C14 · Small for gestational age: whose chart flags whom?

The brief

A hospital network is replacing its newborn-assessment software. Every baby is weighed at birth, and a baby lighter than the 10th centile of birth weight for its gestational age and sex is flagged small for gestational age (SGA): it gets extra glucose checks, a paediatric review and closer follow-up, because SGA babies carry a higher risk of stillbirth, hypoglycaemia and later problems. The network's obstetric lead asks you:

"Build us the 10th-centile chart, by sex, from recent US births - with an honest statement of how sure you are of it, especially for the preterm weeks. And a question our midwives keep asking: should babies of mothers who smoked, or who had gestational hypertension, be judged against their own charts? Those babies are smaller anyway. How many babies per 1000 would that stop - or start - flagging, and would you recommend it?"

This is the sequel to example E83 (Bayesian quantile regression). Do E83 first: this challenge assumes you know the check loss, why the asymmetric Laplace is only a working likelihood, and the sandwich / learning-rate fixes. E83 asked what quantile regression can tell you; here a chart has to be used, by sex, at every week from 24 to 42, and a policy question rides on it.

How this notebook works

Each task states what to deliver, not how. Write your code in the YOUR CODE HERE cells.
Stuck? h.hint("task2") reveals hints one level at a time: nudge → approach → code skeleton. Try to get by on nudges.
h.check("task2", q10_40_girls=...) compares your numbers with the reference solution.
A full worked solution lives in notebooks/solutions/. Open it only when you are done (or truly stuck).

import logging
import time
import warnings

import arviz as az
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import pymc as pm
import pytensor.tensor as pt

from pymc_challenges import Hints, data

RANDOM_SEED = 2023
rng = np.random.default_rng(RANDOM_SEED)
az.style.use("arviz-variat")
logging.getLogger("pymc").setLevel(logging.WARNING)  # several fits: no sampler banner per fit
warnings.filterwarnings("ignore", category=RuntimeWarning, module="arviz")
pd.set_option("display.width", 160)
T_START = time.time()

h = Hints("C14")
h.tasks()

C14 - Small for gestational age: whose chart flags whom?

task0 - Which gestational age? Which records? (3 hints, 1 check(s))
task1 - The quick chart (3 hints, 1 check(s))
task2 - A smooth chart that borrows strength (3 hints, 2 check(s))
task3 - Can you trust the bands? (3 hints, 2 check(s))
task4 - Charts for smokers and for gestational hypertension (3 hints, 2 check(s))
task5 - The decision (3 hints, 2 check(s))

The data

One row per singleton birth. load only parses the raw NCHS codes; it does not clean them.

column	meaning
`dbwt`	birth weight in grams (9999 = unknown)
`combgest`	gestation in completed weeks, combined estimate: from the date of the last menstrual period (LMP), with the obstetric estimate filled in when the LMP date is missing or implausible (99 = unknown)
`oegest_comb`	gestation in completed weeks, obstetric estimate recorded by the clinician (usually from an early ultrasound) (99 = unknown)
`sex`	M / F
`cig_0` ... `cig_3`	cigarettes per day before pregnancy and in trimesters 1, 2, 3 (99 = unknown)
`rf_ghype`	gestational hypertension: Y / N / U (unknown)
others	mother's age, race, education, BMI, weight gain, diabetes ... (see `data.describe`)

data.describe("natality_births")
raw = data.load("natality_births")
raw[["dbwt", "combgest", "oegest_comb", "sex", "cig_1", "cig_2", "cig_3", "rf_ghype"]].describe(include="all").T

natality_births: A simple random sample of 20,000 of the 3,491,735 SINGLETON births of 2023 (raw codes; 9 / 99 / 99.9 / 999 / 9999 = unknown, empty = not reported): dob_mm, mager (mother's age), mrace6 (1 White, 2 Black, 3 AIAN, 4 Asian, 5 NHOPI, 6 more than one race), dmar (1 married, 2 unmarried; not reported for California), meduc (1-8 education, 9 unknown), tbo_rec (total birth order), previs (prenatal visits), cig_0..cig_3 (cigarettes per day before pregnancy and in trimesters 1-3), m_ht_in (inches), bmi (pre-pregnancy), pwgt_r (pre-pregnancy weight, lb), wtgain (lb), rf_pdiab / rf_gdiab / rf_ghype (pre-pregnancy diabetes, gestational diabetes, gestational hypertension: Y/N/U), sex (M/F), combgest and oegest_comb (gestation in weeks, combined and obstetric estimate), dbwt (birth weight, grams).
  source: National Center for Health Statistics (NCHS), National Vital Statistics System, Natality public use file 2023 (all 3,605,081 US birth certificates of 2023; codes as in the NCHS 'User Guide to the 2023 Natality Public Use File'), read from NBER's CSV conversion (the URL; 188 MB). US government work, public domain; NCHS asks users to cite the source and not to attempt to identify anyone. BUILT by tools/build_e83_natality.py (a seeded random subsample) - keep the cached file.
  url:    https://data.nber.org/nvss/natality/csv/2023/natality2023us.zip

	count	unique	top	freq	mean	std	min	25%	50%	75%	max
dbwt	20000.0	NaN	NaN	NaN	3277.88435	593.076428	229.0	2976.0	3300.0	3629.0	9999.0
combgest	20000.0	NaN	NaN	NaN	38.66105	3.007759	17.0	38.0	39.0	40.0	99.0
oegest_comb	20000.0	NaN	NaN	NaN	38.4858	2.685286	17.0	38.0	39.0	39.0	99.0
sex	20000	2	M	10214	NaN	NaN	NaN	NaN	NaN	NaN	NaN
cig_1	20000.0	NaN	NaN	NaN	0.64555	5.98433	0.0	0.0	0.0	0.0	99.0
cig_2	20000.0	NaN	NaN	NaN	0.564	5.834981	0.0	0.0	0.0	0.0	99.0
cig_3	20000.0	NaN	NaN	NaN	0.92785	8.478664	0.0	0.0	0.0	0.0	99.0
rf_ghype	20000	3	N	17989	NaN	NaN	NaN	NaN	NaN	NaN	NaN

Task 0 · Which gestational age? Which records?

A chart is only as good as the gestational ages it is built on, and the file gives you two.

Deliver

The unknown codes that matter for a weight-for-age chart, and how many records they remove.
Evidence for choosing between combgest and oegest_comb: how often do they disagree, by how much, and what would each do to a weekly 10th centile - at the preterm weeks and after 41 weeks? Report the share of births with a known weight that combgest places at 43 weeks or more.
A rule for records whose weight is implausible for their gestational age, and an argument for which side(s) of the distribution that rule may touch, given what the chart is for.
The range of weeks the chart can cover.

Your turn Work this task in the notebook.

Hints for this task — open one at a time

1 Nudge

Two columns claim to be the same thing. Tabulate both, and their difference, and ask what a "45-week" birth means in 2023. Then think about what a misdated term baby does to a chart when it lands at 30 weeks, and what a misdated preterm baby does when it lands at 40. Finally: which babies is the chart for? A cleaning rule that deletes them defeats the purpose.

2 Approach

Drop dbwt == 9999 and 99 weeks. Compare combgest and oegest_comb: value_counts() of each, a histogram of their difference, and per week (at least 10 births) the 10th centile of dbwt and the share of babies over 3 kg under each measure.

For implausible weight-for-age, a robust z-score of log weight within week and sex ((x - median) / (1.4826 * MAD)) finds the outliers. Look at both tails before deciding which side to trim: is a 1.2 kg baby at 39 weeks an error or a growth-restricted baby?

3 Skeleton

known = raw[(raw.dbwt < 9999) & (raw.combgest < 99) & (raw.oegest_comb < 99)]
share_43 = np.mean(known.___ >= 43)
diff = known.combgest - known.oegest_comb
for col in ("combgest", "oegest_comb"):
    q10 = known.groupby(col).dbwt.quantile(___)        # weekly 10th centile
    heavy = known.groupby(col).dbwt.apply(lambda v: np.mean(v > ___))

lw = np.log(known.dbwt)
g = lw.groupby([known.oegest_comb, known.sex])
z = (lw - g.transform("median")) / g.transform(lambda v: 1.4826 * np.median(np.abs(v - np.median(v))))
suspicious = (z > 4) & (known.oegest_comb < ___)        # which side, and where?

Self-checks in the notebook (h.check("task0", …)):

share_combgest_43plus — share of births with known weight and gestation that combgest places at 43+ weeks, about 0.029 (a share, not a percentage)

The analysis data (everyone uses this from here on)

So that numbers can be compared, the rest of the notebook uses the rules above: obstetric gestational age, 24-42 weeks, unknown weight / gestation / smoking (first or second trimester) / hypertension dropped, and the upper-side-only, preterm-only trim. A smoker smoked in any trimester (a third-trimester "unknown" counts as no information, not as a reason to drop: there was no third trimester for many preterm babies, see E83). We model log birth weight: quantiles are equivariant under monotone transforms, so the 10th centile of log weight is the log of the 10th centile, and effects become percentages.

The births are split at random into a training set of 10,000 for fitting the chart and a held-out set for checking it and for the decision.

ok = ((raw.dbwt < 9999) & (raw.oegest_comb < 99) & (raw.cig_1 < 99) & (raw.cig_2 < 99)
      & (raw.rf_ghype != "U") & raw.oegest_comb.between(24, 42))
births = raw[ok].copy()
births["lbw"] = np.log(births.dbwt / 1000)  # log kg
grp = births.groupby(["oegest_comb", "sex"]).lbw
zrob = (births.lbw - grp.transform("median")) / grp.transform(lambda v: 1.4826 * np.median(np.abs(v - np.median(v))))
births = births[~((zrob > 4) & (births.oegest_comb < 37))].reset_index(drop=True)
births["boy"] = (births.sex == "M").astype(int)
births["week"] = births.oegest_comb.astype(int)
births["smoker"] = ((births.cig_1 > 0) | (births.cig_2 > 0) | ((births.cig_3 > 0) & (births.cig_3 < 99))).astype(int)
births["hyp"] = (births.rf_ghype == "Y").astype(int)

WEEKS = np.arange(24, 43)
N_WEEKS = len(WEEKS)
SEXES = ["girl", "boy"]
N_TRAIN = 10_000
perm = rng.permutation(len(births))
train = births.iloc[perm[:N_TRAIN]].reset_index(drop=True)
test = births.iloc[perm[N_TRAIN:]].reset_index(drop=True)
y_tr, wk_tr, sx_tr = train.lbw.to_numpy(), train.week.to_numpy() - 24, train.boy.to_numpy()
y_te, wk_te, sx_te = test.lbw.to_numpy(), test.week.to_numpy() - 24, test.boy.to_numpy()
print(f"{len(births):,} births: training {len(train):,}, held out {len(test):,}; "
      f"smokers {births.smoker.mean():.1%}, gestational hypertension {births.hyp.mean():.1%}")
counts = pd.crosstab(train.sex, train.week)
counts

19,852 births: training 10,000, held out 9,852; smokers 3.2%, gestational hypertension 9.9%

week	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42
sex
F	3	2	5	8	7	5	7	8	19	24	60	61	168	595	819	1918	906	256	11
M	4	6	6	4	3	10	11	8	21	26	61	91	190	619	950	1998	867	230	13

Task 1 · The quick chart

The obvious chart: for each week and sex, the empirical 10th centile of the training births.

Deliver

The chart (both sexes, all weeks 24-42) on a scale where you can see the preterm weeks.
What is wrong with it, in words a neonatologist would accept: look at neighbouring weeks and at the difference between boys and girls where there are few births.
The share of held-out babies it flags, by gestational-age band and sex (24-31, 32-34, 35-36, 37, 38, 39, 40, 41-42 weeks). Is 10% what you get?

Your turn Work this task in the notebook.

Hints for this task — open one at a time

1 Nudge

Count the training births per week and sex before you trust any number. How many babies does it take to estimate a 10th centile? What does an "empirical 10th centile" of seven babies mean?

2 Approach

Loop over sex and week and take np.quantile(..., 0.1) of the training log weights. Plot on a log scale (the preterm weeks are a factor of ten lighter). For the held-out check, flag each held-out baby whose log weight is below its week-and-sex value, then average the flags within each gestational-age band and sex. A binomial standard error sqrt(0.1 * 0.9 / n) tells you how far from 10% a cell can be by chance.

3 Skeleton

emp = np.full((2, N_WEEKS), np.nan)
for s in range(2):
    for w in range(N_WEEKS):
        v = y_tr[(sx_tr == s) & (wk_tr == w)]
        emp[s, w] = np.quantile(v, ___) if len(v) else np.nan

flag = y_te < emp[___, ___]                      # one True/False per held-out baby
for a, b in [(24, 31), (32, 34), ...]:
    m = test.week.between(a, b).to_numpy() & (sx_te == s)
    print(a, b, s, m.sum(), flag[m].mean())

Self-checks in the notebook (h.check("task1", …)):

q10_39_girls — empirical 10th centile at 39 weeks for girls in the training births, about 2,880 g (grams, not log kg)

Task 2 · A smooth chart that borrows strength

Build a Bayesian model for the 10th centile of log birth weight at each week, for both sexes, that

makes the curve smooth across weeks, with the amount of smoothing learned from the data;
shares information between boys and girls: a common curve plus a sex difference that is small and changes slowly;
uses the asymmetric Laplace working likelihood of E83 (pm.AsymmetricLaplace(..., q=0.1)).

Deliver

Your priors, and why the smoothing prior is on the scale you chose.
A fit with clean diagnostics.
The chart with 90% bands on top of Task 1's points, and the boy-girl difference by week.
The 10th centile at 40 weeks for girls and boys (posterior median, grams), and the held-out flag table of Task 1 for your new chart.

Your turn Work this task in the notebook.

Hints for this task — open one at a time

1 Nudge

Weeks are whole numbers, so "a smooth curve" can be 19 numbers whose second differences are small. What prior says that? And how could a boy curve and a girl curve share almost everything?

2 Approach

A second-order random walk on the weekly log 10th centile: f gets a vague prior per week, and a pm.Potential adds Normal(0, s_f) log-densities of D2 @ f, with D2 = np.diff(np.eye(19), 2, axis=0) and a learned s_f (think about how fast the weekly growth rate changes to set its prior scale). The sexes: girls f - h/2, boys f + h/2, where h is a level plus a slow random walk with a small step sd (non-centred via pt.cumsum).

Likelihood: pm.AsymmetricLaplace("y", mu=q[sex, week], b=np.sqrt(tau * (1 - tau)) / sigma, q=tau, observed=...) - remember from E83 that PyMC's b is a rate, not the check-loss scale. The random- walk and cumulative-sum structure makes neighbouring weeks strongly correlated: nutpie's nuts={"adaptation": "low_rank"} helps.

3 Skeleton

D2 = np.diff(np.eye(N_WEEKS), 2, axis=0)
with pm.Model(coords={"week": WEEKS, "sex": SEXES}) as m:
    f = pm.Normal("f", 0.5, 1.0, dims="week")
    s_f = pm.HalfNormal("s_f", ___)
    pm.Potential("rw2", pm.logp(pm.Normal.dist(0.0, s_f), pt.as_tensor(D2) @ f).sum())
    h0 = pm.Normal("h0", 0.0, 0.1)
    s_h = pm.HalfNormal("s_h", ___)
    walk = pt.cumsum(pm.Normal("h_z", 0.0, 1.0, dims="week"))
    h = h0 + s_h * (walk - walk.mean())
    q = pm.Deterministic("q", pt.stack([___, ___]), dims=("sex", "week"))
    sigma = pm.HalfNormal("sigma", 0.2)
    pm.AsymmetricLaplace("y", mu=q[sx_tr, wk_tr], b=___, q=0.1, observed=y_tr)
    idata = pm.sample(nuts={"adaptation": "low_rank"}, random_seed=RANDOM_SEED)

Self-checks in the notebook (h.check("task2", …)):

q10_40_girls — posterior median 10th centile at 40 weeks for girls, about 2,980 g (grams)
q10_40_boys — posterior median 10th centile at 40 weeks for boys, about 3,085 g (grams)

Task 3 · Can you trust the bands?

The asymmetric Laplace is a working likelihood (E83). Find out what that does to this chart.

Deliver

At the data-rich weeks (37-41), compare the posterior sd of each sex's 10th centile with an honest frequentist yardstick. Report the median ratio (posterior sd / yardstick sd).
The held-out flag rates of Task 2 with an interval for each cell that includes both the binomial noise of the held-out cell and your posterior's uncertainty about the curve. How many cells fall outside their 90% interval? What can this check see, and what can it not?
Fix the bands - one of E83's fixes is enough - refit, and redo 1 and 2. Did anything besides the band width change? (Look at the learned smoothness.)

Your turn Work this task in the notebook.

Hints for this task — open one at a time

1 Nudge

Where can you get an honest measure of how much a weekly 10th centile moves from sample to sample, without trusting any likelihood? Where is that measure itself trustworthy? And for the held-out check: how big is the binomial noise of a held-out cell compared with the uncertainty of the curve?

2 Approach

Bootstrap the training births (resample with replacement, a few hundred times) and recompute the empirical 10th centile at 37-41 weeks for each sex; compare its sd with the posterior sd of the same cells. For the held-out check, evaluate every posterior draw of the curve on the held-out babies of a cell: the spread of those flag rates is the curve's uncertainty in "rate units"; add the binomial variance 0.09 / n.

Fix (E83): a generalised posterior, pm.Potential("loss", -w * check_loss(y - mu).sum()), whose learning rate w is the asymmetric Laplace's 1 / sigma times the (geometric mean) ratio of posterior to bootstrap variance. Refit and compare - including the posterior of s_f.

3 Skeleton

TERM = np.flatnonzero((WEEKS >= 37) & (WEEKS <= 41))
boot = np.empty((300, 2, len(TERM)))
for b in range(300):
    i = rng.integers(0, N_TRAIN, N_TRAIN)
    for s in range(2):
        for j, w in enumerate(TERM):
            boot[b, s, j] = np.quantile(y_tr[i][(sx_tr[i] == s) & (wk_tr[i] == w)], 0.1)
ratio = q_draws[:, :, TERM].std(0) / boot.std(0)        # q_draws: (draws, sex, week)
sd_ratio = np.median(ratio)

var_ratio = np.exp(np.mean(np.log(ratio ** 2)))
w = var_ratio / ___                                      # posterior mean of sigma
r = y_tr - q[sx_tr, wk_tr]
pm.Potential("loss", -w * (r * (0.1 - (r < 0))).sum())    # replaces the AsymmetricLaplace

Self-checks in the notebook (h.check("task3", …)):

sd_ratio_ald — median over sex x weeks 37-41 of (asymmetric Laplace posterior sd / bootstrap sd) of the 10th centile, about 0.55
sd_ratio_fixed — the same ratio after your fix, about 0.85 (a little below 1 is expected, since the smooth chart borrows from neighbouring weeks)

Task 4 · Charts for smokers and for gestational hypertension

The midwives' question needs conditional 10th centiles: the 10th centile of birth weight given week, sex, smoking and gestational hypertension.

Deliver

A model for that, built on Task 3's (calibrated) chart. Think about whether the hypertension effect should be the same before and after 37 weeks - and about why it might not be.
The effects at the 10th centile as percentages with 90% intervals, and a check that the intervals of the effect you will use in Task 5 are honest.
Explain why the hypertension effect at the 10th centile, given gestational age, is so much smaller than the roughly -290 g E83 found at the 10th centile without gestational age in the model.

Your turn Work this task in the notebook.

Hints for this task — open one at a time

1 Nudge

A conditional chart is the same model with shifts. On the log scale a shift is a percentage. Why would hypertension in a baby born at 33 weeks mean something different from hypertension at 39 weeks? And is the learning rate you calibrated on the curve automatically right for a coefficient?

2 Approach

Add X @ beta to the mean, with columns smoker, hypertension, and hypertension x (week < 37), and keep Task 3's learning rate. To check the coefficients' intervals, you need a classical estimate and a bootstrap: quantile regression of log weight on one dummy per (sex, week) cell plus the three columns, solved as a linear programme (E83's rq_fn, or scipy.optimize.linprog), resampled ~200 times.

For the comparison with E83: what does hypertension do to the week at which a baby is born?

3 Skeleton

X_tr = pd.DataFrame({"smoker": train.smoker, "hyp": train.hyp,
                     "hyp_preterm": train.hyp * (train.week < ___)})
# inside the model, after mu = q[sx, wk]:
beta = pm.Normal("beta", 0.0, 0.2, dims="cov")
mu = mu + pt.as_tensor(X_tr.to_numpy(float)) @ beta

smoking_pct = 100 * (np.exp(beta_draws[:, 0].mean()) - 1)

cell = sx_tr * N_WEEKS + wk_tr
Xq = np.column_stack([np.eye(2 * N_WEEKS)[cell], X_tr.to_numpy(float)])
Xq = Xq[:, Xq.sum(0) > 0]                                   # drop empty cells
b_hat = rq_fn(Xq, y_tr, 0.1)[-3:]                           # then bootstrap rows

Self-checks in the notebook (h.check("task4", …)):

smoking_pct — posterior mean change of the 10th centile for babies of smokers, in percent, about -5
hyp_term_pct — posterior mean change of the 10th centile for hypertension at term, in percent, about -0.7 (with an interval that includes 0)

Task 5 · The decision

Deliver, on the held-out births, comparing the conditional chart (Task 4) with the population chart (Task 3), with 90% intervals that include both charts' uncertainty and the sampling of the babies:

Per 1000 babies of smokers, and per 1000 babies of hypertensive mothers: how many fewer are flagged under the conditional chart?
Per 1000 births overall: how many babies stop being flagged, how many start being flagged, and the net change. Explain the sign of each.
A recommendation to the obstetric lead in a few sentences - including a reason that does not come out of the posterior.

Your turn Work this task in the notebook.

Hints for this task — open one at a time

1 Nudge

A posterior draw of each chart flags each held-out baby or not. Count per draw. Then ask what a conditional 10th centile does to the total number flagged - and who makes up the difference.

2 Approach

Pair the draws of the two fits by index. For each pair, compute two flag vectors on the held-out babies (population chart; conditional chart with each baby's own shifts). For the sampling of the babies, weight them with rng.dirichlet(np.ones(n)) (a Bayesian bootstrap), a fresh draw per pair. Then: weighted share among smokers under each chart, the difference x 1000; babies flagged by one chart but not the other, per 1000 births; and the net difference.

For the recommendation: what does a chart define as normal growth?

3 Skeleton

for i, (sp, sc) in enumerate(zip(idx_pop, idx_cond)):
    wts = rng.dirichlet(np.ones(len(y_te)))
    f_pop = y_te < q_pop[sp][sx_te, wk_te]
    f_cond = y_te < q_cond[sc][sx_te, wk_te] + X_te @ beta[sc]
    fewer_smk[i] = 1000 * np.sum(wts[smk] * (___)) / wts[smk].sum()
    off[i] = 1000 * np.sum(wts * (f_pop & ~f_cond))
    on[i] = 1000 * np.sum(wts * (___))
    net[i] = ___

Self-checks in the notebook (h.check("task5", …)):

fewer_per_1000_smokers — posterior mean of how many FEWER babies of smokers per 1000 are flagged under the conditional chart (a positive number), about 60
net_per_1000_births — posterior mean net change in flagged babies per 1000 births (conditional minus population), about 0

Going further

A 3rd centile ("severe SGA") line. Fit it separately with the same model and check whether it crosses the 10th anywhere in the posterior draws; then fit both jointly with $\log q_{0.03} = \log q_{0.1} - e^{g}$ and a smooth $g$, which cannot cross. Does the 3rd centile need its own learning rate?
Does overconfidence roughen the curve? Refit both charts on a few other random training sets. Does the asymmetric Laplace sometimes learn a larger $s_f$ (a rougher curve) than the calibrated posterior? Why would an overconfident likelihood push the smoothing prior towards more curvature?
Measurement error in the week. Even the obstetric estimate is uncertain by about a week. Treat the true gestational age as latent (a mixture over neighbouring weeks) and see how much the preterm 10th centiles move.
A mixture for the lower tail. The 10th centile at 37 weeks is partly a statement about which babies are delivered early because they are small. Model birth weight at each week as a mixture of "normally grown" and "growth-restricted" components, and compare the flag it implies with the 10th centile.
Customised charts done right. Add maternal height and parity (physiological), not smoking or hypertension (pathological), and redo Task 5. Which babies change status now?

h.progress()

C14: 0/18 hints used, 10/10 checks passed.

Reference solution

A complete, executed solution with commentary on every task — including the ways the obvious model fails. Try the hint ladder first.

Open the worked solution →

#The brief

#How this notebook works

#The data

#Task 0 · Which gestational age? Which records?

#The analysis data (everyone uses this from here on)

#Task 1 · The quick chart

#Task 2 · A smooth chart that borrows strength

#Task 3 · Can you trust the bands?

#Task 4 · Charts for smokers and for gestational hypertension

#Task 5 · The decision

#Going further

Reference solution

The brief

How this notebook works

The data

Task 0 · Which gestational age? Which records?

The analysis data (everyone uses this from here on)

Task 1 · The quick chart

Task 2 · A smooth chart that borrows strength

Task 3 · Can you trust the bands?

Task 4 · Charts for smokers and for gestational hypertension

Task 5 · The decision

Going further