> Are they accounting for the fact that people who are admitted with suicidal thoughts will tend to be those much more prone to suicide in the first place?

How certain are you that this is a fact? I agree that is seems like common sense on the surface, but that might not be the case. The closest I could find in the study was this:

> However, the findings should curb enthusiasm for restrictive interventions directed at patients labeled as having high risk of suicide by virtue of demographic or clinical variables. Our figures suggest that 0.28% of all discharged patients can be expected to commit suicide during the first 3 months after discharge. The modest statistical strength of suicide risk assessment means that even patients who are classified as having high risk because of their suicide risk factors will have a low absolute probability of suicide over clinically meaningful time frames, whereas patients with a low risk for suicide will still have a probability of suicide that is many times that in the general community.

It also seems that largest factor, and perhaps a better determinant of severity, is the number of times one is (re)admitted.

> People who come home from the hospital after being admitted for cancer treatment will have a much higher cancer death rate than the general population

How much higher?

Do you think this statement is comparable to cancer treatment?

> Our data suggest that the suicide rates among discharged patients have not decreased in the past 50 years. This is a disturbing finding considering the increase in community psychiatry and the availability of a range of new treatments during this period.

I think this is the take away from the study that is also important:

> However, the very high suicide rates calculated in this study and the known limitations of suicide risk assessment suggest that a focus on clinical risk assessment might mislead clinicians into thinking that some patients can be regarded as having low risk after discharge. Our findings better support the views of authors who believe in a more universal approach to suicide prevention that might focus on periods of high risk but that extends for periods of years.

Also, I need to clarify one thing. I apologize for any confusion. I realized how half-finished my initial comment was. I did not mean to imply the damage from facilities comes from treatments per se, though there are still risks with all treatments. I should have clarified that damage can occur from the systems surrounding the facility. The (incorrect) stigma surrounding admission, the potential police interventions, the medical debt from being admitted, loss of certain rights/job prospects, etc.. Yes, the facilities do help some individuals, that is their purpose, but some people are hesitant to say, call the hotline, out of fear of being committed, which can also be damaging.

I'm quite confident that people admitted to institutions for suicidal thoughts are much more prone to suicide.

But it doesn't actually matter to my point. It's a very reasonable hypothesis, true or not. It needs to be addressed as a potential confounding factor, either by showing it's not true, or by showing that the size of the observed effect is greater than the effect from the confounding factor.