Page 159 - 20dynamics of cancer
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144                                                 CHAPTER 8

                              relative, the faster the rate of progression. Those who progressed more
                              quickly appeared to have an inherited polygenic predisposition. Greater
                              polygenic predisposition was associated with lower age-specific acceler-
                              ation. I discuss various hypotheses about why such predisposition may
                              increase incidence and reduce acceleration.

                                                8.1 Comparison between
                                            Genotypes in Human Populations
                                Comparisons between sporadic and inherited cancers provide power-
                              ful support for multistage theory. With new genomic techniques, com-
                              parison of age-specific incidence between human groups with different
                              genotypes will become increasingly easy to accomplish. So, it is impor-
                              tant to have a clear sense of what has already been done and what can
                              be learned in the future.


                                                      RETINOBLASTOMA
                                Bilateral retinoblastoma, in which tumors develop in both eyes, is an
                              inherited disease. Most unilateral cases occur sporadically. Knudson
                              (1971) predicted that bilateral cases follow age-specific patterns consis-
                              tent with one inherited mutation (hit) and the need for only one somatic
                              hit to produce a tumor. By contrast, Knudson predicted that unilateral
                              cases require two somatic hits to form a tumor.
                                Figure 8.1 compares age-specific incidence of bilateral (inherited) and
                              unilateral (sporadic) cases. The typical measure of age-specific incidence
                              is the number of cases in an age group divided by the number of persons
                              at risk in that age group. However, given the small sample sizes and the
                              difficulty of measuring the base population that represents the number
                              of persons at risk, Knudson analyzed incidence as the number of cases
                              not yet diagnosed at a particular age divided by the total number of
                              cases eventually diagnosed, in other words, the fraction of cases not yet
                              diagnosed.
                                Knudson (1971) fit the bilateral cases to the model log(S) =−k 1 t,
                              where S is the fraction of cases not diagnosed, k 1 is a parameter used
                              to fit the data, and t is age at diagnosis. He fit the unilateral cases to
                                                    2
                              the model log(S) =−k 2 t , where k 2 is a parameter used to fit the data.
                              The figure shows a reasonable fit for both models, with k 1 = 1/30 and
                              k 2 = 4 × 10 −5 .
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