Tuesday, March 22, 2011

Breast Cancer Recurrence New York Times Article

There is an interesting article in the New York times about a doctor who refused to discuss the probability of recurrence of breast cancer with one of his patients recovering from breast cancer therapy.  The article is written by the patient’s husband who deems the doctor’s attitude to be quite bizarre.  So far there are 6 pages of comments to this article.  What is notable is that in both the original article and the comments, no one has yet attempted to provide an estimate of the recurrence probability. 

Well, here goes: the following table shows the estimates of the recurrence rates of 5, 10 and 15 year periods.  The results are from an analysis conducted by Freedman et al.

Years after First Occurrence 5 10 15
Local recurrence 2% 5% 7%
Elsewhere recurrence 1% 2% 6%
Contralateral recurrence 13%

“Local recurrence” means occurrence in the same quadrant as the first cancer.  Contralateral means the other breast.

When the NY Times writer asked the doctor what the probability of recurrence was, the doctor replied that it didn’t matter. It would either happen or it wouldn’t.  The writer was stunned by the response.  I am not surprised by the doctor.  The doctor, despite being an breast cancer expert, probably did not know the answer, and if he did, most likely did not understand the significance of the question.  I have discussed on numerous occasions in this blog that the medical profession is generally very weak in understanding probability and risks and this affects its ability to optimize treatment.  The doctor’s answer is yet another example.  Probability should be a required course for medical students.  The risks of a disease of occurring, disappearing or reappearing after a treatment protocol should have a direct impact on deciding about whether to follow the original treatment protocol at all and what kind of monitoring should follow.

Sunday, March 6, 2011

Winning at Rock-Paper-Scissors

The New York Times has a web program that let’s you play Rock-Paper-Scissors online.  The interesting thing about this game is that it can be shown that the most efficient strategy is to to play a completely random game.  If you don’t play a random game, then your opponent can estimate your strategy and eventually begin to predict your moves.  This is the idea behind the the New York Times game, which is frustratingly difficult to beat.


The concept in developing a good R-P-S strategy is to understand that it is difficult for humans to select a truly random sequence.  There is a natural tendency to favor some choices, or  avoid some choices or think that long runs of a choice should not occur, so that the chance of a repeat of the last choice goes down the longer the prior run.  In a random process, the chance of particular choice (e.g. Rock) is independent of how many Rock choices have been made in the past run.  There are all sorts of other subtleties that are discussed by the R-P-S community (yes, there is  such a thing together with organized competition).  These include:

  1. Men tend to lead with Rock
  2. People who know how to play R-P-S, know rule 1, so they tend to lead with paper
  3. Women tend to lead with scissors.
  4. Scissors is chosen less than the others, on average
  5. People tend to switch to the last move that beat them.
  6. and so on….


Thus if you can estimate the probability that a player is following a a non-random strategy, then you can develop a winning strategy.  Of course by developing a winning strategy, your opponent can theoretically figure out a strategy to beat you.  This sort of recursiveness could go on forever….   

Saturday, January 15, 2011

The Mismeasure of Man

Here is a fascinating discussion by Ralph Horwitz, MD, professor of medicine at Stanford, on the subtleties of statistics in medicine:

Sunday, January 2, 2011

Age and Happiness

A couple of weeks back, The Economist magazine published a cover article on age and happiness.  The idea of the  article was based on the following chart:

The article went on to say that the level of happiness tends show a “U” shape and improves with age from about 45 onwards.  Andrew Gellman, a statistician at Columbia University, looked at some of the same data and produced the following graph:


He concludes that the that the “U” shape is not nearly as clear as The Economist suggests.  Reference to other studies suggests that the “U” shape might have more to do with weak scientific method.


I think for me, the more important question, is what really is “happiness”.  For a fun read, try Happier by Tal Ben-Shahar,