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.

Keeping current

It is a bother to keep current with the scientific literature. Everyone knows it is growing exponentially, although if you look at the new publication histograms on Pubmed they look rather linear. At least over the years after which most papers were actually submitted to Pubmed upon publication, i.e. 1990ies and later. If you pull out the number of publications per year on a given search, let us say "blood pressure" it looks like this:

It rises in fits and starts probably depending on how far back different journals have decided to back-register. If you look at the second graph there does seem to be a flattening of the curve in the sixties and onward indicating that the growth may be linear after all. Sadly, for blood pressure that means 18 000 articles per year as of 2014, and the rate increases with another thousand per year every three years. Working in several fields means trying to keep up with each of them, and makes for a grand total that does not bear thinking about.

Luckily the journals provide current contents feeds that one can read using a RSS. I used Google reader until that was cancelled and now I have moved to the brilliant service CommaFeed, which provides a very clean RSS-reader interface. Below is a screenshot of my current list of journal feeds.

With this kind of list you get a couple of hundred new publications every week, so there is no chance of reading all of them. What I do is skim the titles and selected abstracts in the reader, anything that appears interesting and relevant I will send to Papers to read more thoroughly. In addition, I regularly scan Pubmed for relevant articles, as you do when writing papers, grants, and lectures.

Books for anaesthesiology - General textbooks

Having properly started my residency in anaesthesiology and intensive care medicine I have started looking for textbooks to help me.

In my view medicine has four important levels of knowledge: basic science, clinical practice, evidence based medicine, and epidemiology. Clinical practice will be the focus of your general textbook, but each level deserves its own book because the general textbooks are never good enough. For basic science and EBM the demand for detail and precision is much greater, and epidemiology is often ignored completely.

What follows will be a number of book-reviews of books that I have read, which are useful for anaesthesiology residents. If you have any suggestions, please leave a comment.

So far I have these three general anaesthesia books, which I will say something about.

Morgan & Mikhail's Clinical Anesthesiology (2013, 5 ed. edited by John F. Butterworth IV, David C. Mackey and John D. Wasnick), which is actually available in electronic form through the university library. It's an easy read, unless you are easily annoyed by typos and trivial errors. Instead of references it has suggested reading, which is a mix of reviews, book-chapters and original research. To say that it lacks depth is to state the obvious, but it seems to reflect the state of clinical anaesthesia fairly well.

With that I mean that there is sufficiently scarce evidence that the personal opinion and experience of the individual mentor makes huge differences in how and what you are taught. It is a bit annoying, because you spend a couple of weeks with one specialist behind you, until they are confident to let you run things. Then you change to the next specialist, and they basically think you are insane.

Anestesi (2005, 2 ed. edited by Matts Halldin and Sten Lindahl), a swedish textbook, which is helpful for some practices that are more specifically swedish, and it is generally a good book. Not very thick though, so rather basic.

Anestesikompendium (2004, 8 ed. edited by Rainer Dörenberg), the pocket reference produced by the department in Uppsala. It's brilliant for working in Uppsala for obvious reasons, and includes important practical knowledge like which syringes to use for which drugs, and pre- and postoperative guidelines for different operations and different post-op wards at the hospital.

This early in the residency I am in a read and re-read mode for trying to remember and understand the different anaesthetic regimens and why different specialists prefer different ways of doing things, so it is a good thing to have a couple of books to compare. However, in many cases where practice is significantly different between different specialists they give no, or little guidance, which is why I am seriously considering getting a more complete work. Like 500 pages thicker Clinical Anesthesia by Barash and coauthors, or the two-volume over three thousand pages thick Miller's Anesthesia. In addition there are more specific books covering specific subfields of which I will write more later when I have had time to read them.

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?

Newton's law of cooking chicken

Newton's law of cooling can be used to predict the time of death from the temperature of a corpse and the ambient, which is a silly and boring example. On the other hand, when we are cooking chicken and our better half asks when it will be done (and demands that it be done in a given time), then it becomes an interesting and useful equation. Let us say that it has already cooked for almost an hour, it is around half past seven, and dinner is supposed to be at eight.

The important point is that Newton's law of cooling is equally applicable to cooking because physical law is symmetrical, which means that cooling and heating behaves the same way. The law states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient, or

dT(t)/dt = -k(T(t)-Tambient)

where T is the temperature of the object, t is time, k is a constant, and Tambient is the ambient temperature. It is a differential equation that solves to 

T(t) = Tambient + (T(0) - Tambient)e^-kt

which we can use to calculate the temperature we have to cook the chicken at to be able to serve dinner at eight(-ish). The only problem is that we have to know the constant k which is specific to the particular chicken and filling we have in the oven. Luckily, we used an oven-thermometer, and we kind of remember how long it has cooked already. So, if it took 50 minutes to go from 10°C to 53°C with the oven at 150°C then we can calculate the constant as

k = -1/t ln((T(t)-Tambient) / (T(0)-Tambient))

that is

k = -1/50 * ln((53-150)/(10-150)) = 0.0073 min^-1

In turn, we can use this to calculate what temperature we have to use for the chicken to be done in another 30 minutes as

Tambient = (T(t) - T(0)e^-kt) / (1 - e^-kt) 

 which gives

Tambient = (80 - 53*e^-0.0073*30) / (1 - e^-0.0073*30) = 200°C

Luckily, we didn't have to do the calculations by hand because a bigger nerd than us have created a web-app where we just plug in the known values and get the missing one for free.

Finally, here is the money-shot.

Science, because it works bitch.

(Although the higher temperature did burn the skin a little bit, and it would have been jucier if it had cooked at 150°C the whole time.)