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

Table 3 Comparing the suitability of different models relating log RR to amount smoked by current smokers, expressed as d = cigarettes per day/10

Model	Parameter value1	Fitted coefficient(s) (SE)	Deviance	DF	Deviance explained (%)
Null	-	-	24894.53	97
Linear: log RR = β1d	-	β1 = 0.6107 (0.0046)	7265.32	96	70.82
Quadratic: log RR = β1d + β2d2	-	β1 = 1.4121 (0.0130), β2 = -0.1792 (0.0027)	2907.39	95	88.32
Cubic: log RR = β1d + β2d2 + β3d3	-	β1 = 2.1915 (0.0266), β2 = -0.6346 (0.0138), β3 = 0.0633 (0.0019)	1779.05	94	92.86
Power: log RR = β1dY	Y = 0.32	β1 = 1.8922 (0.0124)	1512.49	96
	Y = 0.33	β1 = 1.8691 (0.0122)	1506.19	96
	Y = 0.34	β1 = 1.8457 (0.0121)	1506.07	96	93.95
	Y = 0.35	β1 = 1.8222 (0.0119)	1511.92	96
	Y = 0.36	β1 = 1.7986 (0.0118)	1523.54	96
	Y = 0.50	β1 = 1.4673 (0.0097)	2179.71	96
	Y = 1.00	β1 = 0.6107 (0.0046)	7265.32	96
	Y = 2.00	β1 = 0.0969 (0.0010)	14739.19	96
Log: log RR = β1log d	-	β1 = 1.2265 (0.0107)	11674.70	96	53.10
Exponential: log RR = β1exp d	-	β1 = 0.0120 (0.0002)	19480.21	96	21.75
Log-with-baseline: log RR = β1log (1 + Wd)	W = 7.5	β1 = 0.8520 (0.0056)	1466.21	96
	W = 7.7	β1 = 0.8456 (0.0055)	1465.37	96
	W = 7.9	β1 = 0.8394 (0.0054)	1464.88	96
	W = 8.0	β1 = 0.8364 (0.0055)	1464.76	96
	W = 8.1	β1 = 0.8334 (0.0054)	1464.71	96	94.12
	W = 8.2	β1 = 0.8305 (0.0054)	1464.73	96
	W = 8.3	β1 = 0.8277 (0.0054)	1464.82	96

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