Meta analysis in R

or 

the beneficial effect of teaching on research

I have been fascinated by meta analysis for a long time. It is so obviously the right way to approach the true effect of an intervention. Recently, an old binder presented itself in a pile of shite bunch papers I meant to read but found myself throwing in the bin tidying away. It contained the draft of a database of physiological data from the first years of my PhD. The idea was to compare all the baseline data from our kidney research group in Uppsala to look at the effect of the models as such and the interventions that were used repeatedly. With the insight of the intervening years it seems a lot less interesting now, but I still have the feeling that some areas of experimental research could benefit from meta analysis.

Which brings us to the the story I am about to tell. Four or five years ago, when I moved back to Uppsala, I got offered a lecture on physiological changes in the elderly. It was to be part of a final year course for the master in biomedicine programme. Just a single hour to show how all the physiology from the rest of the programme changed with age. To compare and contrast ageing as such with the accrued ailments of living for a long time, and distinguish these from the chronic and age related disease. It was not a huge success, but given the title I was not too disillusioned. The second year I was given two hours. Still a bit on the short side, but one hundred percent better than one.

It is not the most popular lecture, but I have had it for five years now and one of the things I teach is that some parts of ageing is caused by metabolism itself. The burning of oxygen singes the organism and with time it will break much like the paneling in an old sauna. As proof of this I used the idea of caloric restriction, which can prolong life in many strains of yeast, mice, and rats. Then, in 2012 an article was published on the effect of caloric restriction in the Rhesus monkey, a primate, and reasonably the closest relative to humans in which an experiment could be expected to be finished any time soon. It showed no effect. I happily included this in my lecture as a counter-point. Until in 2014, when updating the lecture for a new semester, I found that another experiment with caloric restriction in Rhesus monkeys had published their data and found a clear difference.

This made it hard to continue the lecture as I had done, I could just show both studies and say that we don't know. But the total number of animals included was quite large, and the effect measure very straight-forward. Death. So, I performed a meta analysis of mortality of these two studies, and a third smaller study published in 2003. This is the story of that analysis.

Quickly I installed the R package rmeta by Thomas Lumley and set to work. It is quite easy really, we start with setting up a table of results from the included studies. The table should include the total number of subjects in each group, and the number of deaths per group.

Hultström, M. Acta Physiol (Oxf). 2015 Feb 14. doi: 10.1111/apha.12468.

The we push this trough the rmeta function meta.MH(). To get a forest plot, we just run the plot() command, which has a default for handling the result of meta.MH() in the form of a forest plot. If you have a larger meta analysis there is also the funnelplot() that can be used to assess publication bias. Anyway, the result is quick and easily understood, which is really one of the major strengths of the forest plot.

Hultström, M. Acta Physiol (Oxf). 2015 Feb 14. doi: 10.1111/apha.12468.

There was no significant effect of caloric restriction on all cause mortality in Rhesus monkeys. Or, rather there was a small, clearly non-significant, effect. One of the reviewers asked what would be needed to show if this effect was true. That is, could I please perform a power analysis. So, I installed the pwr package and ran a 2p2n.test() using the most generous effect estimate, i.e. a hypothetical study that ran to completion where the whole control population had died giving an effect of 0.08. This resulted in a required population of 2806 subjects to reach 85% power. This is the power-level which is normally used as the basis for power calculation in clinical studies. However, the age-related mortality was a different story that you can find in the actual article.

The next thing that surprised me was how difficult it was to get this simple little analysis published. It appears that experimental journals don't publish meta analyses, and clinical journals that publish meta analyses, don't publish experimental results. Finally, I found a benevolent editor at Acta Physiologica who permitted it to be published as an editorial. So that is where it resides today, and finally I can give a fairly clear answer in my lecture on the effect of reducing metabolism by caloric restriction on ageing and on mortality. Only problem is, I now have to explain meta analysis and forest plots before I can show the actual data.

And, no I am not going to starve myself so that I can avoid some diseases we can treat in favour for a frailty for which the only known treatment is eating more.

Are the exercise recommendations insane?

I try to stay fit. I lift weights. I do crossfit. I do judo, and I still practice at a fairly respectable level. Since I found the training diary Funbeat about two years ago I have been keeping a detailed training diary. Recently I went through my training statistics and came up with some interesting numbers. In the last two years I have trained 262 times for a total of 285h 29min. That comes out to about 23 minutes per day or 164min per week on average.

Now, let us have a look at the exercise recommendations from the World Health Organization, Centers for Disease Control, or the Swedish equivalent Folkhälsoinstitutet. Here follows the text from the WHO, the others are exactly the same.

Adults aged 18–64 should do at least 150 minutes of moderate-intensity aerobic physical activity throughout the week or do at least 75 minutes of vigorous-intensity aerobic physical activity throughout the week or an equivalent combination of moderate- and vigorous-intensity activity. Aerobic activity should be performed in bouts of at least 10 minutes duration. 

For additional health benefits, adults should increase their moderate-intensity aerobic physical activity to 300 minutes per week, or engage in 150 minutes of vigorous-intensity aerobic physical activity per week, or an equivalent combination of moderate- and vigorous-intensity activity. 

Muscle-strengthening activities should be done involving major muscle groups on 2 or more days a week.

We immediately notice that I follow the minimum guidelines of 75 minutes of vigorous-intensity aerobic activity, and two days with muscle-strengthening activities. But we cannot say that I fulfil the guidelines for additional health benefits. On average I do 164 minutes of exercise including strengthening activities. Of course, we might argue that I ride my bike to work, walk the dog, and go shopping so that I easily fulfil the quota. However, the guidelines specify at least ten minutes duration, and in the complete text specify that you should raise your heart rate and break a sweat. Even going as far as specifying that just shopping or walking the dog does not count for most people because the intensity is too low, so that argument does not work.

In the end we must find that I have a hard time keeping up with the guidelines. At the same time, with that activity level I am able to practice judo with our ten to twenty year younger elite and junior players. I am stronger than I ever was, and have as high endurance as I have had since I stopped swimming. For those (like me) who like numbers that means a 170kg dead-lift, a 90kg bench-press and a 124kg back-squat, and endurance-wise a VO2max of around 60ml/(min*kg). Nothing spectacular, but clearly very fit for a 35-year-old nephrophysiologist.

How can we possibly expect our patients, and the public in general to be able to train that much? And, would I actually increase my expected life-span and number of healthy days by more than doubling my training? For breast and colon cancer the guidelines say:

Data indicate that moderate- to vigorous-intensity physical activity performed at least 30–60 minutes per day is needed to see significantly lower risks of these cancers.

60 minutes per day? On average? For enough time to affect cancer mortality? Who the fuck even completed these studies?

Fitness for judo

Physical fitness is a complex parameter that is not easily caught in any one number. As any role-playing gamer knows, there are three basic physical characteristics: constitution (CON), strength (STR) and dexterity (DEX).

In addition, judo competition is divided by weight categories so that each of the stats have to be optimised in relation to body weight. Some judoka have, apparently, rolled the perfect 18, 18, 18 and can beat everyone, but the rest of us will have to do with stats that aren't as stellar, and hopefully, bodies (and opponents) that aren't quite as large.

CON:

In judo constitution, or endurance, means that you have to be able to do two things: Control your opponent for at least five minutes, and launch your own attacks. The former is an inherently aerobic task because of it's length, but it is broken into shorter intervals by all sorts of breaks. At the same time the latter is anaerobic on the verge of nonaerobic. That is, during a match you use enormous amounts of energy very quickly, when attacking or defending, and then you have to re-coup this oxygen debt time and time again in the lulls of the fight.

STR:

For any given technical level, the stronger judoka always wins. The easiest way to get stronger is to increase muscle size, this increases the number of motor units and makes you stronger. It also makes you heavier. That's the reason for weight categories. Another way to become stronger is to learn how to activate as many muscle fibers as possible at the same time, while relaxing the opposing muscles as much as possible. This is an important reason for building strength using the movements that will actually be used in judo, and not only by lifting weights.

DEX:

Dexterity can be separated into speed and limberness, where speed is the most important. It is important to be limber enough to perform all techniques, but there are always techniques that require less flexibility. However, if you are faster than your opponent, he will be hard brought to avoid your attacks. Speed in judo means how quickly you can step and turn into your technique or out of your opponents. It also means how quickly you are able to notice and react to an opening in your opponent's defense. Both require very specific training, which is why years of recreational judo has surprisingly little impact on the ability to beat competitive judoka (not to mention that they have higher CON and STR as well, or do they?).

Next up will be a more detailed look at CON. How do competitive judoka perform, and how much do I have to catch up?