How we calculate labor probabilities
We use a Johnson SU distribution to model the probability of spontaneous labor onset. This heavy-tailed distribution accurately captures the full range of delivery times, from extremely preterm (<28 weeks) through post-term.
Why Johnson SU?
• Heavy left tail: Properly models early preterm births that simple distributions miss
• Flexible shape: Fits both the preterm tail and term peak accurately
• Single distribution: Simpler than mixture models while being more accurate
Model vs NHS 2024-25 Data
Bars: All births (includes inductions/C-sections). Curve: Our model for spontaneous labor.
Note: The NHS data peaks at 39 weeks because ~60% of births are induced or scheduled. Our model predicts spontaneous labor onset, which has a wider spread and peaks later (40-41 weeks). This makes our predictions more useful for planning around natural labor timing.
Our model parameters are fitted to match official maternity statistics:
NHS Digital
Maternity Statistics 2023-24
View data →
CDC NCHS
Births: Final Data 2023
View data →
ONS
Birth Characteristics 2022
View data →
The fitted model matches ONS 2022 preterm breakdown:
0.6%
<28w (extremely preterm)
1.0%
28-32w (very preterm)
8.4%
32-37w (moderate)
10%
Total preterm
50%
By due date
All probabilities shown are conditional on not having delivered yet. This means we recalculate based on the fact that you're still pregnant. For example, if you're at 39 weeks, we only consider the remaining probability distribution from 39 weeks onward.
P(labor on day X | still pregnant) = P(labor on day X) / P(labor after today)Research shows several factors can shift the expected delivery date by a few days. We apply these as location adjustments to the distribution:
Parity
First-time mothers tend to deliver ~2 days later
Bergsjø et al. (2001) - BJOG
Fetal Sex
Boys arrive ~1 day later on average (280.6 vs 279.8 days)
Divon et al. (2002) - Am J Obstet Gynecol
BMI
Higher BMI associated with later delivery (up to +5 days)
Denison et al. (2008) - BJOG
Interpregnancy
Short intervals (<12 months) associated with earlier delivery
Shachar et al. (2017) - Obstet Gynecol
Plurality
Twins deliver ~3 weeks earlier (50% preterm), triplets+ ~7.5 weeks earlier
Murray et al. (2018) - TOG
These probabilities are for spontaneous labor onset only. They do not account for:
• Scheduled inductions or cesarean sections
• Medical conditions that may affect timing
• Individual variation beyond the modeled factors
• Research shows individual prediction has limited accuracy (c-statistic ~0.56)
Key research informing this model:
1.
Bergsjø P, et al. (2001)
Duration of human singleton pregnancy. BJOG
2.
Divon MY, et al. (2002)
Male gender prolongs pregnancy. Am J Obstet Gynecol
3.
Denison FC, et al. (2008)
Maternal BMI and timing of spontaneous labor. BJOG
4.
Shachar BZ, et al. (2017)
Interpregnancy interval and obstetric outcomes. Obstet Gynecol
5.
Murray SR, et al. (2018)
Spontaneous preterm birth prevention in multiple pregnancy. TOG
6.
ONS (2024)
Birth characteristics in England and Wales: 2022
7.
NHS Digital (2024)
NHS Maternity Statistics, England 2023-24
8.
CDC NCHS (2024)
Births: Final Data for 2023. NVSR Vol 73 No 1