Erin often warns readers of this blog when she's going to talk about Blaise's output, intestine, feeding habits, or other topics that aren't safe for the squeamish. I feel I should do the same here.

I'm going to talk about math.

This all started innocently enough. A week or so ago, Blaise's milk got bumped up another cc/hour and the morning that followed saw a pretty steep increase in output. At 12 hours post-increase in milk, she was already slightly over the amount she was supposed to be outputting. Her nurse assured us that they were all keeping a close eye on her to make sure she wasn't dehydrating and told us that her output might lessen at night. "Yeah," Erin said to her, "She tends to have lower numbers at night."

Now, I see a lot of parents in the lab, and many of them want to tell me something that they just know is true about their kid. Their kid's really good at holding fixation, he's really attentive, she "gets people," he "just loves science" even though he's 9 months old (seriously...I ain't making that one up). Much of the time, they're probably right to some extent. Much of the time, it's really clear that they just couldn't know the thing they just told you. This sounds cold and callous, but VERY few parents know anything about their kids' microsaccades, for example. So what do you do as a researcher when you hear stuff like this? You take it with a grain of salt, tell them that it's very interesting, and move on.

I don't want to say that our nurse that day didn't believe us, but I've been on the other side of that interaction too often to not notice that she did all three steps: 1) Grain of salt taken. 2) "Hm. That's very interesting." 3) Moved on. My point here is not that this is a problem in any way. It's exactly what I've done many times, and I get it. What struck me however, is that Erin and I both know enough statistics to figure out if our intuition's right or not.

How? Well, first we get some data. We've been tracking Blaise's input and output numbers since early February or so and we can always ask for the numbers for each day from her records. Let's start with Erin's intuition about Blaise having lower output at night...is it true? To do this, we need to know about output in 12-hr periods, which one of our nurses happily put together for us. Given 11 days in late February and early March, a two-sample t-test tells us that Blaise's morning numbers are significantly higher than her evening numbers by about 20mL (t(10)=3.5, p=0.006, two-tailed test). What's that mean? The short version of it that will make statistically-savvy people cringe is that Erin's basically right: Blaise poops less at night, and we're pretty sure that we didn't just see differences that look that way by chance.

Can we find anything else out? Well here's a BIG question that I think nobody knows the answer to: What makes output levels vary day to day? Over a given stretch of days, Blaise gets a constant amount of food, but her output can bounce around a good bit. What's going on? We only have access to so many variables that might explain the data, but let's start with the easy ones and see what we can see. Let's say we know her amounts of milk by bottle (PO) and by feeding tube (ENTERAL) for several weeks and we want to try and use those to guess her output. About the simplest thing we can do here is called a multiple linear regression...it basically tells us how to scale and add PO and ENTERAL so that they add up to the right output numbers for every day. If we do this, we can look at the "best fit" of that model below (blue line), plotted with her output numbers (red line):What's going on here? This mostly shows you that input is NOT the whole story by a long shot. Look how flat the blue line is compared to the red one! Her input is nice and steady while her output bounces around it all over the place. Still, we get a decent fit (Pearson's R = 0.76 for those of you that care) meaning that we can account for about 50% of the "wiggle" in the red line

by the shape of the blue line. Here's a funny detail though: When you look at the model coefficients, only the ENTERAL one comes out to be significantly different than zero. That is, statistically, we can't say for sure that the amount of milk Blaise gets by bottle plays a role in determining her output. Now there's a lot of reasons you shouldn't take that at face value: 1) PO and ENTERAL are highly correlated, which means they're fighting for a lot of the same variance in the data. 2) Her bottle feeds were a lot smaller than her enteral feeds for a lot of this data. Still, it's kind of interesting. More interesting to me is the green line on the figure above...that's the difference between our model (the best guess we can make based on input) and the real output. All the wiggling in that green line is variability we can't explain with the amount of milk she's getting. What makes it wiggle like that? I wish I knew (and so does her GI specialist, I bet), but it does look like it's got some structure to it. I'm trying to figure out if there's anything periodic going on, but we need to get some more numbers.

So now the even bigger question...why did I bore you with this? A couple of reasons, I guess. For one, this is what Erin and I do...we spend our lives trying to figure out how things work using tools like this. On some level, I don't know how else to respond to something like this except by sticking to the things I trust most. The other thing is that we were both looking forward to bringing Blaise into our laboratories and having her be part of our work. I think it's hard to articulate to others sometimes why putting an EEG cap on my baby's head or tracking her eye movements with an IR camera would mean something to me. Plenty of people find such things creepy, but for me it's a combination of "Take your daughter to work day" and finding out about her the best way I know how. I think every parent spends the remainder of their lives fascinated by the endless task of figuring out their kids...Erin and I just have a lot of training in that direction and remain excited about using it. For now, this is what we've got; instead of puppet show tasks and brain recordings we've got an Excel spreadsheet and some multiple regressions. Still, it matters.

The last (and craziest) thing is this: No one knows why that red line jiggles up and down. Nobody. There's still no real test of intestinal function, so we basically have to wait and see how Blaise's growth pans out post-op. I often find myself feeling at loose ends when I try and figure out how I can help Blaise thrive, and it's crazy to think I can add anything to the medical literature...but look, I've got a good computer and a lot of math under my belt.

Like I said, this is what we do.

## Sunday, March 29, 2009

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## 4 comments:

Ben,

I done some calculations and I think your math is off.

We don't have a crib yet, but we have time series plots. Repeat after me, Blaise: Shopping is hard. Let's do math!

Hmm. So if you are essentially looking at conservation of mass (input vs output), how does the model account for Blaise's weight gain? Or, is there a way to look at this from an energy perspective: calories in = her growth plus her cries plus her smiles, times her cuteness quotient (personally I think this would be the more fun model to build).

Now I SERIOUSLY can't want to meet you guys.

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