Dose-response relationship of lung cancer to amount smoked, duration and age starting

Table 8 Comparing the suitability of different models relating log RR to duration of smoking by current smokers, expressed as d = years smoked/10

Model	Parameter value1	Fitted coefficient(s) (SE)	Deviance	DF	Deviance explained (%)
Null	-	-	6161.11	35
Linear: log RR = β1d	-	β1 = 0.5134 (0.0069)	672.01	34	89.09
Quadratic: log RR = β1d + β2d2	-	β1 = 0.6718 (0.0237), β2 = -0.0300 (0.0043)	623.20	33	89.88
Cubic: log RR = β1d + β2d2 + β3d3	-	β1 = 0.6788 (0.0607), β2 = -0.0330 (0.0243), β3 = 0.0003 (0.0025)	623.19	32	89.89
Power: log RR = β1dY	Y = 0.50	β1 = 1.1576 (0.0156)	682.56	34
	Y = 0.72	β1 = 0.8180 (0.0110)	619.30	34
	Y = 0.73	β1 = 0.8049 (0.0108)	618.93	34
	Y = 0.74	β1 = 0.7919 (0.0106)	618.75	34	89.96
	Y = 0.75	β1 = 0.7791 (0.0105)	618.76	34
	Y = 0.76	β1 = 0.7665 (0.0103)	618.95	34
	Y = 1.00	β1 = 0.5134 (0.0069)	672.01	34
	Y = 2.00	β1 = 0.0863 (0.0013)	1426.44	34
Log: log RR = β1log d	-	β1 = 1.5870 (0.0215)	708.96	35	88.49
Exponential: log RR = β1exp d		β1 = 0.0045 (0.0001)	4222.01	35	31.47
Log-with-baseline: log RR = β1log (1 + Wd)	W = 0.10	β1 = 6.4054 (0.0861)	629.58	34
	W = 0.15	β1 = 4.6503 (0.0625)	623.99	34
	W = 0.18	β1 = 4.0572 (0.0545)	622.82	34
	W = 0.19	β1 = 3.9001 (0.0524)	622.69	34
	W = 0.20	β1 = 3.7581 (0.0505)	622.67	34	89.89
	W = 0.21	β1 = 3.6293 (0.0488)	622.74	34
	W = 0.22	β1 = 3.5117 (0.0472)	622.89	34

¹Note that we only sought the best-fitting value of W and Y to two decimal places.