Best 100 Fits for m=4 and n= 1

Fit Result 1 for Cancer of the Lower GI Tract (1890s decade)

for European American Males (EAM)

CAL(g) vs. Cell Doubling (g)

Linear-Linear Plot Log-Linear Plot CLOSEUP of Log-Linear Plot Log-Log Plot

CAL(t) vs. Age (t)

Linear-Linear Plot Log-Linear Plot CLOSEUP of Log-Linear Plot Log-Log Plot

Goodness of Fit

The values of INC(h,t) vary more than a thousand-fold among the 18 age of death intervals recorded from maturity to old age (Fig.1). Statistical comparison of CAL(h,t) to INC(h,t) required a term that gave weight to all 18 intervals. Such a term is |log10 CAL(h,t) - log10 INC(h,t)| which is zero when the terms are identical, i.e. their ratio is equal to 1.0. The square root of the average of the square of these 18 terms is here employed as a goodness of fit parameter, GOF(h,t).

GOF(h,t) = {SUM [log10 CAL(h,t) - log10 INC(h,t)]2 /18}1/2

GOF(h,t) may have practical meaning for the general reader as it is akin to a standard deviation of |log10 CAL(h,t)-log10 INC(h,t)| averaged over all adult life. If GOF(h,t) = 0.1 then the 95% confidence limits of the average ratio of CAL(h,t) /INC(h,t) would be 10-0.2 and 100.2 or 0.63 and 1.58. If GOF(h,t) = 0.03 the 95% limits would be 0.93 and 1.07. A GOF(h,t) of greater than 0.1 indicates a poor fit of the model with stipulated parameters n and m or marked errors in the values of INC(h,t) arising from either sampling error or bias. Errors arising from small sample sizes do not contribute significantly to GOF(h,t) when large U.S. European-American cohorts are studied.

Table of Results

Fit RankGoodness of Fit GOF(h,t)F_promF_initfmuR_initiationR_promotionArea
1 0.04631 0.375 0.445 0.948 0.174 3.511e-008 1.233e-002 0.247
2 0.04677 0.375 0.445 0.896 0.174 3.511e-008 1.233e-002 0.240
3 0.04729 0.375 0.445 1.000 0.174 3.511e-008 1.233e-002 0.253
4 0.04773 0.479 0.380 0.635 0.174 2.848e-008 1.233e-002 0.251
5 0.04921 0.375 0.445 0.844 0.174 3.511e-008 1.233e-002 0.233
6 0.04970 0.479 0.380 0.583 0.174 2.848e-008 1.233e-002 0.240
7 0.04991 0.479 0.380 0.687 0.174 2.848e-008 1.233e-002 0.261
8 0.05010 0.375 0.668 0.792 0.174 6.579e-008 1.000e-002 0.257
9 0.05078 0.323 0.516 1.000 0.174 4.329e-008 1.233e-002 0.232
10 0.05098 0.375 0.668 0.844 0.174 6.579e-008 1.000e-002 0.271
11 0.05112 0.583 0.321 0.427 0.174 2.310e-008 1.233e-002 0.244
12 0.05142 0.583 0.321 0.479 0.174 2.310e-008 1.233e-002 0.260
13 0.05415 0.479 0.380 0.739 0.174 2.848e-008 1.233e-002 0.270
14 0.05415 0.375 0.445 0.792 0.174 3.511e-008 1.233e-002 0.226
15 0.05426 0.427 1.000 0.792 0.142 3.511e-003 4.329e-004 0.261
16 0.05453 0.427 1.000 0.739 0.142 3.511e-003 4.329e-004 0.247
17 0.05456 0.687 0.270 0.323 0.174 1.874e-008 1.233e-002 0.249
18 0.05460 0.323 0.744 1.000 0.174 8.111e-008 1.000e-002 0.262
19 0.05607 0.375 0.668 0.739 0.174 6.579e-008 1.000e-002 0.243
20 0.05627 0.375 0.668 0.896 0.174 6.579e-008 1.000e-002 0.284
21 0.05628 0.427 0.592 0.635 0.174 5.337e-008 1.000e-002 0.251
22 0.05633 0.323 0.516 0.948 0.174 4.329e-008 1.233e-002 0.225
23 0.05655 0.375 1.000 0.896 0.142 1.874e-003 5.337e-004 0.246
24 0.05730 0.427 0.592 0.687 0.174 5.337e-008 1.000e-002 0.267
25 0.05737 0.583 0.321 0.531 0.174 2.310e-008 1.233e-002 0.273
26 0.05784 0.427 1.000 0.739 0.142 1.520e-003 5.337e-004 0.247
27 0.05802 0.479 0.380 0.531 0.174 2.848e-008 1.233e-002 0.227
28 0.05810 0.531 0.516 0.479 0.174 4.329e-008 1.000e-002 0.264
29 0.05811 0.427 1.000 0.687 0.142 1.520e-003 5.337e-004 0.233
30 0.05818 0.323 0.744 0.948 0.174 8.111e-008 1.000e-002 0.250
31 0.05833 0.375 1.000 0.948 0.142 1.874e-003 5.337e-004 0.257
32 0.05839 0.739 0.270 0.271 0.174 1.874e-008 1.233e-002 0.256
33 0.05856 0.479 0.592 0.583 0.174 5.337e-008 1.000e-002 0.272
34 0.05893 0.531 1.000 0.531 0.142 1.233e-003 5.337e-004 0.252
35 0.05902 0.531 0.321 0.531 0.174 2.310e-008 1.233e-002 0.240
36 0.05916 0.479 0.380 0.792 0.174 2.848e-008 1.233e-002 0.278
37 0.05947 0.687 0.270 0.375 0.174 1.874e-008 1.233e-002 0.268
38 0.05972 0.531 0.321 0.583 0.174 2.310e-008 1.233e-002 0.250
39 0.05979 0.427 0.445 0.739 0.174 3.511e-008 1.233e-002 0.255
40 0.05981 0.375 1.000 0.844 0.142 1.874e-003 5.337e-004 0.234
41 0.06006 0.427 0.380 0.792 0.174 2.848e-008 1.233e-002 0.241
42 0.06050 0.427 1.000 0.844 0.142 3.511e-003 4.329e-004 0.275
43 0.06067 0.427 0.380 0.844 0.174 2.848e-008 1.233e-002 0.247
44 0.06085 0.427 0.445 0.792 0.174 3.511e-008 1.233e-002 0.265
45 0.06085 0.427 0.380 0.739 0.174 2.848e-008 1.233e-002 0.234
46 0.06114 0.479 1.000 0.635 0.142 2.848e-003 4.329e-004 0.253
47 0.06118 0.531 1.000 0.531 0.142 2.848e-003 4.329e-004 0.251
48 0.06185 0.531 1.000 0.583 0.142 2.848e-003 4.329e-004 0.272
49 0.06191 0.427 0.445 0.687 0.174 3.511e-008 1.233e-002 0.245
50 0.06199 0.323 1.000 1.000 0.142 4.329e-003 4.329e-004 0.223
51 0.06200 0.375 0.445 0.739 0.174 3.511e-008 1.233e-002 0.217
52 0.06216 0.427 0.380 0.896 0.174 2.848e-008 1.233e-002 0.253
53 0.06234 0.479 1.000 0.583 0.142 2.848e-003 4.329e-004 0.235
54 0.06237 0.323 0.813 1.000 0.163 1.000e-007 1.000e-002 0.261
55 0.06262 0.531 1.000 0.479 0.142 1.233e-003 5.337e-004 0.230
56 0.06262 0.531 0.321 0.635 0.174 2.310e-008 1.233e-002 0.259
57 0.06267 0.531 0.321 0.479 0.174 2.310e-008 1.233e-002 0.228
58 0.06268 0.323 0.813 0.948 0.163 1.000e-007 1.000e-002 0.249
59 0.06276 0.635 0.321 0.375 0.174 2.310e-008 1.233e-002 0.258
60 0.06294 0.635 1.000 0.375 0.142 1.000e-003 5.337e-004 0.245
61 0.06294 0.583 0.516 0.427 0.174 4.329e-008 1.000e-002 0.275
62 0.06303 0.583 0.321 0.375 0.174 2.310e-008 1.233e-002 0.226
63 0.06308 0.479 0.668 0.531 0.163 6.579e-008 1.000e-002 0.249
64 0.06325 0.375 1.000 0.948 0.142 4.329e-003 4.329e-004 0.256
65 0.06336 0.375 1.000 1.000 0.142 1.874e-003 5.337e-004 0.269
66 0.06343 0.479 0.592 0.531 0.174 5.337e-008 1.000e-002 0.251
67 0.06356 0.375 1.000 1.000 0.142 4.329e-003 4.329e-004 0.268
68 0.06363 0.375 0.668 0.948 0.174 6.579e-008 1.000e-002 0.297
69 0.06365 0.427 1.000 0.792 0.142 1.520e-003 5.337e-004 0.262
70 0.06371 0.427 0.380 0.687 0.174 2.848e-008 1.233e-002 0.226
71 0.06372 0.375 0.744 0.792 0.163 8.111e-008 1.000e-002 0.258
72 0.06374 0.375 1.000 0.948 0.142 8.111e-003 3.511e-004 0.255
73 0.06378 0.427 0.592 0.739 0.174 5.337e-008 1.000e-002 0.283
74 0.06381 0.427 0.445 0.844 0.174 3.511e-008 1.233e-002 0.273
75 0.06398 0.323 0.516 0.896 0.174 4.329e-008 1.233e-002 0.217
76 0.06415 0.427 0.380 0.948 0.174 2.848e-008 1.233e-002 0.259
77 0.06428 0.479 0.380 0.844 0.174 2.848e-008 1.233e-002 0.285
78 0.06435 0.427 1.000 0.687 0.142 3.511e-003 4.329e-004 0.232
79 0.06436 0.375 1.000 0.896 0.142 8.111e-003 3.511e-004 0.244
80 0.06459 0.427 0.592 0.583 0.174 5.337e-008 1.000e-002 0.233
81 0.06459 0.375 0.744 0.739 0.163 8.111e-008 1.000e-002 0.242
82 0.06475 0.375 0.922 0.844 0.163 1.520e-007 8.111e-003 0.260
83 0.06476 0.583 0.321 0.583 0.174 2.310e-008 1.233e-002 0.284
84 0.06496 0.479 1.000 0.635 0.142 1.520e-003 5.337e-004 0.254
85 0.06508 0.323 0.592 1.000 0.163 5.337e-008 1.233e-002 0.247
86 0.06511 0.479 1.000 0.635 0.142 6.579e-003 3.511e-004 0.252
87 0.06518 0.479 0.592 0.635 0.174 5.337e-008 1.000e-002 0.293
88 0.06519 0.792 0.187 0.271 0.163 1.233e-008 1.520e-002 0.237
89 0.06523 0.479 0.668 0.583 0.163 6.579e-008 1.000e-002 0.272
90 0.06523 0.375 0.922 0.792 0.163 1.520e-007 8.111e-003 0.245
91 0.06527 0.479 0.445 0.531 0.163 3.511e-008 1.233e-002 0.240
92 0.06534 0.531 0.516 0.427 0.174 4.329e-008 1.000e-002 0.238
93 0.06536 0.635 0.225 0.531 0.163 1.520e-008 1.520e-002 0.239
94 0.06545 0.635 0.225 0.479 0.163 1.520e-008 1.520e-002 0.233
95 0.06549 0.479 1.000 0.687 0.142 6.579e-003 3.511e-004 0.270
96 0.06549 0.531 0.380 0.531 0.174 2.848e-008 1.233e-002 0.261
97 0.06557 0.739 0.270 0.323 0.174 1.874e-008 1.233e-002 0.283
98 0.06559 0.323 0.592 0.948 0.163 5.337e-008 1.233e-002 0.238
99 0.06573 0.635 0.380 0.323 0.163 2.848e-008 1.233e-002 0.242
100 0.06580 0.635 1.000 0.427 0.142 2.310e-003 4.329e-004 0.274
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