A bit of light hearted epidemiology.

As it is Wimbledon I thought I might research some tongue in cheek epidemiology. According to Wikipedia about 10% of us are left handed and wanted to compare the number of left handers who have won the singles vs right handers.

There have been 19 different winners since the open era of 1968 and one would expect 1 to 2 left handed winners, giving us an OR of 1.9. However these people are left handers Rob Laver, Jimmy Connors,  John McEnroe, Goran Ivanisevic,  Rafael Nadal, making 5.

So we can conclude that to be a Wimbledon champion, being left handed increases your chances by 250%.

Come on Rollo trash my work 🙂

http://en.wikipedia.org/wiki/Left-handedness

http://en.wikipedia.org/wiki/List_of_Wimbledon_gentlemen’s_singles_champions

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12 Responses to A bit of light hearted epidemiology.

  1. ChrisB says:

    A GLANTZ at your reasoning – you ignored speed, the court surface and health.
    RE..PACE – Blinkers could make DUFF Your service and DOCK RELLiance on perceived speed. The BAULD on’t travel PELLmell ‘cos there’s a BARRON trajectories to the WEST and
    Ambidextrous tennis DOLLs can destROY CASTLEs when using SAND FOR D surface and when it rains each PUDDLE COTEs the their balls in deep doodoo
    GettinG ILL MORE also affects the QUINNtissential dASH for victory

    A bit pained but….. …. that’s epidemiology.

  2. Rollo Tommasi says:

    Oh dear, I don’t know where to begin…….!!! 🙂

    • ChrisB says:

      Well at least I done one good thing today.

      • Junican says:

        Jolly amusing Chris.

        But you haven’t answered Dave’s question! Trash his work!

        Easy-peasy! It is the confounding factors. In this case, it is one very important confounding factor.

        I am left handed. I used to play a lot of table tennis. I won more games than I should have really. This was because I was used to playing right handers, and so used to seeing how they shaped shots. They were not used to playing left handers, and therefore were not used to seeing how I shaped shots. I therefore had an edge.

        There is a single confounder in the ‘smoking causes cancer’ epidemiological idea, and that is that human beings are not all standard models.

    • Try a roll aids rollo!

  3. psst! the sun was in the losers eyes………

  4. ChrisB says:

    Another confounding factor – omission of data re ambidextrous players who play winning shots with the alternate hand and …….
    the political leanings of players. Those with power to the right and determined to win at all costs play best on courts to the right of centre whereas those with leanings to the left believing everyone should win play best to the left of centre. The ambidextrous, more liberal player with friends on both sides plays best in the centre.
    A simple illustration of the frailty of epidemiological studies – results can be subject to bias depending upon where you stand.

  5. Dave,
    You calculation and analysis is right. You got two words wrong: 1.9 is the expected value of the number of lefty winners, not the OR. And since the OR is 2.5 (lefties are 2.5 times as likely to win as righties), you can call this 250% as likely or an increase of 150% but not an increase of 250%

    Someone might argue that the right reference population is not all people, but some subset (men; men who have every played tennis; men who have ever played competitive tennis), and we would want to know what portion of them are left handed. But it is probably about the same, so it does not matter.

    There is no confounding and no measurement error in the particular analysis (unless you got one of the input factoids wrong), and no selection bias since it is universal. There is definitely room for random sampling error, given the small number of observations, but not enough to deny a plausible hypothesis.

    The reason there is *no* confounding is because you phrase this in terms of the propensity of a left hander to win, rather than whether left-handedness causes someone to win. That claim cannot be confounded. Setting that aside (or allowing that I misinterpreted that — it is ambiguous), could their be confounding in the claim “being left handed and in the target population *causes* you to be 2.5 times as likely to be an winner of that tournament “? It sure is not clear how. A lot of what was identified as possible confounding in the comments is not. You would need a situation where something caused left-handedness and increased the chance of winning through some other pathway, which is difficult to imagine. (There are a few more obscure scenarios, but that is the main one.)

    As for plausibility, as a previous commenter noted, being in the minority creates an advantage since opponents are used to the majority. That might create a “top Canadian hockey players are born in January” feed-forward advantage. Or it just might be a lifelong advantage. So this is quite plausibly causal, and indeed there is no other apparent explanation.

    –Carl

  6. Junican says:

    Nice one, Carl. Am I wrong in interpreting what you say as meaning that there are lots and lots of confounders? It seems to me that what you are saying is that the general level of gammy-handers (or ‘sinistres’, if you like) in the population may not be an appropriate comparison base (among other things). Is that not just another confounder?

  7. Junican,
    Thanks for the chance to clarify. There may be a lot of complicating factors in the causal pathway, certainly, but not confounders. Although I still think most of it could just be the “not used to it” factor, along with “if you are a little better then you get more better over time” factor — unlike in baseball pitching where the relationship is asymmetrical, any advantage from being sinister(!) based on spin and such would be balanced by equal advantages to the opponent, so it seems like that would have to be it. I think the confusion is that some people are thinking of confounders as including steps on the causal pathway from being sinister to winning matches. But these are not confounders. The left-handedness is still causing the victories, and those factors are (perhaps) partially explaining why it does so. No confounding there.

    Confounding occurs when there is a difference between the two populations (usually called exposed and unexposed, but in this case those are funny words, so it is just sinisters and normals) in terms of propensity to win that is not caused by the defining characteristic (exposure/sinisterness). But it is difficult to imagine that there is much of that in this case. Even if it was something like “being sinister causes you to learn different physical skills as a toddler and thus become more athletic” that is a case of the characteristic causing the eventual victory. If you want to re-define the claim to be “at the world championship level, being left handed increases your chance of winning”, then that would be a confounder. In that case, being left handed when you enter the championship was caused by being left handed as a toddler, which also caused you to become more athletic. So there is something different about the sinisters in the tournament that is not caused by their *present* state of left-handedness and thus is a confounder when interpreting the effect of that present state.

    Does that make sense?

    The comparison base depends on what question you want to ask. The answer, and the proper analysis to get to it, varies based on what question you are asking. This was always one of my favorites when advising/teaching, and a student would ask “is this the right way to get the answer”. My answer was almost always “it depends on what question you are asking; that is the right way to get the answer to *some* question”. One of the big problem is that most of the people doing epidemiology (or interpreting it) do not understand this. You can ask whatever question you want, and any analysis is the answer to some question. But a common source of error is to do an analysis and claim it answers some variation on the question that it does not really address.

  8. Junican says:

    OK Carl.

    You are absolutely right. I guess that I was wrong to use the word ‘confounder’ to describe ‘a possible conclusion’ which could be the explanation for lefties’s success at Wimbledon. My conclusion is not a confounder. Lefties are used to playing righties, but not vice versa, which gives lefties an edge. Only when I propose that conclusion do ‘confounders’ come into effect, in the sense that lefties might tend to be better sportsmen because of the propensity for lefties to have to cope with a righthanded world. So, it is possible for lefties to be better golfers (despite the fact that striking a golf ball is indifferent) than righties, by and large, because of the fact that lefties have to try harder, physically, in general terms.

    So, if it were true that, in the 1950s, 80% of the population were smokers, and 95% of lung cancer sufferers were smokers, then I could conclude that the additional 15% SHOWS that smoking causes lung cancer. Only when I make that statement do confounders come into effect. A confounder might be that many of the smokers might have lived in places subjected to high levels of smog – for example.

    The question that arises is this: Is it possible to describe confounders before reaching a conclusion? For example, would it be possible, in my above example, to allow for ‘living in places subjected to high levels of smog’ in advance? Clearly, it could be done ‘in theory’, but could it be done ‘in practise’? But also in my example, the question arises about genetics. Does a question arise about the effect of the combination of smog and (tobacco) smoke on people who are unable, because of their financial circumstances, to leave the area where they live for reasonable periods of time? In which case, which has the greater effect – the smog or the (tobacco) smoke?

    Another thing that springs to my mind is this. If confounders were not taken into account, would it not be possible for hundreds of studies to reach the same erroneous conclusion?

    My little brain is starting to hurt. A study is required.

  9. Junican,
    Yes, you have largely nailed it. I gather from your comments (here and elsewhere) that you are not trained in this area so I just want to commend you for understanding confounding better than most people who consider themselves epidemiologists.

    Allow me to clarify what you said: Confounders can only be defined once you hypothesize a particular causal pathway, with the exposure precisely defined (also the outcome, but that has not been ambiguous in this particular discussion). So “being left handed makes you more likely to win Wimbledon” has very little room for confounding. We can make up some stories (like better athletes who are naturally ambidextrous might choose to be lefties because they perceive an advantage; or pre-birth factors that create left-handedness improve athletic ability), but they seem pretty weak.

    However, if the hypothesis is “playing left handed at Wimbledon or the qualifying tournaments gives you an advantage, all else equal, because most people are right handed” then we introduce possible confounders. These include “lefties are more likely to devote their lives to athletics” or, as you suggest, “the challenges of being wrong-handed in the world create early athletic prowess”. A good test of the alternative explanations for the observed association, as you note, is golf, where one possible explanation (advantage over opponents who are not used to it) is eliminated. That is the type of good scientific thinking that is largely absent from health science.

    Similar things can be said about the smoking example, though since smoking is a choice made later in life and is part of a complicated causal web, it is difficult to construct the unconfoundable hypothesis. It would have to be something like “the chance of getting lung cancer increases with the propensity to become a smoker”. But of course what we really claim is “the physical insult from the act of smoking causes lung cancer”, and that introduces the possibility of confounding due to people who are exposed having some difference other than the physical exposure itself, like living near more air pollution or genetics.

    As for your last point, absolutely: If many studies repeat the same mistake (e.g., not correcting for confounding) they can easily all point to the same erroneous conclusion. Making the same error repeatedly is not informative despite the myth that replication is inherently useful. That is one of the reasons, as I have written several times at EP-ology, that meta-analysis is something of a joke. It takes a bunch of studies that might all suffer from the same error, and claims that we know more by synthesizing their results. But obviously this only creates the illusion of knowing something, and tends to hide the original errors even more deeply.

    Glad to know your brain is hurting. That means it is working 🙂

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