Monday, September 8, 2008

Do Statistics Count as Permission?

Today I drove myself to the clinic via the Essential Baking Company and home again, via Museum Quality Framing and the dry cleaner's. Ian really had to be at work (he's publishing a paper that needs revision, in addition to his real job), and my appointment was entirely midday. So we discussed last night and decided we both felt safe with me taking myself. After all, three buses and 1 ½ hours one way is ridiculous, as is $28 cab fare. Particularly when there's a perfectly good, new vehicle sitting unused in the garage and a perfectly good driver who needs to get somewhere.

I pride myself on my driving. I am attentive and assertive, but rarely aggressive. I signal in plenty of time for people to see my intentions, but not before (I'm also not one of those people who signals a turn after already beginning it, for example). I maintain a safe following distance, even still occasionally checking my position behind the next car by finding a fixed item on the side of the road (a sign, a particular tree), and counting off under my breath "one one thousand two one thousand three one thousand". I tend to drive a little fast, yes, about 5 mph over the speed limit. I tend to drive in the left lane, yes, but I am careful to check my rearview mirror regularly and I have hardly ever held someone up. On two occasions, me being in the left lane and next to the shoulder—i.e. an escape route—has kept me from being in a major accident on the freeway. When we go skiing, I typically want to drive home, because I know I won't fall asleep. I rarely look directly at my passengers when I'm driving, instead keeping my eyes on the road and frequently checking all mirrors to make sure nothing is going to come up from behind and surprise me. If someone is tailgating, or too close behind for my comfort, I increase my following distance. I don't answer my phone. I never take both hands off the wheel at the same time.

In other words, I have spent a lot of time perfecting this skill, so it was particularly disturbing for me to be told, 3 ½ months ago, that I had to stop driving because I was at risk of endangering others simply by being alive. Not because I'm reckless, not because I'm aggressive, not because I'm an alcoholic, but because this disease that's been dogging me for the last almost 10 years decided to mess with my head.

At this point, right now, I can't really imagine not worrying a little for the rest of my life about a seizure causing me to lose control of my vehicle and possibly injure or kill someone. It's such a strange feeling, not having any personal control over what has happened in my brain. I am a true child of the American West—my car is my freedom. I love to drive.

But I want to be as safe as possible while doing it. So Ian did some rough figuring. I've been taking Keppra, the anti-seizure medication, since near the end of May, or probably about 3 ½ months. That's about 100 days, at 24 hours per day, or 2400 hours. I have not experienced a single seizure. It takes me about 30 minutes round trip to get to the clinic by car, so approximately 1/4800th of the time I've been on Keppra. That alone is pretty good, but factor in that I was still driving last spring while I was throwing up every morning (my only symptoms of my beset body)—maybe 2 more months before anything was discovered, so another 1440 hours—and that brings my likelihood of a seizure on the way to the clinic down to 1/7680th, or 0.00013.

Obviously, Ian being a statistician and me living with one, we know that statistics mean nothing for the individual—they're merely demonstrating a trend. But it was a trend that made us both feel pretty good about me getting behind the wheel in this case, so we took advantage. And of course I was fine.

I intend to call Dr Jason's nurse tomorrow and ask her to ask him for his opinion. I can't say I'll abide by it completely, but I won't go on the freeway, or for long distances, until I'm cleared. When I told that to my nurse today at the clinic, she said "He'll tell you no, that you should wait a couple weeks until your next brain MRI and then you'll talk. He's a responsible physician."

"Unless he meant to tell me I could drive last time I saw him, when I got out of the hospital," I replied hopefully.

"No," said my nurse, "he'll tell you no." But she wasn't angry or disappointed in me—she understood.

I know that Jason will tell me not to drive, at least for a little longer. That's probably part of the reason why I didn't call him this morning. But he did say, right before I left the hospital, that my brain had simmered down enough that he no longer thought I was likely to have a seizure. It's not the same as saying "Here are the keys to my new Ferrari, why don't you take it and speed down the freeway and through neighborhoods full of children," but it was a highly educated guess at my level of health, and really, that's the best anyone can ever hope for.


Ian said...

First of all, let me ad the disclaimer that Calin is going to do whatever she wants, and I don't think my statistics have much influence on her either way.

Next let me note that my original calculation of 7680 half-hour periods without a seizure implies that the probability of a bad event in any future half-hour is not equal to, but rather less than 1/7680th.
Now I just spent a few minutes (or maybe an hour) trying to relearn all the statistics I'd forgotten and refine this calculation. Here are my conclusions:

1. The probability of a bad event occurring in a 30 minute period, when it has not yet occurred in 7680 such periods, is unknown. The probability could be high or low. Assuming that all such periods are identical with regard to the event occurring, we can make the following calculations about this unknown probability "p".

2. The "maximum likelihood" value of p is 0. No chance of ever occuring.

3. There is a 63% chance that p is less than the 1/7680 figure that Calin suggested.

4. There is also the possibility that p is big and she's just been lucky all this time. However, the probability that p is greater than 1/10, for example, is about 0.0000000000000000000000000000000003.

5. When Calin beat me every one of the first nine times we played cribbage on the way to St. John, during our whirlwind romance, I used these same methods (which I had just learned and not yet forgotten) to calculate that the probability that I was actually better than her, and simply unlucky nine times in a row, was 0.00097. Which I found to be very very depressing at the time. Now that we've played much more cribbage, I can fairly judge that my skill relative to Calin's is not as bad as predicted from those first nine games. So I'm not sure what the lesson there is. I think I got better at cribbage. Hopefully Calin's brain mets are getting better too, making the calculations above all the more conservative.

Ian said...

oops, I just misspelled "add" in that last post. Hopefully the calculations are more accurate than my spelling.

Anonymous said...

Dr. P, who really knows hist stats, read this noted that my interpretations about the probability of p imply that I'm assuming a Bayesian paradigm, which indeed I was unconsciously doing. I believe my answers are correct if we assume a prior distribution for p that is uniform between 0 and 1.

I know hardly anyone will care, but just in case some hard-core frequentists come upon the comment above, I wouldn't want them to cause a nuisance about my interpretations.

Anonymous said...

= laughing quietly to myself