Table 2 Results of the GAM analyses fitting non-linear trends to receipt of brief interventions for smoking, or alcohol use respectively

Receipt of intervention for smoking

Model 1 (linear trends)

RR

95% CI

z

edf^a

p

AIC

LRT^b

 Social grade C2DE (ref ABC1)

1.12

1.08, 1.16

6.10

-

 < .001

32,505.24

(χ ²(6) = 33.1, p < .001)

 Underlying trend

1.00

1.00, 1.00

-2.05

-

0.04

 Slope change

0.99

0.98, 0.99

-6.89

 < .001

Model 2 (non-linear trends)

 Social grade C2DE (ref ABC1)

1.12

1.08, 1.16

6.00

-

 < .001

32,477.04

 Smooth term (underlying trend)

-

-

0.05

1.00

0.82

 Smooth term (slope change)

-

-

76.8

3.09

 < .001

Receipt of intervention for alcohol (those with AUDIT 8 or higher^c)

Model 1 (linear trends)

RR

95% CI

z

edf^a

p

AIC

LRT^b

 Social grade C2DE (ref ABC1)

1.58

1.38, 1.81

6.59

-

 < 0.001

6578.0

(χ ²(6) = 2.9, p < .02)

 Underlying trend

1.00

1.00, 1.00

-0.38

-

0.70

 Slope change

0.99

0.98, 1.01

-0.67

-

0.50

Model 2 (non-linear trends)

 Social grade C2DE (ref ABC1)

1.58

1.38, 1.81

6.59

-

 < .001

6577.8

 Smooth term (underlying trend)

-

-

0.67

1.00

0.41

 Smooth term (slope change)

-

-

2.68

1.89

0.40