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.

When is the evidence good enough?

Saturday Morning Breakfast Cereal is the name of a web-comic that is just about as good as xkcd, and they pose some very intimidating questions.

Anecdotal evidence is popular in medicine. Obviously it's not called that. It's called a "case report" or an "observational study". Basically you see a number of patients and then you pick one that supports some notion you have and put it on a pedestal. Another manner of doing it is to collect a number of these cases and call them a case-series. The next level is to collect all your cases and dig around until you find some common feature in all of them or in a sub-population. Finally you get to the level of looking at all people with a certain condition, usually nationality and some disease, and then you can call it "epidemiology". The problem with all of these designs is that if you look hard enough you can find something interesting-looking in any collection of data. This is especially true if you don't care what you are looking for.

The next level of scientific quality is to care what you are looking for from the beginning. This means you pick a group of people and say that, for example: "I believe those with higher blood pressure now will die sooner than those with lower", and then you wait. After some time, in the best case a predetermined time, you check how many have died and draw your conclusions. Such a conclusion might be that high blood pressure is a risk factor for death. This is not necessarily such a bad way of doing science. The problem is that then you start muddling through your data to look for a reason for the difference in death rates, and then you are suddenly producing anecdotal evidence again.

The highest level of evidence is not to use a found population with some difference, but to use a homogenous population and induce a change in some of them while comparing them to the rest. This is experimental science and it is the only way to show causal relationships. You still have to preconceive what you are looking for, otherwise you are still just muddling through the data looking for differences. This means that an experimental study is only valid as such for the question it was designed to answer. If you take the population in an experimental study and look at something else then you are back to doing an observational study, producing anecdotal evidence.

So, what is the problem? Anecdotal evidence often turns out to be correct. This is how much science comes about; you have an anecdote (say a case study, or some epidemiological finding, or a post-hoc analysis of an experimental study) that leads you to a hypothesis. Then you test the hypothesis with an experimental study to see if it holds up. Easy. This is how it is supposed to be. The problem is that anecdotal evidence is often taken for true directly (by the media, policy makers and the public at large), without further testing, and the later experimental evidence does not get the same attention even though the science is better.

For scientists this is not as big a problem as for the public. By following the field you learn what questions are being asked and which study was designed to answer which question. With clinical trials this is solved today by publication of the protocol and hypothesis before the study starts. Pre-clinical papers on the other hand are mostly experimental in nature, but they are often written so that it is not clear if the conclusion is based on the original question or if it is something the authors picked up on the way. This is because there is not enough space to tell the story as it happened, and that it frankly wouldn't be that good a read. The principle is that you take what you have and write the best story possible. That's how to get published. What it also means is that, unless you know the investigators and what their main focus is, you don't know if the study was a preconceived experimental study or a post-hoc study.

Getting know the investigators in your field means going to a lot of conferences and listening to a lot of talks. That's when it is a good thing to have some online comics to fall back to. Because falling asleep is embarrassing.