Chapter 13. Simulation

In this chapter I describe my solution to a problem posed by a patient with a kidney tumor. I think the problem is important and relevant to patients with these tumors and doctors treating them.

And I think the solution is interesting because, although it is a Bayesian approach to the problem, the use of Bayes’s theorem is implicit. I present the solution and my code; at the end of the chapter I will explain the Bayesian part.

If you want more technical detail than I present here, you can read my paper on this work at

The Kidney Tumor problem

I am a frequent reader and occasional contributor to the online statistics forum at In November 2011, I read the following message:

“I have Stage IV Kidney Cancer and am trying to determine if the cancer formed before I retired from the military. ... Given the dates of retirement and detection is it possible to determine when there was a 50/50 chance that I developed the disease? Is it possible to determine the probability on the retirement date? My tumor was 15.5 cm x 15 cm at detection. Grade II.”

I contacted the author of the message and got more information; I learned that veterans get different benefits if it is “more likely than not” that a tumor formed while they were in military service (among other considerations).

Because renal tumors grow slowly, and often do not cause symptoms, they are sometimes left untreated. As a result, doctors can observe the rate ...

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