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

Table 13 Comparing the suitability of different models relating log RR to age of starting smoke by current smokers, expressed as d = (70-age at start)/10

Model	Parameter value1	Fitted coefficient(s) (SE)	Deviance	DF	Deviance explained (%)
Null	-	-	2145.30	27
Linear: log RR = β1d	-	β1 = 0.3681 (0.0085)	276.67	26	87.10
Quadratic: log RR = β1d + β2d2	-	β1 = 0.1987 (0.0349)	251.63	25	88.27
		β2 = 0.0318 (0.0064)
Cubic: log RR = β1d + β2d2 + β3d3	-	β1 = -0.0415 (0.2143)	250.34	24	88.33
		β2 = 0.1304 (0.0870)
		β3 = -0.0100 (0.0088)
Power: log RR = β1dY	Y = 0.75	β1 = 0.5515 (0.0129)	316.69	26
	Y = 1.00	β1 = 0.3681 (0.0085)	276.67	26
	Y = 1.42	β1 = 0.1825 (0.0042)	251.27	26
	Y = 1.43	β1 = 0.1794 (0.0041)	251.24	26
	Y = 1.44	β1 = 0.1764 (0.0041)	251.23	26	88.29
	Y = 1.45	β1 = 0.1734 (0.0040)	251.25	26
	Y = 1.46	β1 = 0.1705 (0.0039)	251.28	26
	Y = 1.50	β1 = 0.1592 (0.0037)	251.67	26
	Y = 2.00	β1 = 0.0668 (0.0015)	284.04	26
Log: log RR = β1log d	-	β1 = 1.1460 (0.0270)	340.23	26	84.14
Exponential: log RR = β1exp d	-	β1 = 0.0058 (0.0002)	852.85	26	60.24

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