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## Assessing the Scale and Impact of Illicit Drug Markets in Scotland

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### Appendix 3: Economic and Social Cost Model Sensitivity Analyses

There are two parts to this sensitivity analysis. The first determined the most influential inputs to the costs model. The second tested the robustness of the model to the inputs that were guesstimates or assumptions. Given the reported estimated total social and economic cost in the main body of this report is just that, a point estimate, the final part attempts to give an indication of the possible range for the total social and economic cost.

All parts were carried out by first creating distributions around the point estimates that have been used as inputs in the costs model. The approach we have taken for this analysis is to use the distribution of the number of problem drug users (as that is readily available) and assume that all of the other inputs range from 0.5 times the point estimate to 1.5 times the point estimate. We have truncated these where necessary ( e.g. the percentage of male problem drug users cannot exceed 100). Assuming wide ranges (from 0.5 to 1.5 times the point estimate) is helpful for examining how the different input estimates (such as the percentage of PDUs in treatment) affects the total social and economic costs. Please note however, that inputs of recorded occurrences and unit costs taken from published statistics were assumed to have a constant distribution since these are not treated as estimates. These inputs are not included in the sensitivity analyses.

We begin by examining which input estimates are most highly correlated to the total cost estimate. We do that by simulating 10,000 values for each of the inputs. The 10,000 values for the problem drug use estimate come directly from the national prevalence study, which used similar simulated values in deriving confidence intervals. For all other input values, the 10,000 values were randomly sampled from a uniform distribution, going from 0.5 times the point estimate to 1.5 times the point estimate (truncated where required). The 95% confidence interval for the national prevalence estimate is 54,451 to 57,234, with the point estimate of 55,328. Table 1 summarises the rest of the input estimates with their point estimate and the low and high values of the uniform distribution the simulated values are drawn from. Given the complexity of the model it was necessary to split the model into the five areas of health, criminal justice, social care, economic and wider social costs and examine the inputs within these areas with the total cost for that area.

Table 1 Low and high values of inputs into the sensitivity analyses

Description

Area of cost

Point estimate

Low

High

% Male Problem Drug Users

Health/ criminal Justice/ economic

0.70

0.35

1.00

% PDUs in treatment

Health/ criminal Justice/ economic/ wider social

0.41

0.20

0.61

% Males not in treatment

Health/ criminal Justice/ economic

0.68

0.34

1.00

% Males in treatment < 1 year

Health/ criminal Justice/ economic

0.63

0.32

0.95

% Males in treatment > 1 year

Health/ criminal Justice/ economic

0.58

0.29

0.86

% Deaths from Recreational drugs

Economic

0.05

0.03

0.08

% Deaths of those not in treatment

Economic

0.86

0.43

1.00

% Death in treatment < 1 year

Economic

0.14

0.07

0.21

% Poisonings requiring Ambulance

Health

1.00

0.50

1.00

Health

1.00

0.50

1.00

% Mental disorders requiring Ambulance

Health

0.00

0.00

0.50

% Psychiatric disorders admitted to A&E

Health

0.00

0.00

0.50

% Other cases requiring Ambulance

Health

0.59

0.30

0.89

% Other cases admitted to A&E

Health

0.93

0.47

1.00

% Diagnosed with AIDS

Health

0.28

0.14

0.42

% Asymptomatic of HIV

Health

0.26

0.13

0.39

% Symptomatic of HIV

Health

0.49

0.24

0.73

% Injecting associated Infection

Health

0.90

0.45

1.00

% IDUs receiving antiviral treatment

Health

0.50

0.25

0.75

No of GP visits per male PDU not in treatment

Health

1.88

0.94

2.82

No of GP visits per female PDU not in treatment

Health

1.35

0.68

2.03

No of A&E visits per male PDU not in treatment

Health

1.12

0.56

1.68

No of A&E visits per female PDU not in treatment

Health

0.80

0.40

1.20

No of Outpatient visits per male PDU not in treatment

Health

1.14

0.57

1.71

No of Outpatient visits per female PDU not in treatment

Health

3.23

1.61

4.84

No of days spent as inpatient per male PDU not in treatment

Health

4.57

2.29

6.86

No of days spent as inpatient per female PDU not in treatment

Health

7.17

3.59

10.76

No of GP visits per male PDU in treatment < 1 year

Health

1.30

0.65

1.94

No of GP visits per female PDU in treatment < 1 year

Health

1.48

0.74

2.22

No of A&E visits per male PDU in treatment < 1 year

Health

0.63

0.32

0.95

No of A&E visits per female PDU in treatment < 1 year

Health

0.48

0.24

0.72

No of Outpatient visits per male PDU in treatment < 1 year

Health

1.51

0.76

2.27

No of Outpatient visits per female PDU in treatment < 1 year

Health

2.66

1.33

3.98

No of days spent as inpatient per male PDU in treatment < 1 year

Health

1.72

0.86

2.59

No of days spent as inpatient per female PDU in treatment <1 year

Health

2.45

1.22

3.67

No of GP visits per male PDU in treatment > 1 year

Health

0.02

0.01

0.03

No of GP visits per female PDU in treatment > 1 year

Health

1.08

0.54

1.62

No of A&E visits per male PDU in treatment > 1 year

Health

0.58

0.29

0.87

No of A&E visits per female PDU in treatment > 1 year

Health

0.36

0.18

0.54

No of Outpatient visits per male PDU in treatment > 1 year

Health

1.13

0.57

1.70

No of Outpatient visits per female PDU in treatment > 1 year

Health

2.54

1.27

3.80

No of days spent as inpatient per male PDU in treatment > 1 year

Health

1.23

0.61

1.84

No of days spent as inpatient per female PDU in treatment > 1 year

Health

0.85

0.43

1.28

% Males arrested for Breach of Peace not in treatment

Criminal Justice

0.05

0.03

0.08

% Females arrested for Breach of Peace not in treatment

Criminal Justice

0.02

0.01

0.02

% Males arrested for Driving Under Influence not in treatment

Criminal Justice

0.01

0.01

0.02

% Females arrested for Driving Under Influence not in treatment

Criminal Justice

0.00

0.00

0.00

% Males arrested for Soliciting not in treatment

Criminal Justice

0.00

0.00

0.00

% Females arrested for Soliciting not in treatment

Criminal Justice

0.02

0.01

0.03

% Males arrested for Breach of Peace in treatment < 1 year

Criminal Justice

0.15

0.08

0.23

% Females arrested for Breach of Peace in treatment < 1 year

Criminal Justice

0.07

0.03

0.10

% Males arrested for Driving under Influence in treatment < 1 year

Criminal Justice

0.02

0.01

0.04

% Females arrested for Driving under Influence in treatment < 1 year

Criminal Justice

0.00

0.00

0.00

% Males arrested for Soliciting in treatment < 1 year

Criminal Justice

0.00

0.00

0.00

% Females arrested for Soliciting in treatment < 1 year

Criminal Justice

0.01

0.01

0.02

% Males arrested for Breach of Peace in treatment > 1 year

Criminal Justice

0.09

0.04

0.13

% Females arrested for Breach of Peace in treatment > 1 year

Criminal Justice

0.10

0.05

0.14

% Males arrested for Driving under Influence in treatment > 1 year

Criminal Justice

0.02

0.01

0.03

% Females arrested for Driving under Influence in treatment > 1 year

Criminal Justice

0.00

0.00

0.00

% Males arrested for Soliciting in treatment > 1 year

Criminal Justice

0.00

0.00

0.00

% Females arrested for Soliciting in treatment > 1 year

Criminal Justice

0.00

0.00

0.00

No of thefts from person per male PDU not in treatment

Criminal Justice/ Wider social

4.08

2.04

6.12

No of thefts from person per female PDU not in treatment

Criminal Justice/ Wider social

4.26

2.13

6.39

No of thefts from a house per male PDU not in treatment

Criminal Justice/ Wider social

3.12

1.56

4.68

No of thefts from a house per female PDU not in treatment

Criminal Justice/ Wider social

2.24

1.12

3.35

No of thefts from a shop per male PDU not in treatment

Criminal Justice/ Wider social

54.91

27.45

82.36

No of thefts from a shop per female PDU not in treatment

Criminal Justice/ Wider social

61.08

30.54

91.61

No of thefts from a vehicle per male PDU not in treatment

Criminal Justice/ Wider social

6.73

3.37

10.10

No of thefts from a vehicle per female PDU not in treatment

Criminal Justice/ Wider social

0.11

0.05

0.16

No of vehicle thefts per male PDU not in treatment

Criminal Justice/ Wider social

2.62

1.31

3.92

No of vehicle thefts per female PDU not in treatment

Criminal Justice/ Wider social

0.06

0.03

0.10

No of times handling stolen goods per male PDU not in treatment

Criminal Justice/ Wider social

33.13

16.56

49.69

No of time handling stolen goods per female PDU not in treatment

Criminal Justice/ Wider social

32.34

16.17

48.52

No of times Fraud/Forgery per male PDU not in treatment

Criminal Justice/ Wider social

5.20

2.60

7.80

No of times Fraud/ Forgery per female PDU not in treatment

Criminal Justice/ Wider social

9.29

4.65

13.94

No of assaults per male PDU not in treatment

Criminal Justice/ Wider social

2.61

1.30

3.91

No of assaults per female PDU not in treatment

Criminal Justice/ Wider social

0.89

0.44

1.33

No of Criminal Damage incidents per male PDU not in treatment

Criminal Justice/ Wider social

1.30

0.65

1.95

No of Criminal Damage incidents per female PDU not in treatment

Criminal Justice/ Wider social

0.43

0.22

0.65

No of thefts from a person per male PDU in treatment < 1 year

Criminal Justice/ Wider social

0.58

0.29

0.86

No of thefts from person per female PDU in treatment < 1 year

Criminal Justice/ Wider social

0.22

0.11

0.32

No of thefts from a house per male PDU in treatment < 1 year

Criminal Justice/ Wider social

0.32

0.16

0.48

No of thefts from a house per female PDU in treatment < 1 year

Criminal Justice/ Wider social

0.05

0.03

0.08

No of thefts from a shop per male PDU in treatment < 1 year

Criminal Justice/ Wider social

13.60

6.80

20.40

No of thefts from a shop per female PDU in treatment < 1 year

Criminal Justice/ Wider social

23.30

11.65

34.95

No of thefts from a vehicle per male PDU in treatment < 1 year

Criminal Justice/ Wider social

2.73

1.37

4.10

No of thefts from a vehicle per female PDU in treatment < 1 year

Criminal Justice/ Wider social

0.27

0.14

0.41

No of vehicle thefts per male PDU in treatment < 1 year

Criminal Justice/ Wider social

1.52

0.76

2.29

No of vehicle thefts per female PDU in treatment < 1 year

Criminal Justice/ Wider social

0.00

0.00

0.00

No of times handling stolen goods per male PDU in treatment < 1 year

Criminal Justice/ Wider social

18.13

9.06

27.19

No of times handling stolen goods per female PDU in treatment < 1 year

Criminal Justice/ Wider social

5.32

2.66

7.97

No of times Fraud/Forgery per male PDU in treatment < 1 year

Criminal Justice/ Wider social

8.22

4.11

12.34

No of times Fraud/Forgery per female PDU in treatment < 1 year

Criminal Justice/ Wider social

2.76

1.38

4.14

No of assaults per male PDU in treatment < 1 year

Criminal Justice/ Wider social

0.99

0.50

1.49

No of assaults per female PDU in treatment < 1 year

Criminal Justice/ Wider social

0.70

0.35

1.05

No of criminal damage incidents per male PDU in treatment < 1 year

Criminal Justice/ Wider social

0.35

0.18

0.53

No of criminal damage incidents per female PDU in treatment < 1 year

Criminal Justice/ Wider social

0.00

0.00

0.00

No of thefts from a person per male PDU in treatment > 1 year

Criminal Justice/ Wider social

0.35

0.18

0.53

No of thefts from a person per female PDU in treatment > 1 year

Criminal Justice/ Wider social

0.00

0.00

0.00

No of thefts from a house per male PDU in treatment > 1 year

Criminal Justice/ Wider social

0.14

0.07

0.21

No of thefts from a house per female PDU in treatment > 1 year

Criminal Justice/ Wider social

0.00

0.00

0.00

No of thefts from a shop per male PDU in treatment > 1 year

Criminal Justice/ Wider social

2.88

1.44

4.32

No of thefts from a shop per female PDU in treatment > 1 year

Criminal Justice/ Wider social

16.76

8.38

25.14

No of thefts from a vehicle per male PDU in treatment > 1 year

Criminal Justice/ Wider social

0.50

0.25

0.75

No of thefts from a vehicle per male PDU in treatment > 1 year

Criminal Justice/ Wider social

0.19

0.10

0.29

No of vehicle thefts per male PDU in treatment > 1 year

Criminal Justice/ Wider social

0.07

0.04

0.11

No of vehicle thefts per female PDU in treatment > 1 year

Criminal Justice/ Wider social

0.00

0.00

0.00

No of times handling stolen goods per male PDU in treatment > 1 year

Criminal Justice/ Wider social

8.00

4.00

12.00

No of times handling stolen goods per female PDU in treatment > 1 year

Criminal Justice/ Wider social

3.52

1.76

5.29

No of times Fraud/Forgery per male PDU in treatment > 1 year

Criminal Justice/ Wider social

1.05

0.53

1.58

No of times in Fraud/Forgery per female PDU in treatment > 1 year

Criminal Justice/ Wider social

0.10

0.05

0.14

No of assaults per male PDU in treatment > 1 year

Criminal Justice/ Wider social

0.49

0.25

0.74

No of assaults per female PDU in treatment > 1 year

Criminal Justice/ Wider social

0.10

0.05

0.14

No of criminal damage incidents per male PDU in treatment > 1 year

Criminal Justice/ Wider social

0.28

0.14

0.42

No of criminal damage incidents per female PDU in treatment > 1 year

Criminal Justice/ Wider social

0.00

0.00

0.00

% Families solely affected by drug misuse from new Social Work cases

Social care

0.11

0.06

0.17

% Assumed SW referrals for drug misuse

Social

0.80

0.40

1.00

% Child Protection Orders for Parental substance use

Social

0.78

0.39

1.00

% Services for Adults with illicit drug use

Social

0.75

0.38

1.00

Manual workers who cited drugs or alcohol as a reason for their short term absence

Economic

0.04

0.02

0.06

Non-manual workers who cited drugs or alcohol as a reason for their short term absence

Economic

0.02

0.01

0.03

% Absences due to drugs only

Economic

0.41

0.21

0.62

% Unemployed male PDUs not in treatment

Economic

0.86

0.43

1.00

% Unemployed female PDUs not in treatment

Economic

0.90

0.45

1.00

% Unemployed male PDUs in treatment < 1yr

Economic

0.88

0.44

1.00

% Unemployed female PDUs in treatment < 1yr

Economic

0.92

0.46

1.00

% Unemployed male PDUs in treatment > 1yr

Economic

0.87

0.44

1.00

% Unemployed female PDUs in treatment > 1yr

Economic

0.88

0.44

1.00

When the 1,000 simulated values for each of the inputs are combined to provide a total estimate of the size of the drugs market, the total estimate can be correlated against each of the input values to find out which one is the most highly correlated. This can be done in various ways, including using rank correlations (where each value of the input variables are ranked and the ranked total estimate is correlated against these ranks). Partial correlations can also be calculated, in which each of the other variables is held constant to examine the particular correlation between any single input and the total estimated size of the drugs market. The approach we took was to first identify inputs that are significantly correlated by correlating all input variables for each area with the total estimated cost for that area. Once identified, partial correlations were calculated for these significant inputs while holding all other inputs constant to determine the true extent of the correlation between each input and the estimated cost.

Tables 2, 3, 4, 5 and 6 list the most correlated input variables, in order of decreasing importance for each area. The strongest correlation was the correlation between the percentage of PDUs in treatment and the total criminal justice costs. This was a negative correlation indicating that as the percentage of PDUs in treatment increased, the total estimated criminal justice cost decreased.

Table 2 Five input variables most correlated with the estimated total health cost

Cost group

Input

Correlation

Health

No of days spent as inpatient per male PDU not in treatment

0.86

Health

% PDUs in treatment

-0.85

Health

No of days spent as inpatient per female PDU not in treatment

0.78

Health

% of PDUs who are male

-0.74

Health

No of days spent as inpatient per male PDU in treatment < 1yr

0.24

Table 3 Five input variables most correlated with the estimated total criminal justice cost

Cost group

Input

Correlation

Criminal Justice

% PDUs in treatment

-0.95

Criminal Justice

No of thefts from a house per male PDU not in treatment

0.79

Criminal Justice

No of fraud/forgeries per male PDU not in treatment

0.75

Criminal Justice

No of fraud/forgeries per female PDU not in treatment

0.71

Criminal Justice

No of fraud/forgeries per male PDU in treatment < 1yr

0.51

Table 4 Five input variables most correlated with the estimated total social care cost

Cost group

Input

Correlation

Social care

% families solely affected by drug misuse from new Social Work cases

1.00

Social care

% Child Protection Orders for Parental substance use

1.00

Social care

% Services for Adults with illicit drug use

1.00

Table 5 Five input variables most correlated with the estimated total economic cost

Cost group

Input

Correlation

Economic

% of PDUs who are male

0.87

Economic

% male PDUs not in treatment who are unemployed

0.87

Economic

% male PDUs in treatment > 1yr who are unemployed

0.56

Economic

% male PDUs in treatment < 1yr who are unemployed

0.54

Economic

% female PDUs not in treatment who are unemployed

0.37

Table 6 Five input variables most correlated with the estimated total wider social cost

Cost group

Input

Correlation

Wider costs

% PDUs in treatment

0.64

Wider costs

No of vehicle thefts per male PDU not in treatment

0.37

Wider costs

No of house thefts per male PDU not in treatment

0.25

Wider costs

No of thefts from a vehicle per male PDU not in treatment

0.21

Wider costs

No of shop thefts per male PDU not in treatment

0.19

The second part of the sensitivity analyses tested the robustness of the model to the inputs based on assumptions or guesstimates. These variables were:

• % of poisonings that required an ambulance
• % of poisonings that were treated in A&E
• % of mental and behavioural disorders that required an ambulance
• % of cases seen in a psychiatric hospital that were first treated in A&E
• % of other conditions related to recreational drug use that required an ambulance
• % of other conditions related to recreational drug use that were treated in A&E
• % of referrals to the children's panel on the grounds of "misused drugs or alcohol" were due to drugs only
• % of referrals to the children's panel for parental parental illicit drug use
• % of substance misuse services that are specifically drug services

Bivariate correlations between these inputs and the total social and economic cost were calculated and summarised in table 3 below:

Table 3 Correlation between inputs based on assumptions and the total social and economic cost of illicit drug use in Scotland

Input

Correlation statistic

Significance statistic

% of poisonings that required an ambulance

0.00

0.69

% of poisonings that were treated in A&E

0.00

0.78

% of mental and behavioural disorders that required an ambulance

-0.01

0.30

% of cases seen in a psychiatric hospital that were first treated in A&E

0.01

0.54

% of other conditions related to recreational drug use that required an ambulance

0.00

0.70

% of other conditions related to recreational drug use that were treated in A&E

0.00

0.95

% of referrals to the children's panel on the grounds of "misused drugs or alcohol" were due to drugs only

0.02

0.08

% of referrals to the children's panel for parental illicit drug use

0.02

0.08

% of substance misuse services that are specifically drug services

0.04

0.00

The table above shows that the only input that is significantly correlated to the estimated total social and economic cost is the percentage of substance misuse services that are specifically drug services. However, the correlation statistics for this input is small (0.04). Therefore, varying this percentage will have a small impact on the total estimated social and economic cost.

The final part aimed to provide a range for the total social and economic costs. This was calculated by taking the 2.5 th percentile and the 97.5 th percentile of the distribution produced by combining all of the distributions created around the point estimates that have been used as inputs in the costs model. This gave a total social and economic cost of illicit drug use in Scotland that ranged from £2.7bn to £4.1 bn. However, it must be remembered that all of the distributions (with the exception of the one created for the estimated number of PDUs) were created by assuming that the inputs ranged from 0.5 times the point estimate to 1.5 times the point estimate. The values 0.5 and 1.5 were arbitrary due to the lack of available information.