Plain-language methodology
1. Starting point: real-world birth statistics
Large birth registries show that, among low-risk singleton pregnancies with spontaneous labor, births cluster between 37 and 42 weeks, with the highest likelihood occurring around the 40‑week mark. We base our starting curve on these observed population patterns, focusing on spontaneous (non‑induced) onset to reflect the natural timing of labor.
2. Personalizing the curve
Every pregnancy is unique. Decades of research show that certain factors can shift labor earlier or later—often by a few days, occasionally more. Your answers to our short questionnaire adjust the curve to reflect your situation. For example:
| What you tell us | How it moves the odds* |
|---|
| First baby | Labor often begins a bit later than for those who have given birth before. |
| Smoking during pregnancy | Raises the likelihood of earlier labor. |
| Previous baby arrived early | Increases the chance of another earlier arrival. |
| Higher body-mass index (BMI) | Associated with going slightly past the due date. |
*Effects are based on large medical studies from the U.S., Canada, the U.K., and Sweden.
We treat maternal age under 20 as a modest preterm risk (17% higher odds) without shifting the average date.
3. Accounting for early arrivals
About 1 in 10 U.S. babies are born before 37 weeks. Our model reflects this by allocating appropriate probability to the earlier part of the curve, consistent with observed rates. If your profile includes added early‑labor risks—such as smoking or a prior preterm birth—that earlier portion carries more weight; if not, it carries less.
4. One smooth prediction
We combine the early (pre‑37 weeks) and term portions into a single smooth curve, so the likelihood of labor increases steadily through the due‑date window—without artificial dips or double peaks. This avoids a “step” at 37 weeks and produces a realistic progression.
5. Updating as pregnancy progresses
Each time you use the calculator, we account for how far along you are. We remove days that have already passed and re‑scale the remaining curve. As you approach your due window, the forecast narrows and becomes more precise.
6. What you’ll see
- Most‑probable window – the tightest set of dates that captures about 50% of your remaining chance of going into labor.
- Key milestones – your personal 10%, 50%, and 90% probability dates.
- Early‑labor alert – if your profile suggests higher‑than‑average chance of labor before 37 weeks, we highlight that and link to trusted resources on preterm signs.
These numbers show probabilities, not promises. People with low early‑labor risk can still deliver early, and those who tend to go late can arrive sooner than expected. Use the calculator for planning and curiosity, and keep regular appointments with your healthcare team for personalized medical advice.
Where the numbers come from
We rely on peer‑reviewed research—national birth registries in Sweden and the U.S., cohort studies in the U.K. and Canada, and systematic reviews on topics such as smoking, multiple pregnancies, and maternal characteristics. The model is updated as new, high‑quality evidence becomes available.
Important note on effect sizes: The specific effect sizes used in the model are our best interpretation of the peer‑reviewed literature. They are not exact, but they are directionally correct based on the weight of evidence.
References
- Smith GC. Hum Reprod 2001 16:1497-1502 – baseline gestational length (PubMed)
- Oberg AS et al. Am J Epidemiol 2013 177:531-540 – genetic & maternal factors in post-term (PubMed)
- Shapiro-Mendoza CK, Barfield WD, Henderson Z, et al. CDC Grand Rounds: Public Health Strategies to Prevent Preterm Birth. MMWR Morb Mortal Wkly Rep. 2016; 65(32):826–830 (CDC).
- Patel RR et al. Int J Epidemiol 2004 33:107-113 – ethnic variation in gestation (PubMed)
- Selvaratnam RJ et al. Objective measures of smoking and caffeine intake and the risk of adverse pregnancy outcome. International Journal of Epidemiology. 28 Sept 2023 (IJE)
- Levine LD, Bogner HR, Hirshberg A, et al. Term induction of labor and subsequent preterm birth. American Journal of Obstetrics and Gynecology. 2014; 210(4):354.e1-354.e8 (AJOG)
- Purisch SE, Gyamfi-Bannerman C. Epidemiology of preterm birth. Seminars in Perinatology. 2017; 41(7):387-391 (Seminars in Perinatology)
- Oliver-Williams C, Fleming M, Wood AM, Smith G. Previous miscarriage and the subsequent risk of preterm birth in Scotland, 1980-2008: a historical cohort study. BJOG. 2015 Oct;122(11):1525-34. doi: 10.1111/1471-0528.13276. Epub 2015 Jan 28. PMID: 25626593; PMCID: PMC4611958 (PubMed)
- Erickson EN et al. NPJ Digit Med 2023 6:153 – smart-ring physiology model (PubMed)
- Han Z et al. Int J Epidemiol 2011 40:65-75 – underweight & PTB meta-analysis (Oxford Academic)
1. Overview
The calculator estimates the day-specific probability of spontaneous onset of labor for an individual pregnancy using a single, smooth hazard-based model that covers both pre-term and term/post-term deliveries. The model is probabilistic: it combines (i) a population baseline calibrated to singleton term births, (ii) evidence-based additive day-shifts for user-supplied risk factors applied as horizontal shifts, and (iii) a pre-37-week probability determined from registry rates and covariate odds ratios, injected via the same hazard curve. All code runs locally in the browser; no personal data leave the user's device.
2. Baseline hazard and parametric form
Source data. The baseline timing is anchored to population analyses of low-risk singleton pregnancies (e.g., Smith et al., Kaplan–Meier time-to-event), with median near 40 weeks and realistic right-tail mass (PubMed links below). The current engine parameterizes a flexible exponential hazard that reproduces these features after calibration.
Parametric form (> 32 weeks). For gestational age in days t (LMP-based), we model the instantaneous hazard of spontaneous labor as an exponential function of time with horizontal shift:
$$ \lambda(t \mid X) = h_0(X)\,\exp\{\gamma(X)\,[(t - s(X)) - 259]\}, \qquad t \ge 150 \text{ d}. $$
Here $$h_0(X)$$ and $$\gamma(X)$$ are calibrated to meet baseline survival and tail-shape constraints, and $$s(X) = \mu^*(X) - \mu_{\text{baseline}}$$ is a horizontal shift parameter that incorporates all additive day-shifts. The baseline mean for a reference mother is
$$ \mu_0 = 276.5 \, \text{days}. $$
There is no explicit variance parameter in this formulation; dispersion arises from the integrated hazard shape combined with the horizontal shift.
3. User-level covariates and day-shifts
Predictors listed below are incorporated as either (a) additive day-shifts $$\Delta \mu(X)$$ to the target mean or (b) multiplicative odds ratios that adjust the pre-term probability $$\pi(X)$$ (Section 4). The values used in the current release are shown in the right-hand column.
| Predictor (user entry) | Evidence base | Effect coded in the model |
|---|
| First pregnancy (nullipara) | Smith 2001 (n = 1 514) – median 284 d vs 282 d (PubMed) | +2 days (Δμ) |
| Maternal age ≥ 35 y | Oberg 2013 Swedish registry (n = 475 429) – higher post-term odds (PubMed) | +1 day (Δμ); PTB OR 1.1 applied |
| Maternal age < 20 y | Shapiro-Mendoza et al. 2016 – PTB 12% vs 10% overall (CDC) | –2 days (Δμ); PTB OR 1.17 applied |
| BMI 25–29.9 / ≥ 30 | Oberg 2013 – obesity raises post-term odds (PubMed) | +1 / +2 days (Δμ); PTB OR 1.0 / 0.9 applied |
| BMI < 18.5 | Meta-analysis IJE 2011 – underweight ↑ PTB risk (Oxford Academic) | –2 days (Δμ) and PTB OR 1.4 applied |
| Male fetus | Oberg 2013 – male sex ↑ post-term odds (PubMed) | +0.8 day (Δμ) |
| Current smoker | Selvaratnam 2023 – objective biomarkers; smoking and caffeine vs adverse outcomes (IJE) | PTB OR 2.6 applied to $$\pi(X)$$; –5 days (Δμ) |
| Prior spontaneous PTB < 37 w | Levine et al. 2014 – term induction and subsequent PTB (AJOG) | PTB OR 3.0 applied to $$\pi(X)$$; –6 days (Δμ) |
| Prior post-term (> 41 w) | Oberg 2013 – repeat OR 4.4 same father (PubMed) | +3 days (Δμ); PTB OR 0.6 applied |
| Prior miscarriage | Oliver-Williams et al. 2015 – Scottish cohort 1980-2008 (PubMed) | –2 days (Δμ); PTB OR 1.2 applied |
| Black ethnicity | London 122 415 cohort – median 39 w vs 40 w (PubMed) | –7 days (Δμ); PTB OR (Black 1.6) applied |
| Time since last birth < 12 mo | Purisch & Gyamfi-Bannerman 2017 – short interpregnancy interval epidemiology (Seminars in Perinatology) | –3 days (Δμ); PTB OR 1.8 applied |
All additive effects are combined to form the target mean $$ \mu^*(X) = \mu_0 + \Delta \mu(X) $$ and implemented as a horizontal shift $$ s(X) = \mu^*(X) - \mu_{\text{baseline}} $$. Odds-ratio effects modify the pre-term probability $$\pi(X)$$. There is no separate variance parameter in the current release.
4. Pre-term (< 37 weeks) probability
Population weight. The U.S. obstetric-estimate pre-term birth rate was 10.4% in 2016 (Shapiro-Mendoza et al.). For an individual, the model multiplies the baseline odds by published odds ratios for declared risk factors (e.g., OR 2.6 for smoking, OR 1.6 for Black ethnicity, OR 1.8 for interpregnancy interval < 12 months). The resulting probability $$\pi(X)$$ is truncated to 1–40%.
Injection via the hazard curve. Rather than a separate pre-term kernel, the same exponential hazard with horizontal shift is calibrated so that survival at 37 weeks matches the target pre-term mass:
$$ S(259 \mid X) = \exp\{-H(259 \mid X)\} = 1 - \pi(X), $$
where the integrated hazard is
$$ H(t \mid X) = \int_{224}^{t} \lambda(u \mid X)\,du = \frac{h_0(X)}{\gamma(X)}\Bigl[\exp\{\gamma(X)\,[(t-s(X))-259]\} - \exp\{\gamma(X)\,[(224-s(X))-259]\}\Bigr]. $$
5. Solving for parameters and the full distribution
Two-step calibration. The model uses a two-step approach: (1) Grid-search over $$\gamma$$ to find the pair $$\{h_0(X), \gamma(X)\}$$ that satisfies $$S(259)=1-\pi(X)$$ and tail-shape targets (median = 283 d, P90 = 296 d, P95 ≤ 302 d) with applicable horizontal shifts. (2) Apply the horizontal shift $$s(X) = \mu^*(X) - \mu_{\text{baseline}}$$ so that the unconditional mean delivery day equals $$\mu^*(X)$$.
PDF and CDF. Once calibrated, the unconditional density and distribution are
$$ f(t \mid X) = \lambda(t \mid X)\,S(t \mid X), \qquad F(t \mid X)=1-S(t \mid X), \quad t \ge 224. $$
6. Conditioning on "still pregnant today"
If a user is already g days into pregnancy, the displayed curve is conditional on survival to g:
$$ f^*(t \mid X, g) = \frac{ \lambda(t \mid X) \exp\{-\!\int_{g}^{t} \lambda(u \mid X)du\} }{ S(g \mid X) } \, 1_{(t>g)}, $$
with $$ S(g \mid X)=\exp\{-H(g \mid X)\} $$ where all hazard functions include the horizontal shift $$s(X)$$. All probabilities shown in the app (e.g., "chance of labor in the next 7 days") are computed from this conditional PDF.
7. Outputs
- Most-probable window = narrowest interval containing 50% of the remaining probability mass.
- Point estimates: median (50th pct), P10, P90.
- Pre-term warning: if $$\pi(X) \ge 15\%$$ a banner links to March-of-Dimes resources on recognizing pre-term labor.
8. Limitations
The model relies on published effect sizes and registry summaries rather than raw patient-level datasets; rare interactions may be missed. Inputs such as cervical length or fetal fibronectin are not yet incorporated, but the modular code allows future integration. The current hazard specification does not include an explicit variance parameter; dispersion is governed by the calibrated hazard shape and horizontal shift. The horizontal-shift approach eliminates the need for re-fitting $$h_0$$ and $$\gamma$$ when only the mean changes, improving computational efficiency.
9. Disclaimer
The calculator is for informational purposes only and must not guide medical decision-making. Users with concerns about early or late delivery should consult their healthcare provider.
Important note on effect sizes: The effect sizes implemented here reflect our best interpretation of the peer‑reviewed literature. They are not exact, but they are directionally correct given current evidence. Different model specifications are possible which can change the estimated labor onset timing probabilities.
References
- Smith GC. Hum Reprod 2001 16:1497-1502 – baseline gestational length (PubMed)
- Oberg AS et al. Am J Epidemiol 2013 177:531-540 – genetic & maternal factors in post-term (PubMed)
- Shapiro-Mendoza CK, Barfield WD, Henderson Z, et al. CDC Grand Rounds: Public Health Strategies to Prevent Preterm Birth. MMWR Morb Mortal Wkly Rep. 2016; 65(32):826–830 (CDC).
- Patel RR et al. Int J Epidemiol 2004 33:107-113 – ethnic variation in gestation (PubMed)
- Selvaratnam RJ et al. Objective measures of smoking and caffeine intake and the risk of adverse pregnancy outcome. International Journal of Epidemiology. 28 Sept 2023 (IJE)
- Levine LD, Bogner HR, Hirshberg A, et al. Term induction of labor and subsequent preterm birth. American Journal of Obstetrics and Gynecology. 2014; 210(4):354.e1-354.e8 (AJOG)
- Purisch SE, Gyamfi-Bannerman C. Epidemiology of preterm birth. Seminars in Perinatology. 2017; 41(7):387-391 (Seminars in Perinatology)
- Oliver-Williams C, Fleming M, Wood AM, Smith G. Previous miscarriage and the subsequent risk of preterm birth in Scotland, 1980-2008: a historical cohort study. BJOG. 2015 Oct;122(11):1525-34. doi: 10.1111/1471-0528.13276. Epub 2015 Jan 28. PMID: 25626593; PMCID: PMC4611958 (PubMed)
- Erickson EN et al. NPJ Digit Med 2023 6:153 – smart-ring physiology model (PubMed)
- Han Z et al. Int J Epidemiol 2011 40:65-75 – underweight & PTB meta-analysis (Oxford Academic)