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### My Journal

Maths Grinds
24 Aug 2018

Today both RTÉ and BBC are reporting the results from an interesting study. They are reporting the findings as “No safe level of alcohol consumption, major study concludes”. For those who would like to read the study you can find it here on The Lancet. I was curious so I gave the paper a quick read. For a Mathematics and Statistics student this is a good exercise in interpreting results, in particular reading graphs and understanding uncertainty intervals.

First, I scanned through the paper looking for the statistics and found the relative risk graph. Perfect! This graph shows how one’s relative risk changes as alcohol consumption changes. Relative risk is a like a “multiplier” of sorts, that is, if you have a relative risk of 2 it means you are now twice as likely to see the “risk” event taking place. A simple (pleasant) example is this: if you buy two lottery tickets you are now twice as likely to win so your relative “risk” (although the risky event is a nice outcome) is now 2. Your probability of winning is still small but it is now twice as big. Anyway, on to the graph in the paper:

Figure 5 Weighted relative risk of alcohol for all attributable causes, by standard drinks consumed per day

The black line is the relative risk. However, we can never be 100% sure where the relative risk line sits (due to many reasons such as incomplete data for one) so the green shaded area represents where the line could be. That is, it is an uncertainty interval (UI) on the relative risk. But look at the lower end. It seems rather flat from 0 to 1? Indeed it is possible it is completely flat and one’s relative risk doesn’t increase until you go beyond about 1 drink per day. But we do not need to guess the values from the graph since they are reported to us directly at the lower end. So…

Now, to the second point, the article states that “we found that consuming zero (95% UI 0·0–0·8) standard drinks daily minimised the overall risk of all health loss” . The uncertainty interval is 0 to 0.8 drinks per day and the graph shows this too. What exactly is this UI? Well, it is a range of values for what the minimised safe value could be. The reason for the range is due to missing data. That is, the author had to “estimate standard drinks consumed daily by current drinkers”. This is entirely normal and reasonable. But the point of using a UI in light of missing or estimated data is that one can’t make a point estimate and instead must report a range of values, this UI covers what is called the ignorance interval which is the interval of possible true values consistent with the known data.

Basically and finally, the safe level of consumption that minimizes risk is only partially identified. I feel it is wrong to report “zero” as the value which minimizes risk. The true point value sits somewhere in this UI range (or rather somewhere in the ignorance interval which sits inside the UI). It seems misleading to report the lower end boundary point of the uncertainty interval as the best estimate.  The most honest safe answer to report would be this: “between 0 and 0.8 standard drinks per day does not increase one’s relative risk”.

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