Well, ahhaha is correct that an odds ratio is different than a probability. Take it from somebody trained in epidemiology.
Odds ratios state a mutltiplicative relationship between two outcomes but they are not necessarily exhaustive of all possible occurrences. Taking a published study I just read, the odds ratio of developing post traumatic stress disorder after a car crash if you had a past diagnosis of PTSD is 10:1. This means you are ten times more likely to develop it than somebody without PTSD before their car crash. But it doesn't mean that 10 out of every eleven car crash victims had PTSD before their car crashes. If the probability of developing PTSD after a car crash without premorbid PTSD is .02 and prob of getting it again if you had it is .20, the odds ratio is 10:1, even though you have depleted only 22% of all MVA victims.
Incidentally, when you read about disease prevalence in the newspapers, statistics are usually stated in terms of odd ratios, e.g., if you eat an apple treated with agar, you are 1.5 or 50% more likely to get stomach cancer." Of course, people get frightened and call their congressmen. But the astute reader should always ask "1.5 times what?". If the prevlance is 1 per million, that would mean 1.5 per million people who ate apgar are diagnosed with cancer. And that is the problem with odds ratios: They artificially inflate differences at extremes of a distribution.
Doc Stone |
