Predicting the outcomes of a suicide plan

[ScienceIsScary]

Introduction

I spent a few months in psychiatric care recently. During my stay, I had a lot of time to sit and think about things.

One of the things I thought about is suicide plans. I've been interested in understanding how to estimate how likely a plan is to result in survival, injury or death.

If I had to guess, the single biggest factor is probably the suicide method chosen. Some methods like firearms seem significantly more deadly than overdosing on arbitrary drugs.

One of the ways to measure method deadliness is called case fatality. It is essentially the number of people who died with a method divided by the total number of attempters. A few studies have measured case fatality using medical records. Case fatality could be useful for predicting the outcomes of a plan.

My math knowledge is weak, so I'm hoping others can think of ways to improve or correct what I've started. The numbers are only imperfect estimates or back-of-the-envelope calculations. The real world is messy.

Probability

I'm going to be using percentages to express how likely survival or death are. For example, if a fair coin will come up heads half of the time, I'll write:

P(Heads on a fair coin) = 1/2 = 50%

Or if a fair five-sided die will come up with one side 1 out of 5 times, I'll write:

P(One side) = 1/5 = 20%

Equation 1: Simple

P(Dying) + P(Surviving) = 100%

Explanation:
Dying and Surviving are both mutually exclusive but not independent outcomes so we can add them together. For this equation, we're only interested in Dying and Surviving, so they add up to everything (100%).

Alternate forms:
P(Dying) = 100% - P(Surviving)
P(Surviving) = 100% - P(Dying)

Example 1: How likely is someone to survive hanging?
P(Surviving)
= 100% - P(Dying)
= 100% - 61.4%
= 38.6%

The estimate for the probabiiity of dying comes from the lethality on https://www.hsph.harvard.edu/means-matter/means-matter/case-fatality/.

Equation 2: Including surviving with damage (sequelae)

Sometimes surviving with damage is a possibility. This equation captures that possibility as well.

P(Surviving with damage) + P(Surviving without damage) + P(Dying) = 100%

Alternate forms:
P(Surviving with damage) = 100% - P(Surviving without damage) - P(Dying)
P(Surviving without damage) = 100% - P(Surviving with damage) - P(Dying)

Explanation:
Same as Equation 1 but surviving is split into surviving with and without damage.

Example 2: At the start of an attempt, how likely is someone to end up surviving hanging without brain damage?
P(Surviving without damage)
= 100% - P(Surviving with damage) - P(Dying)
= 100% - 16% - 61.4%
= 22.6%

The estimate for the probability of surviving hanging with brain damage comes from table 2 on my website (https://suicideandrecovery.com/suicide/tables-of-suicide-method-probability-estimates/).

Equation 3: Complex suicides (multiple methods)

Sometimes people combine multiple suicide methods. This equation assumes that the probability of each suicide method is independent. It assumes that combining methods will always result in a greater chance of dying. In practice, combined methods might interact to lower the chance of dying.

P(Dying to at least one method) = 100% - P(Surviving first method) × P(Surviving second method)

Explanation:

P(Dying to at least one method)
= 100% - P(Dying to none)
= 100% - P(Surviving both)
= 100% - P(Surviving first method) × P(Surviving second method)

Example 3: How likely is someone to die from combining both hanging and pesticides?
P(Dying to at least one method)
= 100% - P(Surviving hanging) × P(Surviving pesticides)
= 100% - P(Surviving hanging) × (100% - P(Dying by pesticides)))
= 100% - 38.6% × (100% - 26.3%)
= 100% - 38.6% × 73.7%
= 100% - 28.4%
= 71.6%

The estimate for the probability of dying by pesticides comes from Chen VC-H, Cheng ATA, Tan HKL, et al. A community-based study of case fatality proportion among those who carry out suicide acts. Soc Psychiat Epidemiol. 2009;44(12):1005.

I've started a web page to help find probability estimates from studies: https://suicideandrecovery.com/suicide/tables-of-suicide-method-probability-estimates/.

Future work

* Estimating the harm that a suicide method may cause to others using numbers.
* Estimating the harm of a survived attempt using numbers.
* Including the chance of rescue

Acknowledgements

* Lost All Hope for introducing me to lethality.

 

[Aap]

While I enjoy such posts, the analysis is incomplete and oversimplified. To suggest the probability of surviving shooting oneself in the head, after taking an overdose of N, and then falling from a very tall height is greater than shooting oneself in the head is stupid, providing neither method interferes with the other and that "immediate medical intervention" isn't assumed

An example of interference would be drinking N as then trying to shoot oneself in the head. It may be that the individual waited too long to attempt the gunshot and was unable to aim correctly. However, in this case the probability of survival would not drop below that of N itself, unless you are taking extraordinary assumptions, such as the gunshot alerted an ambulance who promptly took the individual in to the hospital, into account. Another example would be an overdose of cocaine and heroin. Both of these can interfere with the method the other uses to kill.

A more complete analysis using Bayesian statistics could better flesh this out. I suspect either bias of the source or incomplete understanding of statistics is the cause of this analysis.

again, I appreciate the post, but this is skewed very heavily towards some assumptions that are heavily biased in favor of survival. When you combine methods that do not interfere with each other, then the probability of survival won't drop below the most lethal method.