In one Mega study with nearly 50,000 participants the lifetime risk of ultimate mortality after a first attempt was 53%. So while 90% of survivors do not go on to complete suicide, this does not taken to account the entire population, the majority of which is dead and not factored into the model.
During the 21-31 year follow-up, of the 48 649 people admitted to hospital after an attempted suicide, 5740 (11.8%) later successfully committed suicide (table 1)
⇓. Attempted suicide by poisoning was the most common method (83.8% of attempters) and was linked to 4270 later suicides. The highest relative risk for eventual successful suicide (53.9% in men, 56.6% in women) was found for those in whom the index attempt was by hanging, strangulation, or suffocation.
In one large study they found that 59% of first attempt survivors later reported that their attempt was a cry for help but not a genuine repudiation of their life. In another swedish study involving around 10,000 participants, 69% of those who attempted suicide by hanging and had a psychotic disorder died from suicide within one year.
It's counterintuitive that the greatest predictive factor to a subsequent suicide attempt is a previous suicide attempt.
The greatest confounding factor in all studies was that the all suicidal subject sample group were selected from patients that were brought in to the emergency department. The other limitation in these studies was that the suicidal subjects that died we're not included in large part simply because they go straight to the morgue and are unable to be located or confirmed dead.
So if you have 10,000 subjects that have made a previous attempt, 400 would die if one in 25 attempts result in death. The subject study population now becomes the remaining 9,600 who attempted but did not die.
To get an actual reliable statistic one would have to track down those 9,600 subjects over time until natural death. Among the remainder, the difficulty is that most that reattempt and die using the 1:25 ratio are 384 dead, but since ratios can't be used as an assumption the actual study subjects would have to be located. A majority end up as missing persons, overdoses ruled as accidental, end up in the morgue instead of the emergency department where previous studies used records from instead of all sources and/or locating next of kin for collateral information on method of death becomes prohibitive.
If you have a higher chance of reattempting after the first attempt, then we're going to see greater mortality across the board except those that are dead cannot be come back to testify with the 90% of survivors that they would have decided to not attempt again.