Every time there is a suicide there is a criticism that the person should have been admitted. The trouble is that the baseline rate of death, even in those who have made an attempt, is too low to predict. Bayes’ Theorem suggests that, if the ten-year suicide rate following self harm is 2% (as this paper suggests), a perfect test (99% sensitivity, 99% sensitivity) will have a positive likelihood ratio of 99. However, there will be false positive, and the post test likelihood ratio is two thirds. One third of the time you will be wrong… and note that this is over ten years. (I’m using Medcalc to do the math)

Although the literature is difficult to interpret, the suicide rates in the present study (projected as 2% over 10 years) are lower than those reported previously following self-harm. From previous reports, the median suicide rate after self-harm at 1 year is 1%, 3% for 1–5 years, 3% for 5–10 years and 7% for >10 years. The suicide rate in the first year after self-harm, has been reported as being 100-fold higher than the general population . The HATS SMR for suicide was 19.42. The lower suicide rate in the present study may be due to the interventions used in the Hunter region, which include intensive psychiatric assessment and availability of follow-up . This is supported by similar long-term suicide rates from a centre with a similar interest in patients with self-harm. Alternatively the differences may be due to social, cultural or demographic differences between the present study and previous studies. A study performed in Denmark in patients who had presented with self-poisoning found a higher suicide rate and a ratio of male: female suicide closer to unity, than in the present study, but the background suicide rate for that population was also higher.

Should we do simple interventions? Probably yes. But hospitalization is not simple. Or cheap. And it may harm. Better to consider what the hunter do: assess and follow up, even though the intervention trials do not show much difference when doing such.

UPDATE.
This is from an earlier paper, with a suicide rate after self harm attempts of 8% over 12 years. From Finland. It notes that the all death rate is also increased. The baseline rate matters, the positive predictive value is now 89% over the 12 years for a perfect test.

The trouble is that there are no perfect tests, and these are loaded populations.