As Adanya Lustig and Erin Rhoda reported today, Maine is the only state in the U.S. with a worse infant mortality rate in this decade than in the last. Not long ago, Maine had the lowest infant mortality in the country. We were in first place in both 1996 and 2002. In 2013, Maine dropped to 44th place, and only recovered to 37th in 2014.

Could it be that simple randomness is the cause of this drop? Has Maine just had a stretch of bad luck, while other states have not? By the end of this post, I’ll lay out why the probability of Maine losing this much ground is probably not due to random chance. Something other than chance appears to be causing Maine to fall to a new low compared with other states.

In the graphic below, you will see the prior decade (1995-2004, a white bar) displayed behind this decade (2005-2014, in a colored bar). The width of each bar is the range of infant mortality values for that 10-year period (deaths per 1,000 births). These are listed from fewest total births (top) to the most (bottom). Maine, highlighted in red, is the only state that has gotten worse in the last 10 years.

state_ranges (2)

From this graphic we can see there are many states that are routinely worse than Maine. Also, there are two less obvious trends visible here: variability due to size, and the limits imposed as the rate approaches zero.

A closer look at Maine

States with fewer births tend to have wider ranges — more variability. This is due to the fact that a small change in the number of deaths will have a bigger impact on a small state’s infant mortality rate. Maine is certainly on the low end when it comes to baby production.

Variability is also limited as the rate approaches zero. For states with only two or three deaths per 1,000 births, like Alaska and New Hampshire, the rate can’t vary much on the low end because it’s up against a zero-wall. The rate can only vary on the high end of the range.

The reason variability is relevant here is that this has a big impact on the likelihood of a state to lose its position in rankings. With more variability, a state will be more likely to lose its rank position simply due to chance.

Let’s take a closer look at Maine’s infant mortality rate variability.

In the graphic below, there is one heartening and clear trend: that infant mortality is dropping nearly everywhere across the United States. Maine, in red, is the one exception.

The variability of Maine’s rate is not exceptional. The standard deviation of the rate over the study period is 0.0009. That means, from year-to-year, there is generally only a change of, at most, one death per 1,000 births. That is, from one year to the next, we would expect to see the rate only change by between 1 and 0 deaths per 1,000 births.

maines_rate (1)

In contrast to the general expectation of low variability in Maine, in 2011 there were 15 more infant deaths than in the previous year, while the total number of births went down from 12,970 to 12,704. This made for a change of 1.3 deaths per 1,000. That was a bad year for Maine at a time when the rest of the country was on a strong improving trend. 

In the graphic below, we see that Maine has been bearing fewer and fewer new babies (green line). We would expect that the numbers of deaths would get correspondingly lower, but they have not.

maine_births_deaths (1)

These years with fewer births and more infant deaths have meant more pain for families, and they push Maine far down on a ranking of all U.S. states. The next graphic shows the trend in how states have ranked over time for their infant mortality rate. (One is good, and 51 is bad.) Other states’ rankings do fluctuate, but few bounce around as much as Maine’s. And none have dropped like ours has.

maines_rank (1)

Strange events

Is it possible that Maine’s drop in rank, even in the face of fewer births and more infant deaths, is simply a case of a bad roll of the dice? Maybe several states happened to do a little better at the same time that Maine did a little worse? It’s strange, but rare events can actually happen.

For example, if we want to find the probability of rolling 10 threes in a row on a die, that would be 1 chance in 6^10, which equals 1/60,466,176. Those are some long odds. But if you throw enough dice, this rare event is guaranteed to happen. This can also be the case for a state’s ranking in a bad-luck year.

To test how often a state might stand out from its peers, let’s make some simulation data.

We know from the actual mortality rate data that these values follow a gamma distribution. (See the graphic below to check the fit.) We would also expect that, if we randomly pull values from this gamma distribution, they would most often be close to six, and rarely would they be as low as three or as high as 14. 

Imagine that we pull 20 values, one for each year, for 51 imaginary states. These data values will be all over the place, so in this simulation we expect states’ rankings to change quite a bit. In fact, it should be rare for any one state to maintain its rank consistently over the 20 simulated years. 

(Keep in mind that this is a rather naive simulation. It does not distinguish large states from small states or account for regional trends that might put more babies at risk, such as substance use, poverty or limited access to top-notch hospitals.)

gamma_dist (1)

So, rank range is the difference between a state’s best rank position (first is best) and it’s worst rank position. (Fifty-first is worst, since we’re including D.C.) This means that the biggest possible rank range is 50. 

Rank ranges

Above we have two tables: The left is from the actual states’ data, and the one on the right has our simulated data. Each table shows the difference between the highest and lowest rank position between 1995 and 2014. 

The actual states’ data show that most of the states maintain their position quite well. That means if they are good, they stay good, and if they have a bad record, they tend to stay at the bottom. (We’re looking at you, D.C.) It’s interesting to note that Maine and South Dakota have the widest spread with highs to lows of first to 44th and fourth to 50th respectively. 

It’s unusual to see such a substantial shift in ranking over time, even among small states. We would expect Maine’s infant mortality rate ranking to remain at the top, but it seems to have moved to a new place near the bottom.

Each state tends to hold its position in the rankings over time. A state might gain or drop a few spots year over year, but they don’t tend to move far. Maine, however, has moved from a good place near the top of the rankings to a new level nearer the bottom.

The table of simulated data shows that, if a state’s change in infant mortality rank over time was due to random noise, then it would be much more common for states to look like Maine and South Dakota with spreads in the 30s, 40s and even 50s. What is strange here is that, in the real data, that doesn’t happen.

This begs the question: Why do Maine and South Dakota show such a dramatic change? The next graphic shows that these two states behave more like our simulated data than like the rest of the country. (They fall in the right-hand, bottom corner of the graphic.)

rank_ranges (1)

The year 2012 was a bad one for South Dakota with a jump from 72 infant deaths in 2011 (23rd place) to 101 in 2012 (49th place, ahead of Alabama and Mississippi). We also see here, like Maine, that South Dakota has lost more babies in this decade (872) than in the last (784). But, in contrast to Maine, it has seen an increase in its number of births.

south_dakota_births_deaths (1)

What we have seen so far is that Maine is far from the worst state in the union for infant mortality. However, there is an unsettling trend in decreasing births, while the number of infant deaths has increased. Maine has also bucked the common trend for a state to keep its position year over year among other states.

It could be that the high-ranking states have stronger public health policies, lower poverty rates or healthier populations, while the lower-ranked states do not. It doesn’t have to be these things; they are merely examples. But the change is likely due to something other than chance alone.

It is not completely out of the question for Maine’s rank changes to be due to simple randomness, but it’s suspicious that Maine would be unique in both worsening infant mortality rate and big changes in rank.

Although rare events can happen, this new low rank position shows a disturbing trend that runs counter to the rest of the country. There is no doubt that Maine’s infant mortality rate has gone up, and our rank has fallen. There’s a real possibility of a systemic public health-related problem.

Jake Emerson is a data scientist for the BDN and a UMaine Ph.D. student in computing and information science. Check out the open-source code behind this analysis on GitHub.


Jake Emerson

Jake Emerson is the data scientist for the BDN. He has worked in academia, health research, flood warning, and was a an active duty officer the the Army Corps of Engineers.