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.

Death is loosing out

Originally, Death on his pale horse, was the undisputed leader of the Apocalypse. Lately, however, the general feeling is that he has been usurped by War. Today, we have the honour to present indisputable evidence that this is the case.

Google Ngram Viewer (Thanks to David McCandless at Information is Beautiful for pointing it out to me) is an interactive histogram that plots the frequency of words in Google Books from 1800-2000. On the plot below, you can see that Famine and Pestilence always were part of the chorus while Death had the lead in the duet between him and War. Around 1850, War suddenly found his true voice and overtook Death. From about 1814 he seems to have gone on a solo tour leaving the rests of the Horsemen behind.



We should let this warm our hearts, even though War is topping all the charts, Death does not ride with him, and the Horsemen are certainly not going to Ride Forth any time soon. This is corroborated by statistics of actual war deaths. Not when you look at the number of people killed, but when you look at how many people die of war as a proportion of the population, or how big a proportion of the population will die in warfare.



This is a figure from "War before civilization" (fig 6.2, pg. 90) that I borrowed for educational purposes from a presentation I found on the internets. Can't remember where. Anyway, what it shows is that 20-60% of the male population dies at war in present-day and pre-historic tribal societies. The same number for the western world in the war-ridden 20th century is well below 3%. That includes both the World Wars. What it means is that modern wars only directly effect a small part of the population. We all have to watch it, but that isn't as deadly.

In short, the world is much more peaceful than it seems, and certainly much more peaceful than it ever was. In 2008 the rate of violent death, as in murder or assault, for men was 1/100000 and 1/200000 for women. So, even though War is gaining in popularity Death is loosing out. And no one has seen Ronnie Soak for years.