Table 3 Results of the GAM analyses fitting linear and non-linear trends to receipt of brief interventions for smoking, or alcohol use, with an interaction between post-March 2020 slope and social grade, overall (Models 1 and 2) and excluding those who did not visit their GP in the past year (Models 3 and 4)

Overall

Model 1 (linear trends)

RR

95% CI

z

edf^a

p

AIC

LRT^b

 Social grade C2DE (ref ABC1)

1.12

1.07, 1.16

5.45

-

 < .001

32,507.15

(χ ²(6) = 33.8, p < .001)

 Underlying trend

1.00

1.00, 1.00

-2.06

-

0.04

 Slope change

0.99

0.98, 0.99

-5.76

-

 < .001

 Slope x Social grade

1.00

1.00, 1.01

0.30

-

0.76

Model 2 (non-linear trends)

 Social grade C2DE (ref ABC1)

1.12

1.08, 1.16

5.99

-

 < .001

32,480.27

 Smooth term (underlying trend)

-

-

0.10

1.00

0.76

 Smooth term (slope change) x ABC1

-

-

48.53

2.43

 < .001

 Smooth term (slope change) x C2DE

-

-

54.21

3.19

 < .001

Excluding those who did not visit their GP in the past year

Model 3 (linear trends)

RR

95% CI

z

edf^a

p

AIC

LRT^b

 Social grade C2DE (ref ABC1)

1.09

1.05, 1.13

4.93

-

 < .001

23,565.39

(χ ²(6) = 9.04, p < .05)

 Underlying trend

1.00

1.00, 1.00

-1.20

-

0.23

 Slope change

0.99

0.99, 0.99

-4.44

-

 < .001

 Slope x Social grade

1.00

1.00, 1.01

0.30

-

0.76

Model 4 (non-linear trends)

 Social grade C2DE (ref ABC1)

1.10

1.07, 1.14

5.98

-

 < .001

23,561.58

 Smooth term (underlying trend)

-

-

0.14

1.01

0.71

 Smooth term (slope change) x ABC1

-

-

23.57

1.76

 < .001

 Smooth term (slope change) x C2DE

-

-

15.93

2.11

 < .001

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

Overall

Model 1 (linear trends)

RR

95% CI

z

edf^a

p

AIC

LRT^b

 Social grade C2DE (ref ABC1)

1.54

1.32, 1.79

5.43

-

 < 0.001

6579.40

(χ ²(6) = 36.2, p < .001)

 Underlying trend

1.00

1.00, 1.00

-0.42

-

0.67

 Slope change

0.99

0.98, 1.01

-0.96

-

0.34

 Slope x Social grade

1.01

0.99, 1.03

0.79

-

0.43

Model 2 (non-linear trends)

 Social grade C2DE (ref ABC1)

1.59

1.39, 1.82

6.66

-

 < .001

6577.75

 Smooth term (underlying trend)

-

-

0.75

1.00

0.39

 Smooth term (slope change) x ABC1

-

-

4.99

2.06

0.20

 Smooth term (slope change) x C2DE

-

-

0.07

1.00

0.79

Excluding those who did not visit their GP in the past year

Model 3 (linear trends)

RR

95% CI

z

edf^a

p

AIC

LRT^b

 Social grade C2DE (ref ABC1)

1.61

1.38, 1.88

6.12

-

 < 0.001

5913.04

(χ ²(6) = 8.7, p < .05)

 Underlying trend

1.00

1.00, 1.00

-0.72

-

0.47

 Slope change

1.01

0.99, 1.02

0.63

-

0.53

 Slope x Social grade

1.00

0.98, 1.02

0.42

-

0.68

Model 4 (non-linear trends)

 Social grade C2DE (ref ABC1)

1.64

1.43, 1.87

7.20

-

 < .001

5907.60

 Smooth term (underlying trend)

-

-

2.03

1.01

0.17

 Smooth term (slope change) x ABC1

-

-

8.58

2.24

0.04

 Smooth term (slope change) x C2DE

-

-

2.06

1.00

0.15