Ooh... click

It is interesting that the suicide rate for people who have just left a mental ward is over twice that of those who have just started anti-depressants, but:

A. Those who end up in the mental ward are more likely to be in that group because they actually attempted to kill themselves, or because they have a plan, whereas the anti-depressant patients and other groups of people might be experiencing suicidal ideation without an attempt or plan, or simply just depression without suicidal ideation.

B. People who plan or attempt to kill themselves are probably a lot more likely to attempt to kill themselves in the future than people who have never attempted and may not even be thinking about it.

In order to know whether admitting a suicidal person into a mental ward does more harm or more good, we'd need a study where they compare outpatient suicide rates with suicide rates in a control group. A good control group would need to consist of equally suicidal people who were not admitted into a mental ward. In order to ensure they were comparable, they'd need to track things like whether a suicide attempt was made, whether the person was on anti-depressants, etc. Also, if nobody had hospitalized the hypothetical control group, there'd be a reason for that. This reason would have to be the sort of thing that wouldn't impact the suicide rate itself. For instance, if those people are living in a place with no legal way to hospitalize a person against their will, it might produce a great control group. On the other hand, if the control group mostly consisted of people who were not hospitalized because they are alone and have no family members or friends who care enough to call 911, this would not be a great control group.

Now I wonder if there are any places where you cannot legally be admitted to a mental ward against your will... or whether there might have been a point in the past when there was a place like this.

It's hard to imagine that there would ever have been a place like this, but you never know.