We used the number needed to detain (NND) statistic (1) to describe the consequences of seeking to prevent violence by admitting people to psychiatric hospitals.(2) Because it is the inverse of positive predictive value (PPV), NND can also be used as a measure of the predictive validity of the various methods now used to assess the risk of psychiatric patient violence.

We reported an NND of 6. Fazel et al (BMJ 2012; 345:e4692), in their review of violence risk assessment instruments, report an NND of 2. The authors explain the difference in terms of the characteristics of the papers under review. For an explanation, there is no need to look beyond the properties of the NND statistic and the base rate used to calculate it. Fazel et al calculated their NND using a base rate of 32%. We calculated ours using a base rate of 9.5%. Because it is the inverse of PPV, for a given method of assessing risk NND rises as the base rate falls. The size of the change is also what one would expect given this difference in base rates.(3)

Two things follow. First, the data that Fazel et al report become more consistent with those reported by others. A fall in the NND that is not explained by base rates suggests an improvement in the predictive validity of violence risk assessment. In fact, the figures in Fazel et al for area under the ROC curve (AUC) reflect predictive validities similar to those reported in our paper and elsewhere. Second, and despite the authors’ explicit advice to the contrary, concern over psychiatric patient violence will lead some to conclude that an NND of 2 is a price worth paying, especially if detention leads to treatment. But 2 may not be the relevant number.

The implications of an NND depend on what the base rate refers to. The studies that Fazel et al used to generate an NND of 2 had follow-up periods (39 months) that are much longer than the periods over which the risk assessments of out-patient clinicians are usually intended to apply. Some of the studies used broad definitions of violence that did not require victim injury. By way of contrast, the NND using the 6-month violence rate (with a weapon or causing injury) in the clinical setting of the CATIE study (4)is 15.(3) If psychiatric detention is to be used to improve public safety by detaining people using present methods, someone is going to have to build more hospitals.

Alec Buchanan PhD MD FRCPsych
alec.buchanan@yale.edu

1. Fleminger S. Number needed to detain. Br J Psychiatry 1997;171:287.

2. Buchanan A, Leese M. Detention of people with dangerous severe personality disorders: a systematic review. Lancet 2001;358:1955-9.

3. Buchanan A. Risk of violence by psychiatric patients. Psychiatric Services 2008; 59: 184-190.

4. Swanson J, Swartz M, Van Dorn R, Elbogen E, Wagner H, Rosenheck R, Stroup T, McEvoy J, Lieberman J. A national study of violent behavior in persons with schizophrenia. Arch Gen Psych 2006; 63: 490-499.

Competing interests: None declared