Thanks for writing this Siobhan, and sorry this comment is very late. I currently see a few key issues (this comment), and a couple of broader concerns (future comment).
1 in 20 children will experience CSA (at some time). This does not mean 1 in 20 children are experiencing CSA (at the current time).
On average, a child experiencing CSA experiences it for 3 years, at a random point between age 3 and 18 (15 years).
(I’m ignoring children under 3, since it is unlikely they can report, so this intervention probably doesn’t help them much.)
For a given child, there is a 1 in 20 chance they experience CSA over 15 years, and the average duration is 3 years (1/5th of the 15 years), so there is a (1 in 20 * 1/5th = ) 1 in 100 chance that a given child is experiencing CSA in a given year.
So the correct value for Assumption 2 is that 1 in 100 children are (over the 12 months) experiencing CSA. This makes the intervention less cost effective.
I think the £29.7K/year figure is wrong, and £<19.8K/year a better figure.
Using the stats from your cited report:
On your assumptions, this intervention causes 1 less year of CSA per disclosure, and the benefit per year is 1⁄3 of the harm to the victim (‘cost as a consequence’ in the link).
Therefore, the intervention saves (1/3 x £59,300 = ) £19,800 per disclosure.
On your assumptions, this intervention doubles the number of disclosures (from 10% chance to 20% chance).
This does not double the ‘cost in response’ costs, because these are ‘top down’ costs. (See Section 2.5 of the report). However, doubling the number of reports probably would require an increase in ‘costs in response’.
I don’t know what a sensible increase would be, but it would require more spending, and thus reduce the cost saved below the £19,800 above. This makes the intervention less cost effective.
I think the 1 in 20 figure might be wrong, and 1 in 10 a better figure.
The 1 in 20 figure (4.8%) comes from asking a group of 11-17-year-olds.
Asking 18-24-year-olds instead gave a figure of 1 in 10 (11.3%).
The first number will be an underestimate (An 11-year-old might be asked, and truthfully say no, but then experience CSA at 14 years old. This method of asking skews the percentages downwards because the group asked are only partway through the ‘relevant period’ of under-18). This makes your intervention more cost-effective.
Combining these, the new cost effectiveness is (1/5 * (19.8/29.7) * 2 * £4450 = ) £1190 averted per professional per year, which is £1680-£2520 per DALY.
I think it’s possible that I’ve misunderstood some/all of these, so would appreciate sanity checks from others.
Here are some less important/certain factors that I think you could also take into account with your model:
This intervention can’t prevent first incidents, which might make it much less effective.
Intuitively, I agree the harm from the first incident is likely larger than subsequent incidents. At a complete guess, I’d say the first incident is maybe 20-25% of total harm.
This intervention by nature cannot prevent first incidents (reporting requires an incident to take place).
The linear model therefore (perhaps significantly) overestimates the benefits of this intervention.
The bar for ‘interacting with’ 30 children might be high.
A teacher sees a child regularly over a long period of time. They therefore build a rapport that could lead to disclosures.
Doctors or police (mostly) see children relatively few times over a short period. It seems less likely they would be disclosed to because of the weaker rapport.
However, this might be outweighed by these professions being more likely to discover CSA (eg. noticing signs of CSA during a medical checkup; investigating other crimes which correlate with CSA offences).
Not all disclosures result in stoppages (sadly).
More importantly, the important factor is not whether a disclosure causes a stoppage, but how much quicker a stoppage occurs after disclosure, compared to no disclosure.
Depending on the length and complexity of the investigative process, this might not prevent much harm (although I hope I’m wrong).
It might be better to say an average of 1.5 years extra without disclosure.
This is half the time of the average CSA ‘cycle’, and assumes that each disclosure happens at a ‘random’ point.
The 1 year is also sensible, because I assume the chance of disclosing is proportional to the length of abuse taking place.
However, maybe the opposite is true. After a few incidents disclosure is likely, but after several incidents it becomes ‘normalised’ in some way, and the chance of disclosing drops dramatically.
This could make the intervention more or less cost effective, depending on how disclosure rates correlate with length of CSA.
Thanks for writing this Siobhan, and sorry this comment is very late. I currently see a few key issues (this comment), and a couple of broader concerns (future comment).
1 in 20 children will experience CSA (at some time). This does not mean 1 in 20 children are experiencing CSA (at the current time).
On average, a child experiencing CSA experiences it for 3 years, at a random point between age 3 and 18 (15 years).
(I’m ignoring children under 3, since it is unlikely they can report, so this intervention probably doesn’t help them much.)
For a given child, there is a 1 in 20 chance they experience CSA over 15 years, and the average duration is 3 years (1/5th of the 15 years), so there is a (1 in 20 * 1/5th = ) 1 in 100 chance that a given child is experiencing CSA in a given year.
So the correct value for Assumption 2 is that 1 in 100 children are (over the 12 months) experiencing CSA. This makes the intervention less cost effective.
I think the £29.7K/year figure is wrong, and £<19.8K/year a better figure.
Using the stats from your cited report:
On your assumptions, this intervention causes 1 less year of CSA per disclosure, and the benefit per year is 1⁄3 of the harm to the victim (‘cost as a consequence’ in the link).
Therefore, the intervention saves (1/3 x £59,300 = ) £19,800 per disclosure.
On your assumptions, this intervention doubles the number of disclosures (from 10% chance to 20% chance).
This does not double the ‘cost in response’ costs, because these are ‘top down’ costs. (See Section 2.5 of the report). However, doubling the number of reports probably would require an increase in ‘costs in response’.
I don’t know what a sensible increase would be, but it would require more spending, and thus reduce the cost saved below the £19,800 above. This makes the intervention less cost effective.
I think the 1 in 20 figure might be wrong, and 1 in 10 a better figure.
The 1 in 20 figure (4.8%) comes from asking a group of 11-17-year-olds.
Asking 18-24-year-olds instead gave a figure of 1 in 10 (11.3%).
The first number will be an underestimate (An 11-year-old might be asked, and truthfully say no, but then experience CSA at 14 years old. This method of asking skews the percentages downwards because the group asked are only partway through the ‘relevant period’ of under-18). This makes your intervention more cost-effective.
Combining these, the new cost effectiveness is (1/5 * (19.8/29.7) * 2 * £4450 = ) £1190 averted per professional per year, which is £1680-£2520 per DALY.
I think it’s possible that I’ve misunderstood some/all of these, so would appreciate sanity checks from others.
You haven’t misunderstood and I very much appreciate the clarity and candour of your feedback!
Here are some less important/certain factors that I think you could also take into account with your model:
This intervention can’t prevent first incidents, which might make it much less effective.
Intuitively, I agree the harm from the first incident is likely larger than subsequent incidents. At a complete guess, I’d say the first incident is maybe 20-25% of total harm.
This intervention by nature cannot prevent first incidents (reporting requires an incident to take place).
The linear model therefore (perhaps significantly) overestimates the benefits of this intervention.
The bar for ‘interacting with’ 30 children might be high.
A teacher sees a child regularly over a long period of time. They therefore build a rapport that could lead to disclosures.
Doctors or police (mostly) see children relatively few times over a short period. It seems less likely they would be disclosed to because of the weaker rapport.
However, this might be outweighed by these professions being more likely to discover CSA (eg. noticing signs of CSA during a medical checkup; investigating other crimes which correlate with CSA offences).
Not all disclosures result in stoppages (sadly).
More importantly, the important factor is not whether a disclosure causes a stoppage, but how much quicker a stoppage occurs after disclosure, compared to no disclosure.
Depending on the length and complexity of the investigative process, this might not prevent much harm (although I hope I’m wrong).
It might be better to say an average of 1.5 years extra without disclosure.
This is half the time of the average CSA ‘cycle’, and assumes that each disclosure happens at a ‘random’ point.
The 1 year is also sensible, because I assume the chance of disclosing is proportional to the length of abuse taking place.
However, maybe the opposite is true. After a few incidents disclosure is likely, but after several incidents it becomes ‘normalised’ in some way, and the chance of disclosing drops dramatically.
This could make the intervention more or less cost effective, depending on how disclosure rates correlate with length of CSA.
Much for me to reflect on there. Thanks again!