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American Journal of Epidemiology Advance Access originally published online on September 19, 2006
American Journal of Epidemiology 2006 164(11):1126-1136; doi:10.1093/aje/kwj327
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American Journal of Epidemiology Copyright © 2006 by the Johns Hopkins Bloomberg School of Public Health All rights reserved; printed in U.S.A.

PRACTICE OF EPIDEMIOLOGY

Misclassification of Gestational Age in the Study of Spontaneous Abortion

Penelope P. Howards1, Irva Hertz-Picciotto2, Clarice R. Weinberg3 and Charles Poole4

1 Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, Bethesda, MD
2 Department of Public Health Sciences, Divisions of Environmental and Occupational Health and Epidemiology, University of California, Davis, CA
3 Division of Intramural Research, National Institute of Environmental Health Sciences, Research Triangle Park, NC
4 Department of Epidemiology, University of North Carolina, Chapel Hill, NC

Correspondence to Dr. Penelope Howards, Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, 6100 Executive Blvd., Room 7B03C, MSC 7510, Rockville, MD 20852 (e-mail: howardsp{at}mail.nih.gov).

Received for publication October 31, 2005. Accepted for publication April 28, 2006.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 References
 
Most studies of spontaneous abortion are subject to left truncation, because conception is not observed and thus pregnant women are enrolled postconception. Cox regression can account for left truncation but uses gestational age data, which may be inaccurate. Dating is affected by reporting errors and variability in the day of ovulation. These errors may be differential by outcome, because gestational ages are more likely to be clinically corrected in continuing pregnancies than in pregnancies ending in spontaneous abortion. Errors may be differential by exposure status as well, if exposures affect the time of ovulation. The authors designed a simulation to examine bias caused by errors in gestational age. Pregnancies were assigned true and alternative gestational ages using different assumptions about random reporting error and error due to variation in the time between the last menstrual period and ovulation. In separate scenarios, the errors were differential by outcome, differential by exposure, differential by both exposure and outcome, or nondifferential. Hazard ratios were compared using accurate versus erroneous gestational ages. For proportional hazards, bias was only introduced when the error in gestational age was differential by exposure status. Bias was greatest when the magnitude of error for pregnancies at higher risk was much larger than that for pregnancies at lower risk.

abortion, spontaneous; bias (epidemiology); gestational age; pregnancy; proportional hazards models

Abbreviations: LMP, last menstrual period


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 References
 
Most cohort studies of spontaneous abortion recruit women after conception. In clinic-based studies, women are usually recruited when they enter prenatal care or come in for a pregnancy test. Women with pregnancies ending in livebirth have a greater opportunity to be enrolled than women with pregnancies ending in spontaneous abortion, because livebirths occur later in gestation. Some pregnancies terminate spontaneously before women can be enrolled. As a result, time-to-event data in spontaneous abortion studies are usually left-truncated (1–5). Cox regression can account for left truncation by defining a series of risk sets that include only the women who are under observation at the time of each failure (4); time is scaled by gestational age. Cox regression assumes that, within covariate strata, the women who have entered observation by the time of each failure are representative of all pregnancies, observed and unobserved, in the source population that have reached the same time point. Because risk sets are based on gestational age, measurement error in assigning gestational age may introduce bias. More specifically, if the estimated gestational age in a given pregnancy is incorrect, the pregnancy could be inappropriately included in or excluded from a risk set. In this paper, we describe the circumstances in which such erroneous gestational dating will produce bias.

There are numerous potential sources of error in assigning gestational age to a pregnancy. Gestational age is typically calculated from the first day of a woman's last menstrual period (LMP); the underlying assumption is that all conceptions occur on the same day after LMP (classically considered to be day 14 of the menstrual cycle). LMP is first reported by the woman herself, but the date may be subsequently revised on the basis of a physician's judgment or a sonogram. Self-reported LMP has been shown to suffer from digit preference, with days of the month that are multiples of 5 being particularly overrepresented (6–9). Other preferred digits may partially be due to women who cannot remember their LMP being asked if they can remember the week of their LMP and then being assigned a date based on the week reported (8).

Some women are unable to report their LMP because they cannot remember the date, because it occurred many months earlier (e.g., amenorrhea), or because they became pregnant immediately after a previous pregnancy before resuming menstruation. LMP dates are more frequently missing for women of low socioeconomic status and for pregnancies with adverse outcomes (such as low birth weight) (10, 11). There is indirect evidence that some pregnant women mistake spotting for their LMP. Spotting early in pregnancy often occurs around the time the menstrual period is expected; therefore, women can have been pregnant for approximately a month longer than they think they have (12, 13). On the other hand, some women have been pregnant for a month shorter than they think they have, because one cycle ends and another begins without menses' occurring between the two or without the woman's remembering an intervening menstrual period.

Even if a woman reports her LMP date correctly, the gestational age she is assigned may be inaccurate, because there is considerable variability in the length of the follicular phase of the menstrual cycle, the interval from the start of menses to ovulation. This has been observed both among women and among cycles of a given woman (14–17). Therefore, women with the same true LMP date (who will therefore be assigned the same gestational age) may not have been pregnant for the same amount of time, because they could have ovulated (and conceived) on different days. The timing of ovulation has been measured on the basis of peak mucosal level, basal body temperature, serum hormone levels, hormone levels in urine, and serial ovarian sonograms. The literature reports ovulation as early as 8 days and as late as 60 days into a woman's cycle (14, 16–21). Walker (21) pointed out that late ovulation (≥18 days) is not limited to women with a history of long menstrual cycles (≥32 days). Furthermore, older women have shorter follicular phases (14, 17) as well as an increased risk of spontaneous abortion (3). Thus, the accuracy of gestational age could be differential by both maternal age and pregnancy outcome. In addition, irregular menstrual cycles, which are likely to cause gestational age data to be inaccurate or missing, have been reported to be associated with fetal demise (22, 23).

The accuracy of assigned gestational age may also be differential by outcome, because gestational ages in pregnancies ending in livebirth are more likely to be corrected by sonographic dating. Overall, the literature suggests that sonograms predict delivery more reliably than LMP does for livebirths (9, 24, 25), but neither method is perfect. Different fetal measurements are used to assign gestational age on the basis of sonograms taken during different stages of fetal development (13, 15, 26–28). The choice of measurement is based on reported LMP and clinical judgment, both of which can be in error. Fetal measurements are compared with standardized curves, which assume that fetuses with the same measurements are the same age. Not only does sonogram dating ignore potential natural variation (29), typically including that due to the sex of the baby, but there is still some controversy over which curve is most appropriate (30). Nevertheless, on average, sonogram dating tends to be more accurate than LMP for livebirths (9, 24, 25).

The literature on sonography in spontaneous abortion focuses on management of impending spontaneous abortions rather than estimation of gestational ages (31–35). However, it does highlight several issues of concern in using sonograms to date pregnancies that end in fetal demise. First, sonograms would have to be performed very early in pregnancy to precede a significant proportion of spontaneous abortions. Even so, many would be missed, and some ongoing pregnancies would present as an empty gestational sac, a gestational sac with a nonviable fetus, or a deformed gestational sac (33). Sonograms cannot correct errors in LMP-based gestational age estimates for missing or nonviable fetuses. Even if a fetus destined to be spontaneously aborted appears healthy during the sonogram, the sonogram may not improve on LMP dating because the fetus may grow abnormally. In a study of pregnancies in which gestational age was known, some fetuses that were spontaneously aborted appeared viable but small for their true gestational age during the sonogram (34). Faltering growth in some fetuses would result in systematic assignment of gestational ages that were too low. Although it is commonly believed that early sonograms are more accurate than later sonograms (15, 27), some authors caution that fetuses develop at different rates even at young gestational ages (36). In fact, measurement error is reported to be a greater problem among fetuses with a crown-to-rump length of less than 18 mm (approximately 7 weeks' gestation from conception) (36), because even small errors in measurement result in large errors in assessed gestational age (34). Thus, measurement error for gestational age is inevitable in studies of spontaneous abortion. Moreover, the degree of variability introduced by such error is likely to be differential by outcome, because errors in gestational age are more likely to be corrected for livebirths as compared with spontaneous abortions.

The accuracy of LMP-based gestational age estimates may also vary by exposure status. Some exposures, particularly those that affect hormone levels, are associated with changes in menstrual cycle characteristics. Older maternal age is associated with shorter menstrual cycles, whereas obesity is associated with longer cycles (14, 17). Being underweight, exercising intensively, and smoking have been associated with menstrual cycle irregularity (14). Irregular cycles are unlikely to follow the assumed pattern of ovulation 14 days after LMP. Therefore, exposures could cause errors in gestational dating which could in turn bias the hazard ratios.

We performed a simulation to explore biases due to errors in gestational age. We considered four scenarios in which errors were 1) not differential by exposure or outcome, 2) differential by outcome but not exposure, 3) differential by exposure but not outcome, and 4) differential by both exposure and outcome.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 References
 
We simulated 1,000 pregnancy cohort studies for each set of assumptions, and each simulated study included 10,000 pregnancies. We defined spontaneous abortion as pregnancy loss occurring between gestational ages 5 and 20 weeks (35 and 146 days) inclusive, where gestational age was defined as completed weeks and days since LMP, as is typical in pregnancy cohort studies. First, we assigned each pregnancy an exposure status by randomly drawing from a Bernoulli distribution, with the probability of being exposed equal to a set value (0.05, 0.15, 0.35, or 0.65) for each scenario. Next, we assigned each pregnancy an outcome and a true gestational age at termination. Because the risk of spontaneous abortion changes with gestation, we used baseline weekly conditional risks (daily conditional risks were not sufficiently stable) based on life table estimates from a large cohort study (37) to determine whether and when the unexposed pregnancies ended in spontaneous abortion. In each week, the fetus in each unexposed pregnancy that remained at risk was assigned either to be aborted or to survive, using a Bernoulli distribution with the probability of a pregnancy loss equal to the corresponding weekly conditional risk. For the exposed, we multiplied the weekly conditional risks by 2.0, 1.5, or 1.0 to create realistic effect sizes. For each spontaneous abortion, the gestational week of loss (assigned through the weekly conditional risks) was converted to a gestational day of loss by a random draw from a uniform distribution. Pregnancies that did not end in spontaneous abortion were censored at 147 days (when there was no longer a risk of spontaneous abortion).

Next we assigned a true gestational age at entry into the study. A truncated gamma distribution with a shape parameter {alpha} of 19.5 and a scale parameter ß of 3 closely resembled the observed enrollment pattern in the same study from which we extracted the weekly conditional risk estimates (37). Therefore, we sampled from this distribution to assign gestational day of enrollment. The distribution was truncated to mimic the eligibility restrictions of the cohort study by excluding women who entered the study prior to 35 days or after 90 days. Simulated pregnancies that terminated before the assigned entry day represented women who are not enrolled in studies because their pregnancies end before coming under observation.

Once the true gestational ages at entry and termination (or censoring) had been assigned, we calculated simulated observed gestational ages by introducing two sources of error. The first error component represented random error in reported LMP; it was generated from normal distributions with means of zero and different standard deviations for different scenarios (table 1). A minimum standard deviation of 3 days was picked in which 95 percent of the women "recalled" an LMP within ±1 week of their true LMP; a maximum of 9 days was picked as a more extreme example.


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  		TABLE 1 Distributions used to assign error to observed gestational ages (days) compared with true gestational ages in a simulation of a study of spontaneous abortion

 
The second error component represented systematic error due to variation in the menstrual cycle day of ovulation and was informed by published data on follicular phase length (14, 16–21). The gamma distribution could accommodate the long tail composed of women who ovulate after day 14. Therefore, a random draw from various gamma distributions (figure 1) was used to calculate the ovulation-based error. Women could be assigned to ovulate as early as day 8 of the cycle or infinitely late, although ovulation after day 30 was extremely unlikely. The long right tail in the distribution of ovulation days is compatible with the fact that LMP dating is likely to overestimate gestational age in comparison with sonogram dating, on average (7, 38, 39). In theory, LMP dating overestimates gestational age on average because it includes all time prior to ovulation, whereas the sonogram is based on the actual size of the fetus (7, 38).


Figure 1
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  		FIGURE 1 Plots of the transformed gamma distributions used to assign the error in gestational age due to variability in the day of ovulation in a simulation study. Each plot represents a different assumption set, and each assumption set was applied in four scenarios. The distribution represented by the solid line with open triangles in each plot was used for everyone in scenario 1, spontaneous abortions in scenario 2, the exposed in scenario 3, and exposed spontaneous abortions in scenario 4. Each distribution indicated by the dotted line with solid triangles was used for unexposed spontaneous abortions in scenario 4. Each distribution indicated by the solid line with open squares was used for exposed livebirths in scenario 4. Each distribution indicated by the dotted line with solid squares was used for livebirths in scenario 2, the unexposed in scenario 3, and unexposed livebirths in scenario 4. The specific {alpha} and ß for each distribution are reported in the plots themselves. Scenarios are described in the text.

 
Both the random error and the ovulation-based error were added to the true gestational age data to set the observed gestational ages. In the first scenario, we assumed that the error distributions were not differential by exposure or outcome. In the other scenarios, we assumed that just the variance or both the mean and the variance of the error distributions were differential by outcome, by exposure status, or by both outcome and exposure status. Within each scenario, the parameters of the error distributions were varied as described in table 1. Figure 1 shows the gamma distributions used to assign the ovulation-based errors. In ovulation error assumption sets 1 and 4, we assumed a large variance, and in assumption sets 2 and 3, we assumed more peaked distributions. Ovulation error assumption sets 3 and 4 were more extreme than assumption sets 1 and 2 because the means differed by more days. In assumption set 4, the distributions also had a greater proportion of the data in the right tail. For the scenario in which systematic and random misclassification were differential by outcome, we assumed that the spontaneous abortions had less accurate gestational ages than the livebirths. In the scenario in which misclassification was differential by exposure, we assumed that the exposed pregnancies had greater error in their gestational ages than the unexposed pregnancies. When misclassification was differential by both exposure and outcome, we assumed that unexposed livebirths had the least misclassification and exposed spontaneous abortions had the most. We also assumed that unexposed spontaneous abortions had more error than exposed livebirths, because we know that error in gestational age is differential by outcome but are less certain about error due to exposures.

For each set of assumptions, we fitted two Cox models. We used days as the unit of time and Efron's approximation for ties (40). Women who had a pregnancy loss on the same day as they entered observation were included (41, 42). The first Cox model used the correct gestational age data and represented the "gold standard" or truth. The full cohort, including the pregnancies that would not have come under observation, was analyzed because this provided the true experience that we were trying to estimate in the source population. The second model represented what would have been observed in a study and therefore accounted for left truncation but used the erroneous gestational age data. Women were excluded if they entered observation outside of the previously defined enrollment window or had a pregnancy loss before entry. In summary, we compared the hazard ratios that would have been observed with the true hazard ratios in the full cohort.

We present the mean hazard ratios and the empirical 5th and 95th percentiles based on 1,000 simulations for each scenario. The mean effect estimates were compared with the mean gold standard by computing the proportional bias: (mean observed hazard ratio – mean gold standard hazard ratio)/mean gold standard hazard ratio.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 References
 
The mean hazard ratios in the full cohort using the correct gestational age data were consistent with the assigned multiple of increase in risk for the exposed (2.0, 1.5, or 1.0) in each scenario for each error assumption set and each exposure prevalence. As expected, the hazard ratio from individual runs of the gold standard analysis varied across simulations (see the 5th and 95th percentiles). Overall, the results from the models based on the observed gestational ages were quite close to the gold standard hazard ratios, but variability was greater than in the models using the true gestational age data.

In the first scenario, in which the error in observed gestational age was not differential by exposure or outcome, the mean hazard ratio differed from the mean gold standard by less than half a percent across all assumption sets (table 2). The individual observed hazard ratios from the sets of 1,000 runs fell evenly on either side of the true hazard ratio. Overall, the error for the mean effect estimates was trivial for the nondifferential scenario.


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  		TABLE 2 Scenario 1 (nondifferential): summary hazard ratios (HRs) based on 1,000 runs in a simulated spontaneous abortion study with 10,000 pregnancies in which gestational age data were nondifferentially misclassified

 
In scenario 2, in which the error in gestational age was differential by outcome, the results were similar to the results from the scenario in which the error was nondifferential (table 3). The magnitude of error in the observed hazard ratios was small (<1 percent) and approximately the same for all of the error assumption sets and exposure prevalences. The individual observed hazard ratios from the sets of 1,000 runs tended to be slightly greater than the truth (up to 60.5 percent of the time) more often than they were less than the truth for the nonnull true effects. In the case of the null true effect, the observed hazard ratios were balanced on either side of the truth.


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  		TABLE 3 Scenario 2 (differential by outcome): summary hazard ratios (HRs) based on 1,000 runs in a simulated spontaneous abortion study with 10,000 pregnancies in which gestational age data were differentially misclassified by outcome

 
In scenario 3, in which the error in gestational age was differential by exposure, there was generally more substantial error in the effect estimates than for scenarios 1 and 2 (table 4). The mean hazard ratio for the models using the observed gestational age data was up to 14 percent greater than the mean gold standard, depending on the error assumption set. The results were similar for different exposure prevalences. The assumption set in which misclassification of gestational age was the greatest (set 3 in table 1) had the largest error in the mean effect estimates. When the true effect size was 2.0, the mean observed hazard ratio overestimated the truth by approximately 3 percent for the error assumption set with the least misclassification as compared with approximately 12 percent for the assumption set with the most misclassification. Sixty-five to 100 percent of the individual observed hazard ratios overestimated the corresponding true hazard ratio; the percentage decreased as the effect size decreased and increased as differential misclassification became more extreme.


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  		TABLE 4 Scenario 3 (differential by exposure): summary hazard ratios (HRs) based on 1,000 runs in a simulated spontaneous abortion study with 10,000 pregnancies in which gestational age data were differentially misclassified by exposure

 
Finally, in scenario 4, in which misclassification of gestational age was differential by both exposure and outcome, the mean observed hazard ratios differed from the gold standard hazard ratios by up to 6 percent, depending on the error assumption set (table 5). The percent error in the mean observed hazard ratio was similar across true effect sizes and prevalences of exposure but varied for the different assumption sets. Between 54 percent and 97 percent of the observed hazard ratios were greater than the corresponding true hazard ratios, and the percentage decreased with decreasing effect size. Error assumption set 3 (table 1) overestimated the gold standard hazard ratio the most, and assumption set 1 overestimated the gold standard the least.


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  		TABLE 5 Scenario 4 (differential by exposure and outcome): summary hazard ratios (HRs) based on 1,000 runs in a simulated spontaneous abortion study with 10,000 pregnancies in which gestational age data were differentially misclassified by exposure and outcome

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
References
 
Error in gestational age is likely to be differential by outcome, because gestational ages for pregnancies ending in spontaneous abortion are less likely to be corrected by sonogram dating. However, our simulations provided some reassurance that such errors may introduce negligible bias in many circumstances. The Cox models produced reasonable effect estimates when the errors in dating were differential only by outcome or not differential at all. In Cox regression, the specific timing of the event is not important as long as the events are ordered correctly. Although differential error in gestational age by outcome could alter the relative ordering of events and therefore cause some denominators to include pregnancies that did not belong to that risk set or exclude pregnancies that did, these results suggest that the errors produce little bias when the misclassification is not differential by exposure status.

Differential misclassification of gestational age by exposure status, however, introduced more bias. Some exposures are known to affect menstrual cycle characteristics (such as body mass index and maternal age (14, 17)), but it is unclear whether they affect cycles in which conception occurs. On the other hand, social factors (such as educational level) are associated with the accuracy of reported LMP (10, 11). In the scenario in which error was differential by exposure, the magnitude of bias in the effect measure estimate was determined by the magnitude of error in the observed gestational ages. Thus, it appears that if exposure shifted the distribution of the day of ovulation much later or much earlier than the distribution for the unexposed, it could produce marked bias in the effect estimates.

Scenario 4, in which gestational age was misclassified by both outcome and exposure, introduced less bias than scenario 3, in which misclassification was by exposure alone. This is because scenario 3 was more extreme (i.e., the distributions overlapped less) than scenario 4. Misclassification of gestational age by exposure status only required two sets of assumptions, and we used the assumptions that were the most distant from each other (the extreme left and extreme right distributions in figure 1). In contrast, when errors in gestational age were differential by both outcome and exposure (scenario 4), four assumptions were required, so we used the central distributions as well. Presumably, if we had chosen the central distributions for scenario 3, scenario 4 would have yielded greater bias.

In error assumption sets 1 and 4, the difference in the mean day of ovulation varied across distributions largely because of long tails in the distribution. Most of the pregnancies, regardless of exposure or outcome status, would have begun within a few days of each other, but in a small percentage conception would have occurred much later than in the others. Thus, only in a small proportion of pregnancies would concepti have had substantial misclassification of their gestational ages. In assumption sets 2 and 3, the distributions have a similar variance, but they are shifted relative to each other. When misclassification of gestational age was differential by exposure or by both outcome and exposure, assumption set 3 was associated with the most bias, but it may be the least realistic of the four sets. Some exposures are associated with irregular cycles in which ovulation may occur much later than day 14 for a subset of women, but it seems less likely that the whole ovulation distribution would be shifted (a different mean but the same variance) for exposed women compared with the unexposed.

This simulation suggests that errors in gestational age dating will not bias Cox regression substantially in large studies of spontaneous abortion if the error is not differential by exposure or if differential error by exposure is small or mainly due to the tail of the distributions. However, our results are based on simulated cohorts of 10,000 pregnancies. Smaller studies could have substantially greater errors in observed hazard ratios due to random variation.

We only examined differential misclassification of gestational age for scenarios in which the effect of the exposure is proportional. Exposures are likely to have different effects on pregnancies at different stages of gestation, which presumably would violate the proportional hazards assumption. We did not investigate the effect of errors in gestational age in the case of nonproportional hazards. We also limited our simulation to the case of a dichotomous risk factor and did not address protective exposures or exposures with more than two categories. However, a continuous or categorical exposure that was associated with substantial differential misclassification of gestational age might be expected to give rise to bias, given the results of this simulation. We considered random reporting error for LMP and error due to variability in the day of ovulation, but we did not consider error due to the time between fetal demise and fetal expulsion. Ideally, time-to-event data would refer to the time to fetal demise, but demise is usually unobserved. Instead, fetal expulsion is used as a proxy. If an exposure altered the time between demise and expulsion, it would introduce differential error (by exposure) in the observed gestational age at expulsion.

In summary, pregnancies ending in spontaneous abortion are more likely to have errors in their gestational ages than pregnancies ending in livebirth, but these errors alone are not likely to introduce substantial bias into the effect measure estimates under the assumptions that 1) errors are nondifferential with respect to exposure, 2) the hazards are proportional, and 3) exposure does not influence the time between fetal demise and expulsion. Aside from a few social variables, there is limited direct evidence that an exposure will introduce differential error in gestational age dating. However, if a dichotomous exposure caused differential error in estimated gestational age, then on average the observed effect estimates would be expected to be slightly biased on the basis of this simulation; the magnitude of the bias would reflect the magnitude of the differential errors in gestational dating.


   ACKNOWLEDGMENTS
 
This investigation was supported in part by the Intramural Research Program of the National Institutes of Health (NIH), National Institute of Child Health and Human Development. This work was supported in part by the Intramural Research Program of the NIH, National Institute of Environmental Health Sciences. This investigation was also supported by a dissertation fellowship from the Graduate School at the University of North Carolina, Chapel Hill, and grant P30ES10126 from the National Institute of Environmental Health Sciences.

The authors thank Drs. David Savitz and Katherine Hartmann for comments on an earlier draft and assistance during the dissertation process and Peter DeSaix and Paul Mitchell for technical assistance.

Conflict of interest: none declared.


   References
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 References
 

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