Francis Drake, Scurvy, Drimys Winteri and Cluster Randomised Trials.
OK, this is my first blog post, so let's explain how we got here: a year ago I was travelling in Patagonia for my honey moon. Next to one of the dozens of amazing glaciers sitting down the peaks of Tierra del Fuego, a forest of Drimys Winteri.
A guide told us a story. I then started annoying Thea, my fresh wife, with the details of why this was a very interesting story from a statistical perspective. I do this all the time, and she usually bears with me. But this time she asked "why don't you start a blog?". "Why not?". I started collecting all the stories that I found interesting, and now I am ready to share these "Stats of the Quart".
So it is nothing but natural for me to start from that story...
The curse of every sailor
The protagonist of this story is quite an unlikely one: Francis Drake. Since I was a kid, I have always been fascinated by explorers: people with a desire to push themselves beyond known limits in their quest for knowledge. Dante would have put them in Hell with Ulysses just for that. I wouldn't. Yet, one has to ackowledge that most explorers, from Columbus to Magellan, were complete and pure arseholes.
Francis Drake was no exception. He was surely one of the greatest explorers of the 16th century. However, he was also a privateer, a pirate and a slave trader.
In 1577, he sailed aboard the Pelican to start the circumnavigation of the globe. Once landed in Patagonia, Wikipedia tells us of the important records that he set with his people:
In the Magellan Strait Francis and his men engaged in skirmish with local indigenous people, becoming the first Europeans to kill indigenous peoples in southern Patagonia.
Francis' goal was to reach the Pacific Ocean. In order to do that, the only known passage at that point was the Strait of Magellan. This was a very difficult one to sail, and was inhabited by people that had been described by Magellan as "10-Foot Giants". Before adventuring into the strait, Drake and his men spent some time acclimatising in Patagonia, and learned to communicate with locals with words, rather than swords.
After the Atlantic crossing, part of the crew had started to experience the first symptoms of what was known as the curse of all sailors: scurvy. Scurvy is estimated to have killed around 2 million sailors between 1500 and 1850. It causes tiredness, sore limbs, gum disease and bleeding from the skin. Nowadays we know it is caused by a lack of vitamin C, but at that time this was not so well known. The fact that citrus fruits could help prevent scurvy has been reportedly discovered and forgotten tons of times, but nobody (likely) suspected that aboard the Pelican.
Back to the Drimys Winteri
When the natives saw some of the crew getting symptoms, they suggested that a local plant was the solution. They started giving to these sailors an infusion made with its bark. Sailors started indeed feeling better, but it was not clear whether this was due to the bark infusion, or to anything else that had changed since they set foot in Patagonia. Captain Wynter ordered the collection of large amounts of bark of the plant that was henceforth known as Drimys Winteri.
Here the story hits a fork in the road: while our guide, and another local, told us a version of it, on the web I could only find another version. Whichever true, both are, statistic-wise, very interesting, so I am going to tell both of them.
Version #1: the first Cluster-Randomised Trial
According to our guide, Francis was not convinced that the improvement in the sailors' health was per-se a proof that the infusion was working. He then decided to make a simple experiment. By that time, three ships were left in Drake's expedition: the Pelican, the Marigold and the Elizabeth. He then ordered barks to be loaded on one of the ships only, to compare what would happen to the different crews. This was perhaps the first Cluster-Randomised Trial in history.
Randomised trials are experiments where participants are randomly given one of a set of treatments and where a variable of interest (the outcome) is compared between groups at the end of the study. For example, suppose we wanted to know whether paracetamol was better than mint candies against headaches. In a randomised trial, we would take patients with headache, randomly decide which treatment to give them (for example tossing a coin) and compare the proportion of patients in the two groups still with headache after a couple of hours.
Sometimes, though, assigning treatments to individuals can be tricky. This can be for example for ethical reasons. Imagine doing the mint candy/paracetamol trial in a group (what is known as "population") of children aged 5-7. As soon as they found out that some children were getting mint candies, those getting paracetamol would be quite upset. But if the whole class got the same pill, then nobody would complain anymore.
There can be tons of other (more serious) reasons for randomising treatments to whole groups rather than individuals: for example, if treatment is delivered at the group level. One example is when treatment is mosquito disinfestation of an area where several study participants live.
What was the result of this first Cluster Ramdomised Trial? When reaching the Pacific Ocean, sailors aboard the Pelican were feeling much better than on the other ships. Indeed, they were the only ones surviving the strong winds and waves of the not very "pacific" sea, while the Marigold was lost and the Elizabeth forced to sail back to England.
Version #2: a Case-Control study
The second version of the story is that no reasoning was made when the three ships sailed towards the Pacific Ocean. Barks were loaded on all ships, and at the end of the Strait of Magellan fewer sailors than usual were experiencing scurvy symptoms. Drake then reportedly took a sample of "cases" (i.e. sailors with symptoms) and compared them to a sample of "controls" (i.e. sailors feeling absolutely fine). He then asked them whether they had taken bark infusions or not. This is a rather simple example of what is instead known as a Case-Control Study. It does not entail assigning patients to a specific treatment, but only observing what they did in the past. For this reason, it is known as a type of observational, rather than interventional, study.
The evidence collected from one of such studies is generally thought to be less strong, as they are affected by confounding. We will talk about confounding more in depth in another post, but for the moment we can just say that we cannot be sure that it was indeed the infusion preventing scurvy, and not something else that was done/taken more on average by people who also drank infusions.
Going back to our children example: if we took a group of children with and without headache, we could check what proportion of children in the two groups ate mint candies to check whether there was an indication that they prevent headaches. [Not going to talk about paracetamol, as I sincerely hope no child would willingly choose to eat paracetamol instead of mints!]. The end of version #2 of our story, is that most sailors feeling well had drunk infusions, while none of the sailors with scurvy had taken any. Hence, from there on, all sailors were told to consume the miracoulous plant.
Inventions and ideas
Throughout the centuries, there is not a single invention, or discovery, that can really be considered as the property of a single person. That is the reason why often inventions are claimed by more than one person, creating famous debates, such as: "who invented the radio? Was it Marconi or was it Tesla?", "what about the telephone? Was it Meucci, Gray or Bell?".
With statistical concepts, this is even more true. While it was not possible to invent the phone before mastering electricity, stats concepts only require thinking and have, to a certain extent, always been inside human minds. It is for this reason that I always find incredibly difficult to establish who invented things like Clinical Trials. For different reasons, different people are considered by some as the fathers of clinical trials, including Ronald Fisher, Austin Bradford-Hill and James Lind.
If the true version of the Francis Drake story was the first one, then his role in the development of Cluster Randomised Trials would theoretically be not much different from that of James Lind for Individually Randomised Trials: he recognised the importance of randomisation, and applied it for one of the first times to find a (preventive) treatment for scurvy. He did this, though, with a very small sample (only 3 ships!), and was successful only because of the very strong effect of eating food containing vitamin C in the prevention of scurvy. With most treatments, effects are much smaller, and larger samples are generally needed.
Furthermore, the fact that he selected his own ship to be the active group (i.e. the one getting bark infusions) seems far from the definition of randomisation. The strong suspicion is that he chose to load the barks on his own ship because there was no risk associated with them. Then the question arises immediately: similarly to how he decided that his ship would get the barks, he might have always selected the best options for the Pelican. Best sailors, best food, etc etc. Was it really the infusion that led to improvement in scurvy symptoms, or was it the combination of all other factors?
Whatever the truth, Drake did not solve the enigma of what caused scurvy, nor did he really created new statistical techniques ante-litteram. Nevertheless, he showed incredibly smart causal thinking, ages before any of these concepts were clearly defined.