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American Journal of Epidemiology Advance Access originally published online on March 14, 2008
American Journal of Epidemiology 2008 167(7):786-792; doi:10.1093/aje/kwm327
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American Journal of Epidemiology © The Author 2008. Published by the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

PRACTICE OF EPIDEMIOLOGY

The Missing Data Problem in Birth Weight Percentiles and Thresholds for "Small-for-Gestational-Age"

Jennifer A. Hutcheon1 and Robert W. Platt1,2

1 Department of Epidemiology and Biostatistics, McGill University Faculty of Medicine, Montreal, Quebec, Canada
2 Department of Pediatrics, McGill University Faculty of Medicine, Montreal, Quebec, Canada

Correspondence to Jennifer A. Hutcheon, The Montreal Children's Hospital Research Institute, 4060 Rue Sainte Catherine Ouest #205, Westmount, Quebec, Canada H3Z 2Z3 (e-mail: jennifer.hutcheon{at}mail.mcgill.ca).

Received for publication August 10, 2007. Accepted for publication October 9, 2007.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 THE MISSING DATA IN...
 IMPACT OF BIASED WEIGHT...
 CORRECTING THE MISSING DATA...
 CONCLUSIONS
 References
 
Weight-for-gestational-age charts and definitions of "small-for-gestational-age" based on the distribution of livebirths at a given gestational age have conventionally been used to identify infants whose fetal growth is poor. However, references based on the weights of only livebirths have serious shortcomings at preterm ages due to missing data on the weights of fetuses still in utero, and these missing data introduce considerable bias to etiologic studies of fetal growth restriction. Application of standard epidemiologic approaches for missing data is needed to help produce perinatal weight percentiles that provide unbiased assessment of fetal growth and risks of small-for-gestational-age.

bias (epidemiology); fetal growth retardation; infant, small for gestational age; reference values

Abbreviations: AGA, appropriate-for-gestational-age; SGA, small-for-gestational-age


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
THE MISSING DATA IN...
 IMPACT OF BIASED WEIGHT...
 CORRECTING THE MISSING DATA...
 CONCLUSIONS
 References
 
Since their first publication by Lubchenco et al. (1) over 40 years ago, weight-for-gestational-age charts (2–5) have been a cornerstone of screening for infants whose intrauterine development is poor. In these charts, the weight distributions of livebirths at each week of gestation are converted to percentiles, and any infant whose weight falls below a certain statistical threshold of the population, typically the 10th percentile, is labeled as being "small-for-gestational-age" (SGA) and is considered to be at increased risk of perinatal morbidity and mortality (6–8). SGA, an anthropometric characteristic that does not necessarily have any adverse health implications, is therefore commonly (but not necessarily appropriately) used as a proxy for the pathologic outcomes believed to be associated with an inadequate rate of fetal growth (9). Weight-for-age charts are nevertheless considered an improvement over low and very low birth weight cutoffs because they differentiate between infants who are small because they are born early in gestation and infants born later but small relative to their peers (10).

In addition to clinical use for the identification of high-risk infants, weight-for-gestational-age charts and their resulting thresholds to define SGA are frequently used in epidemiologic studies of fetal (intrauterine) growth restriction (11–16). Because fetal growth restriction is typically not measurable in population-based data, the majority of research to identify risk factors for fetal growth restriction consists of comparisons of the risks of SGA among exposed and unexposed groups of infants. Although case definitions for SGA or "appropriate-for-gestational-age" (AGA) established by using conventional weight-for-gestational-age charts are well accepted in perinatal epidemiology, their validity according to general epidemiologic principles has rarely been considered.

The purpose of this article is to argue that size-for-gestational-age charts created from the weight distributions of livebirths have serious shortcomings due to missing data on the weights of fetuses that remain in utero at each gestational age. We will demonstrate how use of a case definition for SGA produced by these charts can introduce considerable bias to estimates of relative risk in etiologic studies of fetal growth restriction, and we will propose that standard statistical and epidemiologic approaches to missing data could be applied to address the bias that currently exists in this field of research.


   THE MISSING DATA IN BIRTH WEIGHT REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 THE MISSING DATA IN...
IMPACT OF BIASED WEIGHT...
 CORRECTING THE MISSING DATA...
 CONCLUSIONS
 References
 
In the study of fetal growth, perinatal researchers have traditionally been faced with what is, in essence, a "missing data" problem (17, 18). Although the biological process of interest is the changing fetal size throughout pregnancy, this process is generally unobservable at a population level. In a cohort of conceptions followed forward in time, information on fetal size at any given week of pregnancy is readily available for only the portion of the cohort born during that week. The weights of the remainder of the conception cohort at that gestational age, the fetuses still in utero, are unavailable (19). Although prenatal ultrasonography has enabled estimation of fetal weight prior to the time of birth (20, 21), this information has not been incorporated into reference charts because of concerns over measurement error (2). National weight-for-gestational-age charts (2–5) therefore continue to be created from the weight distributions of only livebirths at each age and are missing the weights of fetuses in the conception cohort not yet born by the end of a given gestational week. In these charts, calculation of weight percentiles at early gestational ages is based on the weights of an extremely small fraction of the total cohort at risk (since the vast majority remain in utero at preterm ages), and, even for gestational ages as old as 36 weeks, weight data for more than 97 percent of the original cohort are still missing (2).

As with any missing-data situation in epidemiology, the extent to which bias will be introduced by the missing intrauterine weights will depend on the mechanism that caused the missingness (22–24). In order for the "complete case" approach (25) used in conventional weight-for-gestational-age charts to be valid (the use of only those cases for whom complete data are available—i.e., data on livebirths), the unobserved data must be missing completely at random (MCAR). For data to be missing completely at random, they must represent a randomly selected subset of the total cohort at risk. At term, when the weight distribution of those born at a given gestational age (such as 39 weeks) is likely fairly representative of those still in utero (those who will be born at 40 weeks or later), the assumption of being "missing-completely-at-random" may be reasonably valid, and there will be minimal bias from the missing data on intrauterine weights. At preterm ages, however, the available weights are most likely not a random sample of the weight distribution of the total at-risk population. Intrauterine growth restriction is a common indication for medically necessary preterm birth (26, 27), and the observation that preterm livebirths are smaller than their in utero peers (28–33) has led to speculation that there may be a common cause of spontaneous preterm birth and poor growth. As a result, the observed distribution of weights at earlier gestational ages is systematically shifted to lower values than the weight distribution of the remainder of the cohort at risk at the start of that gestational week. The "complete-case" approach used in existing reference charts, when the missing data are clearly not missing completely at random, is therefore inappropriate.

Recognition of the "missing data" problem in weight-for-gestational-age charts is certainly not new. Even with the introduction of the first neonatal weight percentile charts in 1963, Lula Lubchenco warned that "the sample has an undeterminable bias because premature birth itself is probably related to unphysiological states of variable duration in either mother or fetus. Since the weight of fetuses that remain in utero cannot be measured, the curves presented herein are submitted with these reservations ... " (1, p. 793). Differences between the weights of preterm livebirths and their in utero peers may be well acknowledged, but what does not appear to have widespread appreciation is the extent and impact of the bias that the missing data introduce.

The major discrepancy between intrauterine and livebirth weight distributions at preterm ages, as reported in previous publications (30–33), is illustrated in figure 1. In the figure, the distributions of estimated fetal weights (20) of male singletons aged 32 weeks in an unselected obstetric population at the Royal Victoria Hospital, a McGill University teaching hospital in Montreal, Canada (unpublished data), are compared with a Canadian birth weight reference (2). These ultrasound data are from the years 2001–2004 and were obtained through an institutional policy of universal 32-week ultrasound examinations. The median estimated weight of the fetuses still in utero is more than 120 g heavier than that of livebirths, while the 10th percentile (SGA) threshold of the intrauterine population is more than 300 g higher than the 10th percentile of the national birth weight reference. Similar results were obtained for female fetuses (data not shown). This discrepancy between the 10th percentile thresholds of the two distributions means that applying the national birth weight reference to the intrauterine population (which, at this age, constitutes >99.7 of the total conception cohort (2)) will not identify 10 percent of the population as SGA. Instead, since the 10th percentile of the national birth weight reference is much lower than the 10th percentile of the total cohort, the livebirth weight-based reference will identify less than 1 percent of the total cohort as SGA. That is, the SGA threshold produced by a national birth weight reference at 32 weeks will capture the smallest 1 percent of the total cohort instead of the smallest 10 percent. Error arising from the use of a formula to estimate fetal weight will introduce some bias to estimates of the discrepancy between in- and ex-utero weight distributions; however, since most of this error is random, not systematic (20), it is unlikely to explain a major portion of the discrepancy. The genuine discrepancy between the weights of the in- and ex-utero populations is supported by work such as Hediger et al.'s (28), who demonstrated that the 32-week estimated weights of fetuses that were later born preterm were significantly lower than the 32-week estimated fetal weights of those that were subsequently born at term.


Figure 1
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  		FIGURE 1. Comparison of the estimated fetal weight distribution of male fetuses aged 32 weeks in a general obstetric population at the Royal Victoria Hospital in Montreal, Canada, 2001–2004 (clear bars, n = 1,540; mean = 2,043 g, standard deviation, 259) with the distribution of a Canadian livebirth weight reference for males aged 32 weeks (curved dashed line) (2). Hatched shading indicates the smallest 10% of the in utero population, black shading indicates those in the smallest 10th percentile of the in utero population identified as small-for-gestational-age by the livebirth reference (threshold for small-for-gestational-age is indicated by the vertical dashed line). Refer to the text for further details.

 

   IMPACT OF BIASED WEIGHT PERCENTILES ON PERINATAL EPIDEMIOLOGY
TOP
 ABSTRACT
 INTRODUCTION
 THE MISSING DATA IN...
 IMPACT OF BIASED WEIGHT...
CORRECTING THE MISSING DATA...
 CONCLUSIONS
 References
 
Birth weight references that ignore the missing data of intrauterine weights introduce considerable bias into epidemiologic studies of the etiology of fetal growth restriction. In many studies (11–16), the effect of potential risk factors on fetal growth restriction is evaluated by establishing the relative risk of being SGA between exposed and unexposed infants, calculated as

Formula (1)
If the outcome, SGA, is established using a conventional reference based on the distribution of livebirths, an infant's chance of being classified as SGA will change according to his or her gestational age at birth. Consider the case of a male fetus weighing 1,650 g at 320 weeks of gestation (32 weeks, zero days). When the weight of this fetus is compared with the weights of all pregnancies that progressed to 32 weeks, this fetus is at approximately the 5th percentile of the population (based on figure 1 data). If all pregnancies in this cohort continued at similar relative growth rates (i.e., the rank order of weights remains unchanged) until birth at 40 weeks' gestation (term), this infant would be classified as SGA by virtue of being in the smallest 10 percent of the population of births at 40 weeks. However, if this fetus were instead born the following day, at 321 weeks of gestation, under existing national birth weight references (2) it would instead be assigned the 25th percentile and considered AGA. Although its weight relative to that of its peers of similar gestational stage is constant, classification of this infant as AGA or SGA will be different according to the timing of its birth. A younger gestational age at birth therefore becomes "protective" against being classified as SGA when based on a reference created from weights of livebirths.

The impact of gestational age at birth on the criteria for being defined as SGA becomes problematic in perinatal epidemiology because many risk factors for growth restriction (e.g., smoking, preeclampsia/pregnancy-induced hypertension, multiple births, and disadvantaged ethnicity (34–39)) have also been found to be associated with a younger gestational age at birth or increased rate of preterm birth. As a result, this leads to a differential case definition of SGA being applied to exposed and unexposed groups. Exposed infants are more likely to be born at a younger gestational age, and, at younger gestational ages, the threshold to be identified as SGA is more stringent. At 32 weeks, for example, an infant must be among the smallest 1 percent of his or her remaining conception cohort to be labeled SGA, while, at 40 weeks, the infant need be among only the smallest 10 percent. This difference results in relatively fewer exposed infants being classified as SGA compared the unexposed group, for whom the threshold for SGA is less stringent because of older mean age at birth. As evident from equation 1, an underdiagnosis of SGAexposed infants will result in underestimation of the risk of SGA among the exposed and an underestimation or potentially even a reversal of the true measure of effect.

The amount of bias introduced because of differential misclassification of preterm SGA neonates as AGA can be quantified through a simple simulation (table 1). To begin, an estimate of the relative risk of SGA among newborns exposed to preeclampsia (compared with normotensive pregnancies) determined by using a livebirth reference was obtained from previously published research (13), along with the mean gestational ages at birth in each exposure group. The reported unadjusted relative risk of SGA was 2.72, with a mean gestational age among the unexposed of 39.0 weeks (standard deviation, 2.3) and a mean gestational age among the exposed of 37.4 weeks (standard deviation, 3.4). These values were used to generate cohorts of 10,000 exposed and 10,000 unexposed newborns. For each gestational age, the percentage of infants whose weight was in the smallest 10 percent of the total cohort, but not of livebirths, was calculated (i.e., the percentage of SGA infants misclassified as AGA because of the use of a reference based on livebirths was established). The percentage of misclassification at each gestational age was determined by comparing the 10th percentile thresholds of a Norwegian birth weight reference (5) and a Norwegian longitudinal ultrasound reference (40) prior to 37 weeks, at which age the misclassification was zero.


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  		TABLE 1. Bias to the estimate of relative risk of SGA* introduced because of misclassification of preterm SGA infants in a simulated population of 10,000 exposed and 10,000 unexposed infants, with the percentage of misclassification based on Norwegian population data

 
The percentage of misclassifications was then used to "correct" the number of SGA cases at each gestational age for both exposed and unexposed groups. As expected, the number of SGA cases increased more in the exposed than in the unexposed group following the correction, since the younger mean gestational age at birth among the exposed would make them more subject to misclassification as AGA. The relative risk of SGA among the exposed was recalculated with the corrected number of SGA cases. The relative risk of SGA of 2.72 presented in the original study when a livebirth reference was used was recalculated to a relative risk of 3.24, a nontrivial difference in effect size that creates a real possibility that true effects of exposures could be found nonsignificant or even potentially reversed because of the differential misclassification of SGA infants. For example, had a relative risk of 0.8 been found with the use of a livebirth reference, the true measure of effect would actually likely be a nearly null effect (relative risk = 0.95 based on Norwegian data, calculations not shown). Covariate adjustment for gestational age as a means to correct this problem is not appropriate, since stratification by gestational age is similar to calculating gestational-age-specific hazards with a denominator of livebirths, instead of fetuses at risk (41).

The differential misclassification not only will affect observed measures of effect but could also create apparent, but likely spurious, biologic interactions. In a recent study, the relation between SGA birth in a first pregnancy and risk of stillbirth in a subsequent pregnancy was examined (42). The authors reported that the risk of stillbirth in a second pregnancy increased with decreasing gestational age at birth of an SGA infant in the woman's first pregnancy (odds ratio of stillbirth after "very preterm SGA birth" > odds ratio after "preterm SGA birth" > odds ratio after "term SGA birth" when compared with AGA of all ages) and concluded that "interestingly, the results in this study also reveal that SGA should be considered a heterogenous disease in terms of risk amplitude for subsequent stillbirth. A woman with a term SGA in an index pregnancy is at lower risk level than her counterpart who experiences a preterm SGA, and the greatest risk for stillbirth occurs in women with very preterm SGA" (42, p. 855). Before concluding that there may be effect modification in the effects of SGA on the risk of stillbirth by gestational age at birth, the potential impact of the bias from livebirth references in this study should be considered. Because those "very preterm infants" classified as SGA were in approximately the lowest 1 percent of their conception cohort (based on figure 1 data), whereas the SGA infants at term were in only the lowest 10 percent, it is perhaps not surprising that the more severe cases of growth restriction that consisted of the "very preterm" group were found to be a marker for a much greater risk of subsequent stillbirth.


   CORRECTING THE MISSING DATA BIAS
TOP
 ABSTRACT
 INTRODUCTION
 THE MISSING DATA IN...
 IMPACT OF BIASED WEIGHT...
 CORRECTING THE MISSING DATA...
CONCLUSIONS
 References
 
To correct the missing data problem in weight-for-gestational-age charts, epidemiologic methods for missing data that are consistent with the nature of the missingness should be applied (22, 23). At preterm ages, the missing data in neonatal weight references are clearly not missing completely at random, making the current "complete-case" approach inappropriate. If the distribution of missing intrauterine weights were similar to that of the available birth weight data within strata of known covariates (i.e., if we were able to predict the missingness based on known covariate information), the data would be missing at random (MAR). With missing-at-random data, approaches such as multiple imputation (23) or inverse weighting (43) could be used to build references that accounted for the missing weights. However, since our ability to explain the missingness (amounting to predicting gestational age at birth) is generally agreed to be poor, even considering all known social and medical risk factors (44), these data are likely not missing at random. The missing data in neonatal weight references are therefore likely missing not at random (MNAR), meaning that the missingness process depends on unobserved variables, and any weight-for-gestational-age reference must take this missing data mechanism into account.

A variety of attempts to address the bias from missing intrauterine weights have been proposed in the literature, but none have appropriately addressed the missing-not-at-random nature of the data. Population references based on the distribution of estimated fetal weights (32, 40, 45) represent an improvement at preterm ages (46, 47) but, later in gestation, will introduce missing data bias of their own because of missing weights for those in the population who have been born. "Hybrid" references, which either average the growth curves created from livebirth and intrauterine weights (48) or switch from intrauterine weight distributions to birth weight distributions at 37 weeks (49), have also been proposed. While correct in spirit, neither of these approaches accurately reflects the portions of the population in- and ex-utero at each gestational age.

Although options for analyzing missing-not-at-random data are usually limited (22, 23), the case of neonatal weight references represents a relatively rare situation in which external data can be incorporated to produce valid results. With missing-not-at-random data, the weight distributions will be different between those with and without missing data, even within strata of observed covariates. Here, estimates of the weight distributions of those with missing data can be obtained from estimates of fetal weight produced by obstetrical ultrasound (20, 21). Although such estimates have a considerable amount of random error (50), this problem is mainly of concern for predicting weight at the individual level, not for the weight distributions of the population as a whole. Since the magnitude and direction of error in estimates of fetal weight have been reported in validation studies for fetal weight formulae (20, 21), correction for error (both systematic and random) when estimating the weight distribution of the population with missing data should be feasible by using simple Bayesian methods (51). Information on weight distributions of the in- and ex-utero portions of the population can therefore be combined to simulate a cohort with the weights of all fetuses at risk at the beginning of each gestational week.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 THE MISSING DATA IN...
 IMPACT OF BIASED WEIGHT...
 CORRECTING THE MISSING DATA...
 CONCLUSIONS
References
 
The missing intrauterine weight data in conventional birth weight references have resulted in a case definition for SGA that reflects "a birth weight below the population 10th percentile, corrected for gestational age" (52, p. 870) only at term ages. At preterm ages, the threshold for SGA reflects a much lower percentage of the total at-risk population, leading to a case definition of SGA that is inconsistent across gestational ages. This case definition is problematic for epidemiologic studies, where exposures of interest are often associated with gestational duration and therefore can affect case status through mechanisms independent of their effect on weight. To correct the missing-data bias that currently exists in studies of fetal growth restriction, the following changes are needed:

  1. References to assess neonatal weight must be developed that reflect the weight distributions of all fetuses in the population at the beginning of a given gestational week, not just livebirths. By definition, preterm births are not "normal" pregnancies and should therefore not be used to characterize the growth patterns of the full conception cohort. Thus, the correct reference chart is neither a livebirth weight reference nor an intrauterine estimated fetal weight reference, but a perinatal one that combines the weights of both livebirths and fetuses in utero at each week of gestation. At preterm ages, it will constitute predominantly in utero weights; as term ages approach, livebirth weights will make up a larger and larger portion of the distribution.
  2. The case definition of SGA must be established as the bottom 10 percent of the total population at risk of being small, not just those who happen to be born at a given week of gestation. To establish that an infant of 32 weeks is small for its gestational age, its size needs to be compared with that of all other pregnancies that progressed to 32 weeks, regardless of whether those pregnancies went on to end at 32 weeks or 40 weeks. Researchers should stop classifying as normal the weights of growth-restricted preterm infants simply because there are many other growth-restricted preterm livebirths who are even smaller than they are. This case definition is particularly important for etiologic studies of growth restriction, to prevent differential misclassification of SGA cases as noncases. Until an unbiased reference is available, the use of birth-weight-for-gestational-age charts should be restricted to term ages (53).
Adopting the same approaches to the missing data in neonatal weight charts as we would for missing data in other areas of epidemiology will likely do much to further our understanding of perinatal population health.


   ACKNOWLEDGMENTS
 
J. A. H. is supported by a Canadian Institutes of Health Research (CIHR) Doctoral Research Award, and R. W. P. holds a Chercheur-Boursier from the Fonds de la Recherche en Santé Quebec (FRSQ).

The authors thank Dr. Maala Bhatt for comments on earlier versions of the manuscript and Dr. Jean-François Boivin for helpful suggestions following a seminar presentation of this work.

Conflict of interest: none declared.


   NOTES
 
Editor's note: An invited commentary on this article appears on page 793, and the authors' response is published on page 797.


   References
TOP
 ABSTRACT
 INTRODUCTION
 THE MISSING DATA IN...
 IMPACT OF BIASED WEIGHT...
 CORRECTING THE MISSING DATA...
 CONCLUSIONS
 References
 

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