RCTs are not a club, and other stories of science as rhetorical gloss

2019 November 8
by Daniel Lakeland

Increasingly, "science" is being used as club to wield in order to have power, for example the power to influence policy, or to get career advancement, or the like. The stories are legion on Andrew Gelman's blog: Brian Wansink is an excellent example, he received millions in funding to do his "food industry" research... that didn't have a hope of being correct.

So when my friend posted this video claiming that randomized controlled trials have proven that sugar does not cause kids to become hyperactive, I was skeptical, to say the least.

But at least it's based on the "gold standard" of randomized controlled trials, and presented by someone with a biology background who understands and is an expert on this topic right? (actually, sure he's an MD, but his "research focuses on the study of information technology to improve pediatric care and areas of health policy including physician malpractice..." and he's publishing on an Econ blog. Is he perhaps a bit too credulous of this research?)

So here is where we unpack the all too common situation where meta-analysis of various randomized controlled trials is used as a club to beat people with, regardless of what those trials even say.

Let's start with the meta-analysis linked on the YouTube video. This is Wolraich et al. 1995, a review of quite a few different somewhat related RCTs... which is hidden behind a paywall. If you manage to access it you will find that it cites 37 studies. Some of the results are summarized in this graph:

Hmm... what is up with Sarvais et al? (actually the correct spelling of her name is Saravis, not Sarvais). In any case, I looked through the cited research summarized in table 1.

You can see, this is a lot of studies of ADHD, "sugar reactors", "Delinquent", "aggressive", "Prader-Willi syndrome" and other unusual populations. Furthermore the vast majority are 100% male subjects. Finally, almost all of these studies use a sweet beverage as their "control". Unless they have an additional control for "not sweet" condition, this means they have zero chance to understand the difference between giving a kid say a sugary beverage, vs say water or a candy bar vs say a piece of whole wheat bread. In other words, sweetness may itself be the mechanism by which sugar makes kids hyperactive. If you were a biology major and proposed a mouse experiment like this to my wife she would say "where's your negative control?" and send you back to the lab to think about how to run an experiment. Some of the papers do have a negative control.

Among the "normal" populations, number of subjects is typically less than around 25... I wasn't going to chase down all these studies myself, so I decided to look at selected few that use "normal" population and have more than just a handful of subjects.

The ones I chased down were: Rosen et al 1988, Saravis et al 1990, and Wolraich et al. 1994

Let's start with the last one, also by Wolraich. Like a number of these studies, Wolraich et al. 1994 is designed to investigate whether an overall diet of high sugar leads through time to an overall increase in hyperactivity... Although this is an interesting question, it is not the relevant question being discussed in the YouTube video. When a parent says their kid gets hyperactive after eating sugar, what they mean is "my kid got a candy bar from his friend and ate it, and now he's bouncing off the walls for the next hour while I'm trying to get him to get ready for bed". Of course there are kids with more general hyperactivity issues, but that is a more complicated issue. The YouTube video strongly suggests that sugar in any form, bolus or through time, never makes kids hyperactive ever.

The Wolraich et al 1994 article says: "The subjects and their families were placed on a different diet for each of three consecutive three-week periods. One of the three diets was high in sucrose with no artificial sweeteners, another was low in sucrose and contained aspartame, and the third was low in sucrose and contained saccharin (the placebo). So we can totally ignore this study as the design simply doesn't address the question, and it fails to have any negative control. But, even if we don't ignore it, what do we find... Table 4 is a summary (stupid, where's the graph?)

It's clear, from a Bayesian perspective, that the study was vastly underpowered to detect anything of interest. For example in the "Parent's rating of behavior... Conduct" the numbers are 8.1+- 6.7 meaning expected random noise is almost as big as the average score... How meaningful is this rating if people ranged from say 1 to 14? Furthermore, the scores were complicated tests of a wide variety of things "administered in the mobile laboratory each week on the same day of the week and at the same time of day". Any short term effect of a bolus of sweet foods would only be detectable if they had just given them the foods in the minutes before testing. So the results of this study are simply *irrelevant* to the main question at hand.

Let's move to Rosen et al 1988: this study at least is designed to measure a bolus of sugar... of course it's based on two studies with 30 preschool kids and 15 elementary school kids. They designed the study around a "high-sugar condition, a low-sugar condition, and a control aspartame condition (low in sugar but with a sweet taste)." The diet was randomized for each kid each day, and everyone was blinded as much as possible (obviously, the kids could tell if their diet was sweet or not, but weren't told if it had sugar vs aspartame because no-one involved supposedly knew). The manipulation was by giving the kids controlled breakfast meals. The children were tested

"approximately 20-30 min following the completion of breakfast... on several measures sensitive to cognitive functioning..." as well as "each day teachers completed... [a] global rating scale... immediately preceding the child's lunch time...to reflect the child's behavior for the entire morning."

The research is under-powered to really measure much of anything as well, but when they looked at global rating across all kids they found

"An analysis of the means for this measure revealed that the ratings during the high-sugar condition (M = 6.2, SD = 1.08) were only slightly, although significantly (Tukey p < .05) higher than those during the low-sugar condition (M = 5.9, SD = 1.04) (see Figure 2). The control condition (M = 6.0, SD = 1.07) was not significantly different from either the high or low condition. No other significant differences were observed for the teacher rating measures."

So by the "rules" of standard frequentist statistics, we should determine that "high sugar" leads to hyperactivity (the scale increases with increasing hyperactivity) so this is (very weak) evidence but it tends *against* the YouTube video.

Now we get to the Saravis et al. paper. This paper fails to have a non-sweet control. The goal of the study was to determine if there was some difference between sugar vs aspartame, and not to determine the difference between "sweet" and "not sweet" diets. So right away it's going to be weak evidence as to whether something like "feeding your child candy will cause them to be hyperactive for the next few tens of minutes"... But we'll soldier on anyway, especially because if you look back above at the meta-analysis graph, you'll find Saravis (misspelled Sarvais in the graph) is an utter outlier in terms of results...

The design of the Saravis study is that:

"Two experiments were conducted. The objective of the first study was to compare the effects of consuming a large dose of aspartame or sodium cyclamate...with carbohydrate on measures of learning, behavior, and mood in children. The treatment consisted of an ice slurry ... of unsweetened strawberry Kool-Aid containing carbohydrate (as Polycose ...) plus either the test dose of aspartame or the equivalent in sweetness as sodium cyclamate..."

...

"The objective of the second study was to compare the effects of aspartame with a common nutritive sweetener (sucrose) on the same variables. In this experiment, the treatments consisted of ... Kool-Aid, plus either 1.75 g/kg of sucrose or the equivalent sweetness of aspartame. The drink with sucrose provided the same amount of carbohydrate as in the first experiment."

So the study is always giving the kids a sweet drink, and only the second study even varies the amount of carbohydrate in the dose... The studies were 20 children 10 boys and 10 girls ages 9-10...We'll soldier on...

Guess when they gave the high sweetness drink? Well they claim it was at 10:30, but if you know anything about a pre-school, you'd know that it takes time to pour out the drinks, get the kids in line, etc etc. So you can guess that at 10:25 the kids were aware that they were about to get a bolus of sweetness... and of course their activity level is very high right at that point in time, and continuing.

So the study is not designed to test the main question of interest "if you give kids candy/sweets do they go bonkers" but to the extent that they did give kids sweet stuff... they did go bonkers afterwards, independent of what kind of sweet stuff... Because there was "no difference" between the two kinds of sweet syrupy Kool-Aid, this is taken by the YouTube video as evidence that "sugar doesn't cause hyperactivity", essentially the opposite of the conclusion I draw, which is that sugar, and other super-sweet foods, given in a bolus, may very well make kids crazy, but the study actually can't really determine that... Maybe just getting kids in line and giving them anything makes them crazy... who knows. Welcome to modern science, where a study completely incapable of determining anything of use which nevertheless is entirely consistent with out prior guess, and under-powered to determine anything precisely, is taken as definitive proof that our prior expectation is completely false. RCT as billy-club, wielded by econo-physician to show that stuff "everyone knows" is nevertheless wrong and only heroic econo-physician can save us from irrationality.

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