FITTING A ONE-HIT MODEL TO DATA IN TABLE 5-2

Since 1-hit model gives LCR(0) = 0, fit to number of excess tumors:

Best estimate of "background number with tumors" is 8.
Work with "excess tumors" = (number of rats with tumors) - 8.
Number of excess tumors is out of 62 = 70 - 8, not out of 70.
Compare with proportion of excess tumors out of 62.

A	B	C	D	E	F	G	H
# rats	# with tum	Excess tumors	prop excess	rat dose	hum dose	p_i	lnlike
70	8	0	0	0	0	0
70	26	18	0.290	6.25	1.785	0.0517	-55.64
70	33	25	0.403	20	5.714	0.1563	-54.04
70	41	33	0.532	62.5	17.857	0.412	-48.90
70	48	40	0.645	200	57.142	0.817	-59.07

	q=	0.0297				log lik =	-217.6

C = B - 8 D = C/62 F = E/3.5 G = 1 - Exp(-qF)

H = C*ln(G) + (62 - C)*ln(1-G)

Seed 0.001 doesn't give solution. To find better seed, graph ln(1 -excess prop) vs dose and fit line without intercept: ln(1-c7) = - 0.0211 hum dose, so try seed 0.02.

Note: Graph suggests one-hit fit won't be good:

hum dose	1-hit	exs prop
0	0	0
1.785	0.0521	0.29
5.714	0.1575	0.403
17.857	0.4147	0.532
57.142	0.8199	0.645