The Wilcox-Russell Hypothesis, Page 2
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Figure 6: Frequency distributions of birth weight and weight-specific neonatal mortality rates for Colorado and the United States, 1984, after adjustment to a z scale of birth weight. x____x, United States; O---O, Colorado. (Figure reproduced from Am J Epidemiol, 1993; 137; 1098-1104, with permission.)

With this adjustment, the two weight distributions correspond nearly exactly, as do the two mortality curves (Fig. 6). The simplest explanation for the convergence of mortality curves is that altitude affects birth weight but not mortality.

The two mortality curves are essentially the same curve, with the one in Colorado carried along with the shift in birth weight. For babies weighing less than the optimum weight, this shift gives the appearance of lower mortality at any given birth weight. For babies heavier than the optimum weight, the shift gives the appearance of higher mortality. In fact, the birth weight distribution and its accompanying mortality curve has shifted without any change in the survival of individual babies.

In this example, fetal growth retardation (on the population level) has no effect on mortality.

We can conclude from this example that the moderate reduction of in utero growth does not necessarily increase an individual baby's mortality risk - nor does it increase the number of small babies at higher risk. This might be regarded as a counter-example to Geoffrey Rose's highly-cited thesis that a modest shift in the population mean of a continuous variable (such as blood pressure) will place more individuals into the high-risk group at the extreme. This appears not necessarily to be true for the birth weights of term babies.

Now imagine a more complicated but plausible scenario. What if a factor decreases birthweight and also increases infant mortality? The same analytic approach can be applied. In the process, we can discover the underlying sense behind the LBW paradox.

Figure 7: Frequency distributions of birth weight and weight-specific perinatal mortality rates for infants exposed and unexposed to mothers' smoking: Missouri, 1980-1984. x___x, nonsmokers; O---O, smokers. (Figure reproduced from Am J Epidemiol, 1993; 137; 1098-1104, with permission.)

The effect of smoking

Mothers who smoke have smaller babies. Their babies have higher infant mortality as a group. If we look at the birth weight and mortality curves for smokers and non-smokers, the initial picture is rather similar to Colorado-US. There are different birth weight distributions, and the two mortality curves intersect. Small babies do better if their mothers smoke. This is the paradox with which Yerushalmy defended smoking.

Figure 8: Frequency distributions of birth weight and weight-specific perinatal mortality rates for infants exposed and unexposed to mothers' smoking, after adjustment to a z scale of birth weight: Missouri, 1980-1984. x---x, nonsmokers; O---O, smokers. (Figure reproduced from Am J Epidemiol, 1993; 137; 1098-1104, with permission.)

When the picture is adjusted to relative weight (the z-scale), there emerges a new relation between the mortality curves (Fig. 8). Mortality with mother's smoking is higher across the whole range of weights. Thus, smoking has two discrete effects. It retards fetal growth, shifting the birth weight distribution (and, as always, the mortality curve). In addition, smoking also shifts the mortality curve upwards, to higher rates.

In the previous example of altitude, the shift of the birth weight distribution to lower weights was not sufficient to increase infant mortality. In the example of smoking, there is increased mortality that occurs equally at every adjusted birth weight (on a multiplicative scale). In other words, this effect of smoking on weight-specific mortality is independent of birth weight.

The increase of mortality across all weights - crucial evidence of the harmful effect of smoking on infants - is initially hidden by the leftward shift of the mortality curve as it follows the birth weight distribution. Small babies of mothers who smoke seem to be at lower risk, when in fact they are at higher risk. This is apparent on the relative weight scale (the z-scale) but not on the absolute scale.

MacMahon anticipated this conclusion when he proposed that the LBW paradox was an artifact due to comparison of absolute weights (see The Low Birth Weight Paradox). Relative weights are needed to uncover the essential relation between smoking and infant mortality. To the extent that smoking increases weight-specific mortality proportionately across all (relative) weights, smoking acts on infant mortality independent of birth weight.

As discussed earlier, the intersection of weight-specific mortality curves is not uncommon. It can be found in nearly any setting where populations have different mean birth weights. In each case, the true difference in weight-specific mortality is revealed after adjustment to a relative scale of birth weight.

If you have not yet read A Short History of Low Birth Weight, now would be a good time to do so. If you've already read it, go now to The Analysis of Infant Mortality.

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Why study birth weight?

A Short History of Low Birth Weight

The Low Birth Weight Paradox

Frequency Distribution of Birth Weight

Birth Weight Specific Mortality

The Wilcox-Russell Hypothesis   Page 1 Page 2

The analysis of infant mortality

Beyond low birth weight

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