01.12.2013 | Research article | Ausgabe 1/2013 Open Access

# Estimation of gestational age in early pregnancy from crown-rump length when gestational age range is truncated: the case study of the INTERGROWTH-21^{st}Project

- Zeitschrift:
- BMC Medical Research Methodology > Ausgabe 1/2013

## Electronic supplementary material

## Competing interests

## Authors’ contributions

^{st}Century

## Background

^{+0}to 13

^{+6}weeks’ gestation, but not beyond [3]. Assessment of gestational age based on ultrasound (US) biometry was first introduced in 1969 by Campbell [4], and it has become the preferred method for dating pregnancy.

^{+0}to 13

^{+6}weeks) ultrasound alone, or c) LMP and ultrasound combined. Use of LMP is based on the assumption that pregnancy has a constant duration from the first day of the LMP with ovulation on the 14

^{th}day [3]. This method of dating pregnancies, even for women whose menstrual history is certain, has been shown to be unreliable [5, 6]. Caution is recommended regarding use of last menstrual period (LMP) alone for dating because up to 50% of women are uncertain of their dates, have an irregular cycle, have recently stopped the oral contraceptive pill, are lactating or did not have a normal last menstrual period [7].

^{+6}weeks which can reduce the need for induction of labour after 41 weeks of gestation. Although there is always a margin of error in US-based estimation [9], this error is relatively small compared to LMP-based estimations [8, 10].

^{st}Project, described below, aims to generate fetal growth charts and also a new dating chart. In the study gestational age is based on the first day of LMP and corroborated by CRL using a known dating equation [16]. Therefore, only women between 9

^{+0}-13

^{+6}weeks gestation whose estimation by both methods agreed within 7 days were recruited into the fetal growth longitudinal study.

^{+6}weeks. In this paper we describe an exploration of strategies to overcome truncation of GA when developing equations and charts for dating pregnancies from CRL measurements.

## Methods

^{st}Century (INTERGROWTH-21

^{st}) is a large-scale, population-based, multi-centre project involving health institutions from eight geographically diverse countries (i.e. Brazil, China, India, Oman, Kenya, UK, USA and Italy), which aims to assess fetal, newborn and preterm growth under optimal conditions, in a manner similar to that adopted by the WHO Multicentre Growth Reference Study [18]. This approach is important in the creation of fetal growth standards by selecting women regarded as “healthy”, educated, affluent and living in areas with minimal environmental constraints on growth [19].

^{st}Project has three major components, which were designed to create: 1) Longitudinally derived, prescriptive, international, fetal growth standards using both clinical and ultrasound measures; 2) Preterm, postnatal growth standards for those infants born ≥26

^{+0}but <37

^{+0}weeks of gestation in the longitudinal cohort, and 3) Birth weight, newborn length, and head circumference for gestational age standards derived from all newborns delivering at the study sites over an approximately 12 month period [19]. To ensure that ultrasound measurements are accurate and reproducible, centres adopted uniform methods, used identical ultrasound equipment in all the study sites; adopted standardised methodology to take fetal measurements, and employed locally accredited ultra-sonographers who underwent standardisation training and monitoring.

^{st}Project is to develop a new gestational age estimation equation based on the crown-rump length (CRL) from women recruited between 9

^{+0}-13

^{+6}weeks. This will be the largest prospective study to collect data on CRL in geographically diverse populations, and with a high level of quality control measures in place.

^{st}data to develop centiles for the distribution of GA for CRL values between 15 mm and 100 mm. The statistical challenge is this: How can we model data when the outcome variable (GA) is truncated at both ends, i.e. at 9 and 14 weeks, given the need to obtain estimates in the truncated regions? This restriction is part of the design of the INTERGROWTH-21

^{st}study based on the fact that CRL measurements are less reliable outside this range of GA [1, 7, 23–25].

^{st}Project CRL data, which we used to explore the performance of different methods of analysis of these data when we imposed truncation at 9 and 14 weeks of gestation. The choice of which approach is best is hard to justify through formal statistical testing, and is likely to depend on the specific data being analysed.

### Statistical methods

^{th}centile and -1.88 for the 3

^{rd}centile, and the SD in this equation are the predicted estimates from the regression analysis. Fitted curves (3

^{rd}, 50

^{th}, and 97

^{th}centiles) from different models were assessed visually for a good fit and by comparing the deviances from each model. The choice of centiles presented was purely based on what is commonly reported in the literature and also used in clinical practice as standard centiles. In addition; the INTERGROWTH-21

^{st}Project aims to complement the WHO-Multi-centre Growth Reference Study (MGRS) which produced reference standards for children aged 0-5 years where they also presented the 3

^{rd}and 97

^{th}centiles [18]. Goodness of fit was assessed by a scatter plot of the distribution of residuals in z scores by CRL and also by counting the number of observations below the 3

^{rd}and above the 97

^{th}centiles.

^{st}Project data to estimate GA from CRL.

^{st}data and is large enough to remove effects of sampling variation. The GA was between 5 and 17 weeks, the GA range of original data from which the equations were obtained. We log transformed GA in all analyses to stabilise variance [2, 15, 20, 26].

### Validation of the simulated data

Verburg’s original reported equation | Equation from the simulated data | ||
---|---|---|---|

CRL (mm) | Median GA (Weeks) predicted from CRL | Median GA (Weeks) predicted from CRL | Difference in GA (days) |

5 | 6.336 | 6.324 | 0.082 |

10 | 7.503 | 7.497 | 0.041 |

15 | 8.312 | 8.310 | 0.015 |

20 | 8.962 | 8.962 | -0.003 |

25 | 9.519 | 9.521 | -0.017 |

30 | 10.015 | 10.019 | -0.026 |

35 | 10.469 | 10.474 | -0.032 |

40 | 10.892 | 10.897 | -0.035 |

45 | 11.290 | 11.296 | -0.036 |

50 | 11.670 | 11.675 | -0.036 |

55 | 12.034 | 12.039 | -0.033 |

60 | 12.386 | 12.390 | -0.029 |

65 | 12.727 | 12.731 | -0.023 |

70 | 13.060 | 13.063 | -0.016 |

75 | 13.386 | 13.387 | -0.008 |

80 | 13.706 | 13.706 | 0.001 |

85 | 14.021 | 14.019 | 0.012 |

90 | 14.331 | 14.328 | 0.023 |

95 | 14.638 | 14.633 | 0.036 |

100 | 14.942 | 14.935 | 0.050 |

^{st}data set. We note that truncation is only a problem when we want to model GA as a function of CRL and not CRL as a function of GA (size chart) (Figure 2, panel A). All three suggested approaches make use of this fact, but in different ways.

### Approach 1-simulation for small crown-rump length, restriction and extrapolation

^{st}data set) as there remains a truncation problem at the upper end of the CRL distribution (Figure 4, panel B). We then extrapolated the mean and SD equations obtained to the rest of the data (Figure 4, panel C). The predicted GA from this approach was compared to that originally reported by Verburg (Table 2). A sensitivity analysis to establish which lower cut-off, i.e. truncating CRL at 10 mm, 15 mm or 20 mm had the best prediction, was performed by comparing the predicted GA obtained using the derived equation to that reported by Verburg. We note that the choice of a cut-off affects the fit for large CRL and so has clinical implications, because it is desirable to have predictions of GA from CRL between 15 mm and 95 mm (Table 2).

Verburg’s original equation | Approach 1 | ||||||||
---|---|---|---|---|---|---|---|---|---|

Estimated GA (weeks) | Estimated GA (weeks) | Difference (days) | |||||||

CRL (mm) | 3 ^{rd}centile | Median | 97 ^{th}centile | 3 ^{rd}centile | Median | 97 ^{th}centile | 3 ^{rd}centile | Median | 97 ^{th}centile |

10 | 6.88 | 7.50 | 8.18 | 6.85 | 8.18 | 8.22 | 0.21 | -4.76 | -0.28 |

15 | 7.63 | 8.31 | 9.06 | 7.60 | 8.53 | 9.09 | 0.21 | -1.54 | -0.21 |

20 | 8.22 | 8.96 | 9.77 | 8.20 | 9.02 | 9.80 | 0.14 | -0.42 | -0.21 |

25 | 8.73 | 9.52 | 10.38 | 8.72 | 9.51 | 10.40 | 0.07 | 0.07 | -0.14 |

30 | 9.19 | 10.02 | 10.92 | 9.18 | 9.99 | 10.93 | 0.07 | 0.21 | -0.07 |

35 | 9.60 | 10.47 | 11.41 | 9.60 | 10.45 | 11.41 | 0.00 | 0.14 | 0.00 |

40 | 9.99 | 10.89 | 11.87 | 10.00 | 10.88 | 11.86 | -0.07 | 0.07 | 0.07 |

45 | 10.36 | 11.29 | 12.31 | 10.37 | 11.30 | 12.29 | -0.07 | -0.07 | 0.14 |

50 | 10.70 | 11.67 | 12.72 | 10.73 | 11.69 | 12.69 | -0.21 | -0.14 | 0.21 |

55 | 11.04 | 12.03 | 13.12 | 11.08 | 12.07 | 13.07 | -0.28 | -0.28 | 0.35 |

60 | 11.36 | 12.39 | 13.50 | 11.41 | 12.43 | 13.44 | -0.35 | -0.28 | 0.42 |

65 | 11.67 | 12.73 | 13.87 | 11.74 | 12.77 | 13.80 | -0.49 | -0.28 | 0.49 |

70 | 11.98 | 13.06 | 14.24 | 12.05 | 13.11 | 14.15 | -0.49 | -0.35 | 0.63 |

75 | 12.28 | 13.39 | 14.59 | 12.37 | 13.43 | 14.49 | -0.63 | -0.28 | 0.70 |

80 | 12.57 | 13.71 | 14.94 | 12.67 | 13.74 | 14.82 | -0.70 | -0.21 | 0.84 |

85 | 12.86 | 14.02 | 15.28 | 12.98 | 14.04 | 15.15 | -0.84 | -0.14 | 0.91 |

90 | 13.15 | 14.33 | 15.62 | 13.27 | 14.34 | 15.47 | -0.84 | -0.07 | 1.05 |

95 | 13.43 | 14.64 | 15.96 | 13.57 | 14.62 | 15.79 | -0.98 | 0.14 | 1.19 |

100 | 13.71 | 14.94 | 16.29 | 13.86 | 14.90 | 16.10 | -1.05 | 0.28 | 1.33 |

### Approach 2 – simulation for small and large crown-rump length

Verburg’s original equation | Approach 2 | ||||||||
---|---|---|---|---|---|---|---|---|---|

Estimated GA (weeks) | Estimated GA (weeks) | Difference (days) | |||||||

CRL (mm) | 3 ^{rd}centile | Median | 97 ^{th}centile | 3 ^{rd}centile | Median | 97 ^{th}centiles | 3 ^{rd}centile | Median | 97 ^{th}centile |

10 | 6.88 | 7.50 | 8.18 | 7.08 | 7.71 | 8.39 | -1.41 | -1.45 | -1.48 |

15 | 7.63 | 8.31 | 9.06 | 7.70 | 8.38 | 9.12 | -0.52 | -0.47 | -0.41 |

20 | 8.22 | 8.96 | 9.77 | 8.25 | 8.98 | 9.77 | -0.21 | -0.12 | -0.02 |

25 | 8.73 | 9.52 | 10.38 | 8.75 | 9.52 | 10.36 | -0.11 | 0.00 | 0.12 |

30 | 9.19 | 10.02 | 10.92 | 9.20 | 10.01 | 10.90 | -0.09 | 0.02 | 0.15 |

35 | 9.60 | 10.47 | 11.41 | 9.62 | 10.47 | 11.39 | -0.11 | 0.01 | 0.14 |

40 | 9.99 | 10.89 | 11.87 | 10.01 | 10.89 | 11.86 | -0.13 | -0.01 | 0.13 |

45 | 10.36 | 11.29 | 12.31 | 10.38 | 11.29 | 12.29 | -0.14 | -0.02 | 0.12 |

50 | 10.70 | 11.67 | 12.72 | 10.72 | 11.67 | 12.70 | -0.13 | 0.00 | 0.15 |

55 | 11.04 | 12.03 | 13.12 | 11.05 | 12.03 | 13.09 | -0.09 | 0.04 | 0.20 |

60 | 11.36 | 12.39 | 13.50 | 11.37 | 12.37 | 13.46 | -0.03 | 0.11 | 0.28 |

65 | 11.67 | 12.73 | 13.87 | 11.67 | 12.70 | 13.82 | 0.06 | 0.21 | 0.39 |

70 | 11.98 | 13.06 | 14.24 | 11.96 | 13.01 | 14.16 | 0.18 | 0.35 | 0.54 |

75 | 12.28 | 13.39 | 14.59 | 12.23 | 13.31 | 14.49 | 0.33 | 0.51 | 0.73 |

80 | 12.57 | 13.71 | 14.94 | 12.50 | 13.60 | 14.81 | 0.50 | 0.71 | 0.95 |

85 | 12.86 | 14.02 | 15.28 | 12.76 | 13.89 | 15.11 | 0.71 | 0.94 | 1.20 |

90 | 13.15 | 14.33 | 15.62 | 13.01 | 14.16 | 15.41 | 0.95 | 1.20 | 1.49 |

95 | 13.43 | 14.64 | 15.96 | 13.25 | 14.42 | 15.70 | 1.22 | 1.50 | 1.81 |

100 | 13.71 | 14.94 | 16.29 | 13.49 | 14.68 | 15.98 | 1.51 | 1.82 | 2.17 |

### Approach 3 – interchanging the X and Y axes from a model for size

^{rd}, 50

^{th}and 97

^{th}centiles for CRL. We can obtain a new equation for the median by regressing GA on the predicted median CRL. Similarly, we can obtain equations for the 3

^{rd}and 97

^{th}centiles (Figure 6, panel C). The predicted GA from this approach was compared to that originally reported by Verburg (Table 4). Since we do not have an equation for the SD, the full model cannot be written down simply. We describe how we obtained an equation for the SD as function of CRL that also allows prediction of any desired centiles.

Verburg’s original equation | Approach 3 | ||||||||
---|---|---|---|---|---|---|---|---|---|

Estimated GA (weeks) | Estimated GA (weeks) | Difference (days) | |||||||

CRL (mm) | 3 ^{rd}centile | Median | 97 ^{th}centile | 3 ^{rd}centile | Median | 97 ^{th}centiles | 3 ^{rd}centile | Median | 97 ^{th}centile |

10 | 6.88 | 7.50 | 8.18 | 6.97 | 7.29 | 8.15 | -0.60 | 1.49 | 0.23 |

15 | 7.63 | 8.31 | 9.06 | 7.66 | 8.17 | 9.08 | -0.26 | 1.00 | -0.14 |

20 | 8.22 | 8.96 | 9.77 | 8.23 | 8.85 | 9.81 | -0.10 | 0.79 | -0.25 |

25 | 8.73 | 9.52 | 10.38 | 8.73 | 9.42 | 10.42 | -0.02 | 0.68 | -0.29 |

30 | 9.19 | 10.02 | 10.92 | 9.19 | 9.93 | 10.96 | 0.00 | 0.62 | -0.29 |

35 | 9.60 | 10.47 | 11.41 | 9.60 | 10.39 | 11.45 | 0.00 | 0.57 | -0.28 |

40 | 9.99 | 10.89 | 11.87 | 9.99 | 10.81 | 11.91 | -0.02 | 0.54 | -0.26 |

45 | 10.36 | 11.29 | 12.31 | 10.36 | 11.22 | 12.34 | -0.05 | 0.52 | -0.24 |

50 | 10.70 | 11.67 | 12.72 | 10.72 | 11.60 | 12.75 | -0.08 | 0.50 | -0.22 |

55 | 11.04 | 12.03 | 13.12 | 11.05 | 11.96 | 13.15 | -0.11 | 0.48 | -0.20 |

60 | 11.36 | 12.39 | 13.50 | 11.38 | 12.32 | 13.53 | -0.14 | 0.47 | -0.18 |

65 | 11.67 | 12.73 | 13.87 | 11.70 | 12.66 | 13.90 | -0.16 | 0.47 | -0.15 |

70 | 11.98 | 13.06 | 14.24 | 12.01 | 12.99 | 14.25 | -0.17 | 0.47 | -0.12 |

75 | 12.28 | 13.39 | 14.59 | 12.30 | 13.32 | 14.61 | -0.18 | 0.47 | -0.09 |

80 | 12.57 | 13.71 | 14.94 | 12.60 | 13.64 | 14.95 | -0.18 | 0.48 | -0.05 |

85 | 12.86 | 14.02 | 15.28 | 12.88 | 13.95 | 15.29 | -0.16 | 0.49 | -0.01 |

90 | 13.15 | 14.33 | 15.62 | 13.17 | 14.26 | 15.62 | -0.14 | 0.52 | 0.04 |

95 | 13.43 | 14.64 | 15.96 | 13.44 | 14.56 | 15.94 | -0.11 | 0.55 | 0.10 |

100 | 13.71 | 14.94 | 16.29 | 13.72 | 14.86 | 16.27 | -0.06 | 0.58 | 0.16 |

### Computing an equation for the standard deviation

^{rd}, 50

^{th}and 97

^{th}centiles by regressing GA on the predicted p

^{th}centile of CRL measurements. Using these equations (3

^{rd}, 50

^{th}and 97

^{th}centile) relating log GA and CRL we can get two estimates of the SD at a given CRL from the difference between 97

^{th}and 50

^{th}centiles and between the 50

^{th}and 3

^{rd}centiles. Note that the two are not exactly the same but are very similar because GA was modelled on the log scale. It is thus reasonable to estimate the SD for each value of CRL by simply taking the average of the 2 SDs. An equation for the SD relating GA to CRL was then obtained by regressing this SD (of GA) on CRL. Estimates of any desired centiles can then be obtained using the relation:

^{th}centile and -1.88 for the 3

^{rd}centile, and the SD in this equation are the predicted estimates from the regression analysis just described.

## Results

^{rd}centile and 120/4600 (2.6%) above the 97

^{th}centile for CRL between 20 mm and 100 mm (Figure 4).

^{rd}centile and 232/7640 (3.0%) above the 97

^{th}centile for CRL between 20 mm and 100 mm (Figure 5).

^{rd}centile and 221/6448 (3.4%) above the 97

^{th}centile for CRL between 20 mm and 100 mm (Figure 6). The estimates obtained from the computation of SD for approach 3 were remarkably similar to those obtained from the three sets of X, Y coordinates of GA and the predicted 3

^{rd}, 50

^{th}and 97

^{th}centiles for CRL (Figure 6 panels B and C).

^{st}project CRL data set (Figure 8). Hence we are confident that we can use these approaches to get reliable estimates based on INTERGROWTH-21

^{st}CRL data as demonstrated in the next section (Figures 9, 10, 11 and 12). We do not discuss any results of the INTERGROWTH-21

^{st}CRL data as the data collection is still on-going and for demonstration purposes we have used ~35% of the overall target sample in this paper. Results of the full sample and the new international dating equation will be published in a separate paper.

## Discussion

^{st}population which is carefully selected and actively followed up during pregnancy with a known outcome at birth provides a population that is ideal for developing such an international standard equation and chart. The INTERGROWTH-21

^{st}project is the biggest study so far to prospectively collect data on CRL. These data are of very high quality, with ultrasound measurements made by highly trained sonographers following a standardised protocol using standard ultrasonography equipment with latest technology across 8 geographically diverse sites.

^{st}CRL data is not unique in that it has been present in other studies, but has never been adequately addressed. This feature of the data has the potential to introduce considerable bias, mostly at the extremes of CRL, unless analysed carefully. Altman et al. [17] addressed a similar problem in the estimation of GA using head circumference by restricting the range of measurements included in the regression analyses. As opposed to their HC data, for which the GA range was 12-42 weeks, the INTERGROWTH-21

^{st}CRL data span only 5 weeks so using CRL data unaffected by truncation leads to a large loss of data and limited clinical usefulness.

## Conclusion

^{st}project. They are more suitable for large data sets to reduce the effect of sampling variation and ensure reasonable extrapolation. We are thus confident that we can use these approaches to get reliable estimates based on INTERGROWTH-21

^{st}CRL data. Although only examined for CRL, these methods may be a solution to other truncation problems involving similar data and their applicability to other settings would need to be evaluated.

### Details of ethics approval

^{st}Project was approved by the Oxfordshire Research Ethics Committee ‘C’ (reference:08/H0606/139) and the research ethics committees of the individual participating institutions and corresponding health authorities where the Project was implemented.

## Authors’ information

^{st}Project and DGA is Professor of Medical Statistics.

^{1,2}, Aris T. Papageorghiou

^{1}, Jose Villar

^{1}, and Douglas G Altman

^{2}

^{1}Nuffield Department of Obstetrics & Gynaecology and Oxford Maternal & Perinatal Health Institute (OMPHI), Green Templeton College, University of Oxford, Oxford, OX3 9DU, UK: for the International Fetal and Newborn Growth Consortium for the 21st Century (INTERGROWTH-21st Project)

^{2}Centre for Statistics in Medicine, University of Oxford, Botnar Research Centre, Windmill Road, Oxford OX3 7LD, UK.

## Funding

^{st}Grant ID# 49038 from the Bill & Melinda Gates Foundation to the University of Oxford, for which we are very grateful. DGA is supported by a programme grant from Cancer Research UK (C5529). AT is supported by the Oxford Partnership Comprehensive Biomedical Research Centre with funding from the Department of Health NIHR Biomedical Research Centres funding scheme.