Thursday, May 17, 2018

Increasing Disparities in Infant Mortality? How a Narrative Can Hinge on the Choice of Absolute and Relative Change

An April, 11th, 2018 article in the NYT entitled "Why America's Black Mothers and Babies are in a Life-or-Death Crisis" makes the following alarming summary statement about racial disparities in infant mortality in America:
Black infants in America are now more than twice as likely to die as white infants — 11.3 per 1,000 black babies, compared with 4.9 per 1,000 white babies, according to the most recent government data — a racial disparity that is actually wider than in 1850, 15 years before the end of slavery, when most black women were considered chattel.
Racial disparities in infant mortality have increased since 15 years before the end of the Civil War?  That would be alarming indeed.  But a few paragraphs before, we are given these statistics:

In 1850, when the death of a baby was simply a fact of life, and babies died so often that parents avoided naming their children before their first birthdays, the United States began keeping records of infant mortality by race. That year, the reported black infant-mortality rate was 340 per 1,000; the white rate was 217 per 1,000.
The white infant mortality rate has fallen 217-4.9 = 212.1 infants per 1000.  The black infant mortality rate has fallen 340-11.3 = 328.7 infants per 1000.  So in absolute terms, the terms that concern babies (how many of us are alive?), the black infant mortality rate has fallen much more than the white infant mortality rate.  In fact, in absolute terms, the disparity is almost gone:  in 1850, the absolute difference was 340-217 = 123 more black infants per 1000 births dying to 11.3-4.9 = 6.4 more black infants per 1000 births dying.

Analyzed a slightly different way, the proportion of white infants dying has been reduced by (217-4.9/217) 97.7%, and the proportion of black infants dying has been reduced by (340-11.3/340)= 96.7%.  So, within 1%, black and white babies shared almost equally in the improvements in infant mortality that have been seen since 15 years before the end of the Civil War.  Or, we could do a simple reference frame change and look at infant survival rather than mortality.  If we did that, the current infant survival rate is 98.87% for black babies and .9951% for white babies.  The rate ratio for black:white survival is .994 - almost parity depending on your sensitivity to variances from unity.

It's easy to see how the author of the article arrived at different conclusions by looking only at the rate ratios in 1850 and contemporaneously.  But doing the math that way makes it seem as if a black baby is worse off today than in 1850!  Nothing could be farther from the truth.

You might say that this is just "fuzzy math" as our erstwhile president did in the debates of 2000.  But there could be important policy implications also.  Suppose that I have an intervention that I could apply across the US population and I estimate that it will save an additional 5 black babies per 1000 and an additional 3 white babies per 1000.  We implement this policy and it works as projected.  The black infant mortality rate is 6.3/1000 and the white infant mortality rate is 1.9/1000.  We have saved far more black babies than white babies.  But the rate ratio for black:white mortality has increased from 2.3 to 3.3!  Black babies are now 3 (three!) times as likely to die as white babies!  The policy has increased disparities even though black babies are far better off after the policy change than before it.

It reminds me of the bias where people would rather take a smaller raise if it increased their standing relative to their neighbor.  Surprisingly, when presented with two choices:

  1. you make $50,000 and your peers make $25,000 per year
  2. You make $100,000 and your peers make $250,000 per year
many people choose 1, as if relative social standing is worth $50,000 per year in income.  (Note that relative social standing is just that, relative, and could change if you arbitrarily change the reference class.)

So, relative social standing has value and perhaps a lot of it.  But as regards the hypothetical policy change above, I'm not sure we should be focusing on relative changes in infant mortality.  We just want as few babies dying as possible.

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