the cottage garden they grew vegetables and fruits: peas, cabbages, cauliflowers, kale, beans and potatoes, fresh greens, radishes and onions. Rhubarb, currants and gooseberries would be made into jam. They had the advantage of fresh and organic produce. They also did not waste the natural produce around them. Children went out gathering mushrooms; sloes, blackberries and elderberries could be made into jams or jellies - or brewed into wine.

Nevertheless, there were occasional variations to the diet. Eggs were eaten, but only when affordable or only by those who kept chickens. Milk was available, at very low cost, if you walked the mile and a half to the farmhouse. It was hand-skimmed, so some cream was left and it was raw. Interestingly, she says that most people did not bother and so most children did not drink milk once they were weaned.

A travelling fishmonger who also sold fruit called weekly. If it could be afforded a bloater would be bought for a penny, "but it had to be a soft-roed one, for, in nearly every house there were children under school age at home; so the bloater had to be shared, and the soft roes spread upon bread for the smallest ones." (p. 119). Oranges and, on one occasion, a tomato bought from this vendor were merely curiosities, tried out once.

Small birds were another frequent and popular addition. Older boys would go out at night and net groups of sparrows where they were nesting in the hedgerows. These could be plucked and put into a pudding. One or two would be toasted over the fire. Women and children also lured and trapped birds. To take anything bigger than a sparrow or a blackbird or thrush, even to pick up a dead hare, was poaching. But it was done, not habitually, but if the opportunity should arise.

* My edition of the book is: Flora Thompson, Lark Rise to Candleford, Penguin Modern Classics, Penguin Books, 1973.

[1] McGee, H. On Food and Cooking, London: Unwin Hyman Ltd, 1984.

LCHP Part 2 - the punchline

It’s all very well to show that the LCHP (LowCarbohydrate-HighProtein) score doesn’t completely and accurately reflect protein and carbohydrate intake, but what about the claimed results of an increased risk of mortality with an increasing score?

How was the relationship to mortality calculated?

The relationship to mortality was calculated through Cox proportional hazards models which are used to relate the risk of death with either the deciles of nutrient intake or the LCHP score, taking into account confounding factors (gender, age, socioeconomic status, smoking, BMI, physical activity, alcohol consumption). One thing to note about Cox proportional hazards models is that they represent the assumption of a model in which the thing being investigated (in this case carbohydrate vs. protein consumption) is being assumed to be directly causal in the decease of the affected individual. Cox models were originally used in drug and treatment trials where a terminally-ill patient’s survival might be expected to vary directly – and over a relatively short time-period (months to only a few years) depending on whether they were receiving drug or placebo. While it is likely that diet does have an impact on mortality, it is not at all clear that the link is as direct and immediate as assumed by these models.

Four different models (i.e. essentially differently constructed equations) were used to hunt for links between the supposed diet culprits – low carb/high protein – and death. In model 1 (not energy adjusted), increased protein intake (per decile) was found to be significantly linked to increased mortality (1.13 increased risk, CI: 1.03-1.23). However, as protein intake was the best predictor of total energy intake (correlation coefficient 0.93) it is likely that the one is a proxy for the other and the authors note that

‘mortality … increased with … total energy intake’ (p.577)

Model 2 assessed the LCHP score but found that an association with increased risk of mortality was non-significant (P=0.14; CI: 0.97-1.20). Model 3 looked at energy-adjusted individual nutrient intake and found that energy-adjusted carbohydrate intake was inversely related to mortality: reduced risk 0.94 (CI:0.89-0.99) but the apparent link with protein had disappeared (possibly because of the energy-adjustment). However, according to the authors, this model is flawed because it does not take into account

‘the complementary changes that have to be introduced for the preservation of total energy intake, when carbohydrates and proteins change’ (p.578).

Most interesting is model 4 which finds a significant relationship between the LHCP (using energy-adjusted protein/carb deciles) and mortality (increased risk 1.08 CI:1.03-1.13, P=0.001). What this actually means is that increased mortality is associated with a decreased fat intake! Yes, because a 2-point increase in the LCHP score is caused 57% of the time by increasing intake of protein and/or carb. In an energy-adjusted formulation, when one or more macronutrients is increased, then necessarily the others decrease – as a proportion of energy intake – so what this finding may really be telling us is that – as fat intake declines as a proportion of energy, mortality increases!

Interlude: the LCHP (LowCarbHighProtein) score

Oh, dear, they’ve been at it again. Someone asked about this study on Dr Eades’ boog and I decided to take a look. I have to admit I’d been avoiding it because of a bit of cognitive dissonance due to the conclusion touted in the abstract:

In models with energy adjustment, higher intake of carbohydrates was associated with significant reduction of total mortality,… Even more predictive of higher mortality were high values of the additive low carbohydrate-high protein score (per 5 units, mortality ratio 1.22 with 95% CI 1.09-to 1.36). Positive associations of this score were noted with respect to both cardiovascular and cancer mortality.

Sounds scary, doesn’t it – has it been discovered lower carb/higher protein diets are really bad for us after all? Well, no not really – once you look into this low carbohydrate-high protein score (hereafter abbreviated as LCHP) it turns out they’re not measuring quite what they think they are…. So read on.

This study is based on the same cohort of Greek EPIC participants as used in the famous Mediterranean diet study. As such food consumption data is based on food frequency questionnaire data – albeit interviewer administered – with all the caveats that appy to that . The 22944 subjects were followed until December 2003 – not quite 5 years on average – but making 113230 person-years. However, there were only 455 deaths. This makes 22944 a trojan number because although the comparison is done on the 455 with the much larger group of 22489 survivors, data is effectively only available relating diet to death for 455 people.

How was the LCHP score calculated?
The key to the study is how the LCHP score is calculated. The study participants are classified by deciles (10% steps) of ascending protein intake and descending carbohydrate intake. For example: let’s say the range of protein intake was 50-90g: a decile is 4g; so protein intake of 50-54g would be assigned a score of 1, 54-58g – assigned a score of 2, and so on. Carbohydrate intake is scored in reverse order, so that a score of 1 indicates the highest decile of consumption and 10 the lowest. The additive LCHP is then created by adding the two scores together. Or as they put it:

Thus, a subject with LC/HP score 2 is one with very high consumption of carbohydrates and very low consumption of protein, whereas a subject with score 20 is one with very low consumption of carbohydrates and very high consumption of protein.

However, as we shall see – this isn’t quite how it works.

Imagine we have 10 individuals with protein consumption that puts each one of them into a different protein decile. So we score these individuals

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

Now these same 10 individuals also have the carbohydrate consumption so that their carbohydrate scores are:

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

Adding these together, these individuals have LCHP scores:

[2, 4, 6, 8, 10, 12, 14, 16, 18, 20]

But what if we had another 10 individuals with the same protein scores but different carbohydrate consumption –so that they scored respectively [2, 3, 4, 5, 6, 7, 8, 9, 10, 1] ? These individuals’ LCHP scores would be: [3, 5, 7, 9, 11, 13, 15, 17, 19, 11]. In the second group someone in the highest decile of protein consumption had a final LCHP of 11 because their carbohydrate consumption was also high. What about the other person with an LCHP of 11 in that group? They had middling consumption of each.

In fact for any individual with a protein score of 1 – their carb score could be anywhere from 1 to 10 – giving them a LCHP of anywhere from 2 to 11. Any individual with a protein score of 2, could score an LCHP from 3 to 12 and so on. You might argue that you can’t increase both protein and carbohydrate – but when comparing individuals like this you can – because consumption also depends on other factors such as weight, age, gender, activity level. There has been no consideration here that there is a certain minimum requirement of protein for health (usually expressed as at least 0.5 -1g/ kg body weight) and it doesn’t follow that if one macro-nutrient goes up, the other always goes down because fat is a third variable in the equation which can also be manipulated by the eater and which is left unconsidered in this score.

Another problem
The second problem with the score concerns what the detail of what differs between two individuals with different scores. Consider an individual with what is clearly considered to be a ‘low’ score by the authors – 6. This can be made up from these possible combinations of protein + carb deciles:

1 + 5, 2 + 4, 3 + 3, 4 + 2, 5 + 1

Let’s say this person has 3+3: a quite low (only 3rd decile) protein consumption and a quite high carb intake too. Now, someone else has a LCHP score 2 points higher, i.e. 8. This can be made up of these possible combinations of protein + carb:

1 + 7, 2 + 6, 3 + 5, 4 + 4, 5 + 3, 6 + 2, 7 + 1

Now, if the second person’s score was 4+4 – we could say that yes they had higher protein and lower carb intake. But what if their score was 6+2? Then they would indeed have a higher protein intake but also a higher carb intake. On the other hand if their score was 2+6, they would have a much lower carb intake but also a lower protein intake. In fact, for a difference between scores of 2 points, there are: 5 differences due to increasing protein intake only, 5 due to decreasing carb intake only, 5 due to increasing protein and decreasing carb, 10 due to either increasing both protein and carb and 10 due to decreasing both protein and carb! Hence 20/35 or 57.1% of the possible score differences could involve a change in what is considered to be a ‘good’ direction of one component of the score (increasing carb or decreasing protein). A further 10/35 or 28.6% involve no change in one component of the score. Only 5/35 or 14.3% involve the typical 'increased protein and decreased carb' posited by the authors!

For evidence that this ambiguity really does exist, one need look no further than Table 2 in the paper where the correlation coefficients between various measures used in the paper are given. They show that the correlation between the LCHP score and protein consumption is only 0.32 (0.28 when energy-adjusted) and only -0.31 (-0.31 when energy-adjusted) for carbohydrates! Compare this with the correlation between protein and carbohydrate consumption which is 0.78. This suggests protein and carbohydrate consumption tend to move together strongly whereas changes in the LCHP score only very weakly reflect changes in protein and carbohydrate consumption!

This problem of working out exactly what numbers contribute to the differences between two LCHP scores is in fact a very complex mathematical problem belonging to the field of combinatorics and was probably not foreseen by the creators of the score! However, it hugely muddles the interpretation of the 'results'.