99% of subjects found alive are found within about 50 hours. Think about that. Should you call off a search after 50 hours?
Tonight I finished Chapter 7 of Lost Person Behavior. On the last page, I made a mistake, and I should have known better.
On page 89, we read:
A recent comprehensive study looking at just the Oregon database suggests ... that searches may become futile after 51 hours.
Maybe it's just sample size. That study used "only" about 1300 cases, with 185 fatalities. But no, the book reveals that the ISRID data (13,500 cases) backs up the study. However, there is more:
While ISRID results support the conclusion that 99% of subjects who are found alive are found within approximately 50 hours, ISRID results clearly show that a significant number of subjects survive past 50 hours.
Here I thought, By "significant" you just mean 1% of a large number! And that's where I went wrong.
Bob continues: Even out at 72 hours 55% of dementia subjects are found alive. Wait, 55%? I stopped to figure out what I had missed. Intuitively, I had taken the 1% number to indicate my chances of still being alive after 50 hours. But that's not what it said at all. Rather, it looked at all the live finds, and asked how long they'd been out. Going through Chapter 8, I found that in most categories, the chance of being alive after 50h was greater than 60%. I think better in symbols:
- P( >50h | alive ) = 1%
- P( alive | >50h ) = ~60%
When deciding whether to continue the search, use the second line.
What's going on?
It's Bayes again. Basically, very few searches last >50h, and most searches end up in live finds. We want P( alive | >50h ). We have P( >50h | alive ). We need: P(alive | >50h) = P(>50h | alive)*P(alive)/P(>50h) Using the NZ data, which I happen to have here: P( >50h | alive ) = 5/487, or about 1%. That agrees. P( >50h ) = 10/536, or about 2% P( alive ) = 598/651, or about 92% --------------------------------------- So: P( alive | >50h ) = 0.01 * 0.92 / 0.02 = 0.46, or 46%So, overall in the NZ dataset using about 650 cases, about half of searches >50h result in a live find, even though only 1% of those found alive are found after 50h.