I was responding to the suggestion that, even if the effects that they found are real, they are too small to matter. To me, that line of reasoning is a cue to do a Fermi estimate to get a quantitative sense of how big the effect would need to be in order to matter, and how that compares to the empirical results.
I didn't get into a full-fledged Fermi estimate here (translating the measures that they used into the dollar value of the health benefits), which is hard to do that when they only collected data on a few intermediate health measures. (If anyone else has given it a shot, I'd like to take a look.) I did find a couple effect-size-related numbers for which I feel like I have some intuitive sense of their size, and they suggest that that line of reasoning does not go through. Effects that are big enough to matter relative to the costs of additional health spending (like 3 lives saved in their sample, or some equivalent benefit) seem small enough to avoid statistical significance, and the point estimates that they found which are not statistically significant (8-18% reductions in various metrics) seem large enough to matter.
My overall conclusion about the (based on what I know about it so far) study is that it provides little information for updating in any direction, because of those wide error bars. The results are consistent with Medicaid having no effect, they're consistent with Medicaid having a modest health benefit (e.g., 10% reduction in a few bad things), they're consistent with Medicaid being actively harmful, and they're consistent with Medicaid having a large benefit (e.g. 40% reduction in many bad things). The likelihood ratios that the data provide for distinguishing between those alternatives are fairly close to one, with "modest health benefit" slightly favored over the more extreme alternatives.
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Most Medicaid proponents did not have expectations about the statistical results of this particular study. They did not make predictions about confidence intervals and p values for these particular analyses. Rather, they had expectations about the actual benefit of Medicaid.
You cite Ezra Klein as someone who expected that Medicaid would drastically reduce mortality; Klein was drawing his numbers from a report which estimated that in the US "137,000 people died from 2000 through 2006 because they lacked health insurance, including 22,000 people in 2006." There were 47 million uninsured Americans in 2006, so those 22,000 excess deaths translate into 4.7 excess deaths per 10,000 uninsured people each year. So that's the size of the drastic reduction in mortality that you're referring to: 4.7 lives per 10,000 people each year. (For comparison, in my other comment I estimated that the Medicaid expansion would be worth its estimated cost if it saved at least 1.5 lives per 10,000 people each year or provided an equivalent benefit.)
Did the study rule out an effect as large as this drastic reduction of 4.7 per 10,000? As far as I can tell it did not (I'd like to see a more technical analysis of this). There were under 10,000 people in the study, so I wouldn't be surprised if they missed effects of that size. Their point estimates, of an 8-18% reduction in various bad things, intuitively seem like they could be consistent with an effect that size. And the upper bounds of their confidence intervals (a 40%+ reduction in each of the 3 bad things) intuitively seem consistent with a much larger effect. So if people like Klein and Drum had made predictions in advance about the effect size of the Oregon intervention, I suspect that their predictions would have fallen within the study's confidence interval.
There are presumably some people who did expect the results of the study to be statistically significant (otherwise, why run the study?), and they were wrong. But this isn't a competition between opponents and proponents where every slipup by one side cedes territory to the other side. The data and results are there for us to look at, so we can update based on what the study actually found instead of on which side of the conflict fought better in this battle. In this case, it looks like the correct update based on the study (for most people, to a first approximation) is to not update at all. The confidence interval for the effects that they examined covers the full range of results that seemed plausible beforehand (including the no-effect-whatsoever hypothesis and the tens-of-thousands-of-lives-each-year hypothesis), so the study provides little information for updating one's priors about the effectiveness of Medicaid.
For the people who did make the erroneous prediction that the study would find statistically significant results, why did they get it wrong? I'm not sure. A few possibilities: 1) they didn't do an analysis of the study's statistical power (or used some crude & mistaken heuristic to estimate power), 2) they overestimated how large a health benefit Medicaid would produce, 3) the control group in Oregon turned out to be healthier than they expected which left less room for Medicaid to show benefits, 4) fewer members of the experimental group than they expected ended up actually receiving Medicaid, which reduced the actual sample size and also added noise to the intent-to-treat analysis (reducing the effective sample size).