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Think Bayes by Allen Downey

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Serial Correlation

The results so far are based on a number of modeling decisions; let’s review them and consider which ones are the most likely sources of error:

  • To convert from linear measure to volume, we assume that tumors are approximately spherical. This assumption is probably fine for tumors up to a few centimeters, but not for very large tumors.

  • The distribution of growth rates in the simulations are based on a continuous model we chose to fit the data reported by Zhang et al, which is based on 53 patients. The fit is only approximate and, more importantly, a larger sample would yield a different distribution.

  • The growth model does not take into account tumor subtype or grade; this assumption is consistent with the conclusion of Zhang et al: “Growth rates in renal tumors of different sizes, subtypes and grades represent a wide range and overlap substantially.” But with a larger sample, a difference might become apparent.

  • The distribution of growth rate does not depend on the size of the tumor. This assumption would not be realistic for very small and very large tumors, whose growth is limited by blood supply.

    But tumors observed by Zhang et al ranged from 1 to 12 cm, and they found no statistically significant relationship between size and growth rate. So if there is a relationship, it is likely to be weak, at least in this size range.

  • In the simulations, growth rate during each interval is independent of previous growth rates. In reality it is plausible that tumors that ...

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