Saturday, November 8, 2008

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'.

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