The Frequency Distribution of Birth Weight

Figure 1: An empirical distribution of 400,000 birth weights (Norway, all births, 1992-1998)

The frequency distribution of birth weight is strikingly Normal (or bell-shaped), with an extended lower tail. The bar graph in Fig. 1 shows the observed distribution of weights for 400,000 births.

In Figure 2, the curve superimposed on the bar graph describes the Normal component of the birth weight distribution, called the "predominant" distribution. The predominant distribution (defined by its mean and standard deviation (SD)) comprises the vast majority of births.

The remainder of the birth weight distribution is the "residual" distribution. This residual comprises all births in the lower tail of the curve that falls outside the predominant distribution. In a typical population, 2 to 5% of births are in the residual distribution. The residual distribution is shown twice in Figure 2, once as the lower tail of the whole distribution, and then enlarged by itself in the bottom panel.

Special statistical methods are needed to estimate the predominant and residual distributions (see below).

A small excess of large births is less often found in the upper tail of the birth weight distribution. Methods have been developed to assess both tails of the distribution simultaneously. However, (Umbach 1996), a residual distribution in the upper tail has little impact on infant mortality.

Figure 2: An empirical distribution of 400,000 birth weights, with the estimated predominant and residual distributions

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Biological interpretation

The predominant distribution corresponds closely to the birth weight distribution of term births (37 or more completed weeks of gestation, counting from the last menstrual period). This can be demonstrated in any large data set - the empirical distribution of term births alone is almost purely Normal, with a mean and standard deviation closely approximated by the predominant distribution of all births (Wilcox 1983a). (Thirty-seven weeks is admittedly an arbitrary definition of "term births". The Normality of the distribution of term birth weights remains robust against modest adjustments in the definition of "term".)

It follows that virtually all births in the residual distribution are preterm. However, not all preterm births are in the residual distribution - just the small ones, which also happen to be the ones at highest risk. Populations with a larger percent of births in the residual distribution would be expected to have a greater number of small preterm births.

Thus, the predominant distribution and the residual distribution of birth weight provide indirect information about aspects of gestational age without actually requiring gestational-age data. The predominant distribution closely approximates the weight distribution of term births. The residual distribution estimates the percent of births that are small and preterm. No other approach to birth weight (certainly not a fixed criterion such as 2500 grams) provides this glimpse into a population's gestational-age characteristics.

Independence of components

The predominant and residual distributions of birth weight are independent of one another. An exposure that affects fetal growth does not necessarily affect the risk of preterm delivery. (The mean of the predominant distribution can change without affecting the percent of births in the residual distribution.)

Conversely, a factor that increases the risk of preterm delivery would not necessarily change the average weight of babies delivered at term. (The percent in the residual distribution can change without affecting the predominant distribution). In order to understand birth weight as an epidemiologic endpoint, it is essential to grasp this functional independence of the two components of the birth weight distribution.

Implications for infant mortality

When comparing populations of births, a difference in the percent in the residual suggests a difference in the percent of small preterm births. Since these are the very babies at highest risk, a population with more babies in the residual distribution will have higher infant mortality (all else being equal).

In contrast, if two populations of babies have different predominant distributions, there is no predictable difference in their infant mortality. Populations with lighter babies do not necessarily have worse mortality. For example, the predominant distribution of Mexican-American babies is shifted to lower weights compared to US white babies, but Mexican-American babies have the better overall survival. The mean or standard deviation of the predominant distribution are not reliable indicators of infant mortality. (This is discussed more fully in The Wilcox-Russell hypothesis.)

Reconsidering LBW

How do the two components of the birth weight distribution relate to LBW? Babies less than 2500 grams include the whole residual distribution plus the lower tail of the predominant distribution (Fig. 2). An increase in residual births (which suggests a health problem) will increase the percent of LBW. However, the percent LBW also increases with a decrease in the mean of the predominant distribution, or with an increase in the SD. Such changes in the weight distribution of term births may or may not be associated with changes in mortality. This is why, on a population level, the percent of LBW is an unreliable marker of perinatal risk.

Summary

The birth weight distribution tells something about small preterm births, but not by using a simple cut-off of 2500 grams. A more complicated estimation procedure is needed to describe the residual distribution. This website includes a birth weight Analysis Program that estimates the predominant and residual distributions for any birth weight distribution. But before using this program, please read more about the birth weight story in Birth-weight-Specific Mortality.

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

The analysis of infant mortality

Beyond low birth weight

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