Use of time to event analysis to estimate the normal duration of human pregnancy

Gordon C.S. Smith

University of Glasgow, Department of Obstetrics and Gynaecology, The Queen Mother's Hospital, Yorkhill, Glasgow G3 8SH, UK


    Abstract
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Acknowledgements
 References
 
BACKGROUND: Current estimates of the average duration of human pregnancy are flawed by inaccurate estimation of the time of conception and by failure to account adequately for the effect of routine elective delivery post-term. METHODS: In this study, 1514 healthy pregnant women were studied in whom the discrepancy between the menstrual history and first trimester crown–rump length estimated gestational age was within –1 to +1 day difference. The duration of gestation was estimated using time to event analysis: non-elective delivery was taken to be the event, and elective delivery was taken to be censoring. RESULTS: The median time to non-elective delivery using the Kaplan–Meier product limit estimate was 283 days after last menstrual period (LMP) and there was no difference comparing male and female fetuses. The median was significantly greater for nulliparous women compared with multiparous women (284 versus 282 days, P < 0.0001). Multivariate analysis using Cox's proportional hazards model confirmed the independent effect of nulliparity on duration of pregnancy [hazard ratio, 0.75; 95% confidence interval (CI) 0.67–0.85] and demonstrated no effect of maternal age, previous abortions, fetal sex, high parity, or bleeding before 24 completed weeks of gestation. Bleeding in the third trimester of pregnancy was, however, associated with an earlier onset of spontaneous labour (hazard ratio, 1.38; 95% CI 1.03–1.84). CONCLUSION: This study provides a basis for predicting the probability of labour at a given gestational age at term.

Key words: duration/human/pregnancy/proportional hazards models/survival analysis


    Introduction
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Acknowledgements
 References
 
Attempts to characterize the normal duration of pregnancy extend back through history, because of the importance of establishing paternity. Prior to modern obstetric methods, reference points for conception were taken as the first day of the last menstrual period (LMP) or the date of an isolated act of sexual intercourse (Reid, 1850Go). The LMP is a poor surrogate of the time of ovulation since, even among women with a regular 28 day cycle, the timing of ovulation is skewed to the second half of the cycle (Lenton and Landgren, 1985Go). Establishing the date of intercourse is clearly subject to multiple sources of error.

Modern obstetric techniques can be used to provide an unbiased estimate of gestational age. However, modern obstetric practice also involves routine elective delivery post-term (Grant, 1994Go). When attempting to estimate the duration of pregnancy, the effect of routine elective delivery cannot be avoided using current methods. If these pregnancies are excluded, then there is a systematic exclusion of pregnancies which are prolonged. If they are included, then the average duration of pregnancy includes cases where the end was never fully established.

A range of statistical techniques has been developed to estimate the average time period to the onset of a non-recurrent event, typically death (Hosmer and Lemeshow, 1999Go). These methods (typically referred to as `time to event analysis' or `survival analysis') take into account censored observations, i.e. observation of an individual to a given point until they no longer became at risk of the event. In the present study, it was sought to determine the average duration of human pregnancy among a previously described cohort of normal women (Smith et al., 1998Go) where gestational age had been confirmed by first trimester ultrasound and where the estimate was adjusted for the effect of elective delivery using time to event analysis. A preliminary account of some of this work has been presented in abstract form (Smith, 2000Go).


    Materials and methods
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Acknowledgements
 References
 
The results of all ultrasound scans performed between 1985 and 1995 at the Queen Mother's Hospital, Glasgow, UK were entered into a computer database along with details of the woman's medical, gynaecological and obstetric history, antenatal complications and pregnancy outcome. The database included all pregnant women referred for antenatal care because all were scanned at their first antenatal visit. Those women referred early for antenatal care were usually seen after having amenorrhoea for 12 weeks.

Over the 10 year period, 31269 embryos or fetuses had at least one scan and a known date of delivery. Gestational age at delivery was recorded in 31259 and birth weight was recorded in 30789. Of the 480 infants for whom birth weight was missing, 460 were delivered at <24 weeks.

Any pregnancies with the following (number of cases) were excluded: history of rhesus iso-immunization (279), essential hypertension (324), cardiac disease (128), type 1 diabetes mellitus (115), other medical problems (992), non-viable embryo or fetus at first scan (115), amniocentesis (1259), chorionic villous sampling (929), multiple pregnancy (364), antenatal detection of fetal abnormality (515), therapeutic termination of pregnancy (224), post-natal detection of fetal abnormality (560), intra-uterine contraceptive device seen on ultrasound (42), and second sac seen on ultrasound (85). There were a total of 4568 exclusions (some cases had multiple exclusions).

The crown–rump length was measured by the sonographer using electronic callipers on a frozen image on a monitor. The technique is described elsewhere (Evans et al., 1990Go). The crown–rump length was recorded as the equivalent number of days gestational age on the basis of an equation [gestational age (weeks) = 8.052 ÷ crown–rump length + 23.73] previously derived at The Queen Mother's Hospital (Robinson and Fleming, 1975Go). The scans analysed in the present study were performed by real-time ultrasonography using several machines, the majority were trans-abdominal scans through a full bladder.

The inclusion criteria based on the ultrasonography record were a single viable embryo or fetus present at the first ultrasound scan and a crown–rump length at the time of this scan less than the expected size after having amenorrhoea for 13 weeks. A total of 11314 of the 26701 non-excluded cases fulfilled these criteria.

The inclusion criteria from the menstrual history were: (i) there was a date recorded for the first day of the last menstrual period and that it was recorded as certain; (ii) there had been no oral contraceptive use in the preceding 3 months, and (iii) the menstrual cycle was 28 days and regular. Of the 11 314 cases with no exclusion criteria who had an early ultrasound scan, 4229 fulfilled the menstrual inclusion criteria and had a birth weight recorded. The study group consisted of 1514 cases where the discrepancy between the estimated gestational age by the menstrual history was within ±1 day of the ultrasound estimate.

Statistical analysis
Delivery by emergency Caesarean section or vaginal birth following non-induced labour were taken to be the event. Elective Caesarean section or any mode of delivery following an induced labour were taken as censoring. The cumulative probability of non-elective delivery at each day of gestation was estimated using the Kaplan–Meier product limit estimate. Univariate comparisons were made using the log rank test. Multivariate modelling was performed using Cox's proportional hazard's method. These techniques are described in detail elsewhere (Hosmer and Lemeshow, 1999Go). Statistical analysis was performed using Stata version 6.0 (Stata Corporation, College Station, TX, USA).


    Results
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Acknowledgements
 References
 
The basic characteristics of the study group are summarized in Table IGo. The simple arithmetic median interval from the first day of the LMP to the date of delivery was 281 days.


View this table:
[in this window]
[in a new window]
 
Table I. Characteristics of study group (n = 1514)
 
When the effect of censored observations was taken into account using the Kaplan–Meier product limit estimate, the median time from LMP to non-elective delivery was 283 days (95% confidence interval (CI), 282–284 days). There was no significant difference in the median comparing male and female fetuses and the number of elective deliveries was similar comparing the two sexes (female 23.1%, male = 24.3%). The median time from LMP to non-elective delivery was 2 days longer among nulliparous women compared with multiparous women (Table IIGo and Figure 1Go) and the difference was highly statistically significant (P < 0.0001). The proportion electively delivered was virtually identical comparing the two groups (nulliparous 23.3%, multiparous 24.0%). Excluding women with antepartum haemorrhage and treating emergency Caesarean sections as censored observations had no effect on the estimate of the median duration of pregnancy (Table IIGo).


View this table:
[in this window]
[in a new window]
 
Table II. Median time to delivery from Kaplan–Meier product limit estimate
 


View larger version (16K):
[in this window]
[in a new window]
 
Figure 1. Cumulative probability of non-elective delivery at each day of gestational age (dGA) for multiparous (filled symbols, n = 837) and nulliparous (hollow symbols, n = 677) women. Points are cumulative probability. Comparison of curves: P < 0.0001 (log rank test).

 
Multivariate analysis confirmed the independent effect of nulliparity on duration of pregnancy and demonstrated no effect of maternal age, previous abortions, fetal sex, high parity, or bleeding before 24 completed weeks of gestation (Table IIIGo). Bleeding in the third trimester of pregnancy was, however, associated with an earlier onset of spontaneous labour. Exclusion of deliveries by emergency Caesarean section had very little effect on the hazard ratios for primparity [0.80 (95% CI, 0.70–0.91)], third trimester bleeding [1.41 (1.03–1.92)] or any of the other covariates (data not shown).


View this table:
[in this window]
[in a new window]
 
Table III. Multivariate proportional hazards model of factors determining onset of labour at term
 

    Discussion
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Acknowledgements
 References
 
One of the most basic descriptive variables of a mammalian species is the average duration of pregnancy. All previous estimates of the average duration of human pregnancy are flawed either by sub-optimal gestational dating or by the failure to correct adequately for the effect of routine elective delivery post-term. The study group in this paper had optimum dating by menstrual history and this was confirmed by close agreement with first trimester ultrasound. This provides the most accurate estimate of gestational age currently possible in spontaneous conceptions (Evans et al., 1990Go). The effect of elective delivery was addressed in this study by the use of survival time analysis whereby elective deliveries were treated as censored observations. Using survival analysis in this cohort, the overall average duration of pregnancy was 283 days, two days longer than the simple arithmetic median interval from LMP to date of delivery.

Unlike previous studies (Bergsjo et al., 1990Go), there was no apparent difference in the duration of pregnancy comparing male and female fetuses (Tables II and IIIGoGo). Previous findings of a difference in gestational duration according to fetal sex may reflect a relationship between the timing of fertilization relative to the LMP and fetal sex (James, 1994Go). The duration of pregnancy was approximately two days longer in nulliparous women. This was not due to a confounding effect of associated variables (maternal age, previous abortions etc) since nulliparity was still associated with later delivery after adjusting for these variables (Table IIIGo). The event used in the current analysis was birth, rather than the onset of labour. Labour in nulliparous women is, on average, three hours longer than in multiparous women (Nesheim, 1988Go). This is clearly not sufficient to explain the observed 2 day difference in duration of pregnancy comparing nulliparous and multiparous women.

The physiological regulation of the onset of parturition in the human is still only partially understood. Current models postulate key roles for the fetal hypothalamo–pituitary–adrenal axis (Nathanielsz et al., 1998Go) and for the placenta (Majzoub and Karalis, 1999Go). The observed effect of parity does not exclude a key role for the fetus and placenta since important fetal variables, such as weight, differ between nulliparous and multiparous women (Kramer, 1987Go).

The clinical significance of this study is that it provides a basis for predicting the probability of labour at a given gestational age at term. This may be useful when planning trials of, for instance, routine induction of labour, or for the timing of procedures such as elective Caesarean section. The present data allow the probability that a woman might go into labour prior to a scheduled date for elective delivery to be estimated. Furthermore, the cumulative probability of delivery tended towards 1.0 at 300 days. However, the increased risk of stillbirth with very advanced gestational age (Yudkin et al., 1987Go) means that virtually no pregnancy would be allowed to continue into the 43rd week and very high rates of censoring undermine the estimates of the probability of delivery at these advanced gestational ages.

The observation that bleeding in the third trimester was associated with an earlier onset of spontaneous delivery is plausible. However, given the relatively small number of women affected by third trimester bleeding, there was virtually no effect on the median duration of pregnancy when these cases were excluded (Table IIGo). It is likely that a proportion of these cases were due to abruption which can initiate uterine activity. It is likely that labour in these women was initiated before the physiologically determined onset by a pathological process. However, the `event' was non-elective delivery, i.e. including delivery by emergency Caesarean section. This was done since over 75% of emergency Caesarean sections are performed after the onset of labour (Macara and Murphy, 1994Go). It might be argued that third trimester bleeding due both to abruption and placenta praevia could lead to emergency Caesarean section before the onset of labour and that the apparent association between third trimester bleeding and early onset of labour may simply reflect an association between bleeding and emergency Caesarean section. However, the hazard ratios associated with both third trimester bleeding and nulliparity were very similar when emergency Caesarean sections were excluded. Treating emergency Caesarean sections as spontaneous births might also be criticized since a small proportion of these will have been performed prior to the onset of labour. Furthermore, when Caesarean section is performed during labour, birth necessarily occurs earlier than if vaginal birth had been awaited. However, the influence of these factors would be expected to be relatively minor and, indeed, treating emergency Caesarean section as censoring had no significant effect on the estimated median duration of pregnancy (Table IIGo).


    Acknowledgements
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Acknowledgements
 References
 
I am grateful to Dr Margaret McNay and Mr John Fleming for providing access to the ultrasound database and to Mr Malcolm Smith for technical assistance. The author was funded by the Wellcome Trust.


    Notes
 
To whom correspondence should be addressed. E-mail: gcs4{at}cornell.edu


    References
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Acknowledgements
 References
 
Bergsjo, P., Denman, D.W., Hoffman, H.J. et al. (1990) Duration of human singleton pregnancy: a population based study. Acta Obstet. Gynecol. Scand., 69, 197–207.[Medline]

Evans, E., Farrant, P., Gowland, M. et al. (1990) Clinical applications of ultrasonic fetal measurements. British Medical Ultrasound Society/British Institute of Radiology, London, UK.

Grant, J.M. (1994) Induction of labour confers benefits in prolonged pregnancy. Br. J. Obstet. Gynaecol., 101, 99–102.[ISI][Medline]

Hosmer, D.W. and Lemeshow, S. (1999) Applied survival analysis: regression modeling of time to event data. Wiley, New York, USA.

James, W.H. (1994) Cycle day of insemination, sex ratio of offspring and duration of gestation. Ann. Hum. Biol., 21, 263–266.[ISI][Medline]

Kramer, M.S. (1987) Determinants of low birth weight methodological assessment and meta-analysis. Bull. WHO, 65, 663–738.[ISI][Medline]

Lenton, E.A. and Landgren, B.M. (1985) The normal menstrual cycle. In Shearman, R.P. (ed.) Clinical reproductive endocrinology. Churchill Livingstone, Edinburgh, pp. 81–108.

Macara, L. and Murphy, K.W. (1994) The contribution of dystocia to the Cesarean section rate. Am. J. Obstet. Gynecol., 171, 71–77.[ISI][Medline]

Majzoub, J.A. and Karalis, K.P. (1999) Placental corticotropin-releasing hormone: function and regulation. Am. J. Obstet. Gynecol., 180, S242–S246.[ISI][Medline]

Nathanielsz, P.W., Jenkins, S.L., Tame, J.D. et al. (1998) Local paracrine effects of estradiol are central to parturition in the rhesus monkey. Nat. Med., 4, 456–459.[ISI][Medline]

Nesheim, B.J. (1988) Duration of labor: an analysis of influencing factors. Acta Obstet. Gynecol. Scand., 67, 121–124.[ISI][Medline]

Reid, J. (1850) On the duration of pregnancy in the human female. Lancet, i, 438–440.

Robinson, H.P. and Fleming, J.E.E. (1975) A critical evaluation of sonar `crown–rump length' measurements. Br. J. Obstet. Gynaecol., 82, 702–710.[ISI][Medline]

Smith, G.C.S. (2000) Use of time to event analysis to estimate the normal duration of human pregnancy (abstract). J. Soc. Gynecol. Invest., 7 (supplement), 245A.

Smith, G.C.S., Smith, M.F.S., McNay, M.B. et al. (1998) First-trimester growth and the risk of low birth weight. N. Engl. J. Med., 339, 1817–1822.[Abstract/Free Full Text]

Yudkin, P.L., Wood, L. and Redman, C.W. (1987) Risk of unexplained stillbirth at different gestational ages. Lancet, i, 1192–1194.

Submitted on November 1, 2000; accepted on March 14, 2001.