The interval that spans two IPC phases

The number the survey exists to produce

Everything so far has been preparation. The survey was funded to answer one question — how much acute malnutrition is there — and this lesson produces the answer in the form it has to take: a prevalence, an interval, and a phase.

The estimate, with the design

A SMART survey is a cluster survey. The survey course established what that means; here it arrives with a threshold attached.

import numpy as np
import pandas as pd

analysable = smart[smart["whz"].between(-5, 5)].copy()
analysable["gam"] = (analysable["whz"] < -2) | (analysable["oedema"] == True)
analysable["sam"] = (analysable["whz"] < -3) | (analysable["oedema"] == True)


def cluster_prevalence(df, column, cluster="cluster"):
    n = len(df)
    p = df[column].mean()

    totals = df.groupby(cluster)[column].agg(["sum", "size"])
    residual = totals["sum"] - p * totals["size"]
    m = len(totals)

    variance = m / (m - 1) * (residual**2).sum() / n**2
    se = np.sqrt(variance)
    srs = p * (1 - p) / n
    return {"p": p, "se": se, "deff": variance / srs, "clusters": m, "n": n}


for column in ["gam", "sam"]:
    r = cluster_prevalence(analysable, column)
    t = 2.045                                  # t(0.975, 29 df)
    print(f"{column.upper()}: {r['p']:.1%}  95% CI {r['p'] - t * r['se']:.1%} to "
          f"{r['p'] + t * r['se']:.1%}  deff {r['deff']:.2f}  n {r['n']}")

library(survey)

design <- svydesign(ids = ~cluster, weights = NULL, data = analysable)

svyciprop(~I(whz < -2 | oedema), design, method = "logit")
svymean(~I(whz < -2 | oedema), design, deff = TRUE)

	Estimate	95% CI	Design effect	n
GAM	14.9%	11.1 – 18.7%	2.29	852
SAM	3.8%	2.3 – 5.2%	1.20	852

Two things to hold about that table before reading the phase.

The design effect is 2.29 for GAM and 1.20 for SAM. Two indicators, one survey, two design effects — because malnutrition clusters geographically and severe malnutrition, being rarer, clusters less detectably. The survey’s 852 children are worth about 372 independent ones for GAM.

The naive interval would be 12.5 – 17.3%. Ignoring the clustering makes the interval 37% narrower, and the next section is what that narrowing would have cost.

The IPC phases

The IPC classifies acute malnutrition prevalence into five phases, and they are what turn a percentage into a decision.

Phase	GAM by weight-for-height
1 — Acceptable	under 5%
2 — Alert	5 to 9.9%
3 — Serious	10 to 14.9%
4 — Critical	15 to 29.9%
5 — Extremely critical	30% and above

def ipc_phase(gam):
    for threshold, phase in [(0.05, 1), (0.10, 2), (0.15, 3), (0.30, 4)]:
        if gam < threshold:
            return phase
    return 5


r = cluster_prevalence(analysable, "gam")
t = 2.045
low, high = r["p"] - t * r["se"], r["p"] + t * r["se"]

print(f"point estimate: phase {ipc_phase(r['p'])}")
print(f"interval spans: phase {ipc_phase(low)} to phase {ipc_phase(high)}")

c(point = 0.149, low = 0.111, high = 0.187)

The point estimate is 14.9%, which is Phase 3 — by one tenth of a point.

The interval runs 11.1% to 18.7%, which spans Phase 3 and Phase 4.

What that means, said plainly

This is the moment the whole course has been building to, and the honest statement is uncomfortable.

Global acute malnutrition is estimated at 14.9% (95% CI 11.1–18.7). The point estimate falls in IPC Phase 3 (Serious). The confidence interval spans Phase 3 and Phase 4 (Critical), so this survey cannot determine which phase the population is in.

Three things that sentence does.

It refuses to round to the threshold. 14.9% reported as “about 15%” has made a phase classification by rounding, and the difference between Phase 3 and Phase 4 is a difference in response.

It states the interval before the phase. A reader who sees “Phase 3” first will not revise it when they reach the interval.

It says the survey cannot decide. That is the three-branch verdict the survey course insisted on, and here the third branch is the correct one.

What would have happened without the design effect

srs_se = np.sqrt(r["p"] * (1 - r["p"]) / r["n"])
print(f"naive interval: {r['p'] - 1.96 * srs_se:.1%} to {r['p'] + 1.96 * srs_se:.1%}")

p <- 0.149; n <- 852
c(p - 1.96 * sqrt(p * (1 - p) / n), p + 1.96 * sqrt(p * (1 - p) / n))

12.5% to 17.3%. Still spanning both phases — so on this survey the design effect does not change the verdict, and saying so is worth as much as a finding.

But note how close it came. Had the estimate been 13.5%, the naive interval would have sat inside Phase 3 and the design-adjusted one would have crossed into Phase 4. The clustering decides the classification whenever the estimate is within about two points of a threshold, which in this sector is most of the time.

Read it with the plausibility report

The previous lesson found four failed checks, and two of them push in a known direction.

• The inflated standard deviation (1.22) raises GAM. A wider distribution puts more children past a fixed cut-off.
• Team 3’s low measurements raise GAM. Its clusters give 22.3% against 9.2 to 16.2% for the others, and it contributes a quarter of the sample.

So the estimate is more likely to be too high than too low, which pushes the true value toward the lower half of the interval — toward Phase 3 rather than Phase 4.

without_team3 = analysable[analysable["team"] != 3]
r3 = cluster_prevalence(without_team3, "gam")
print(f"excluding team 3: {r3['p']:.1%} on n={r3['n']}, "
      f"{r3['clusters']} clusters")

analysable |> filter(team != 3) |> summarise(gam = mean(gam), n = n())

Report the sensitivity, do not substitute it. The headline stays the full-sample estimate; the exclusion goes beside it as evidence about direction. Silently dropping a quarter of a survey because it gives an inconvenient answer is the thing this whole module exists to prevent.

The full reporting block

Global acute malnutrition (weight-for-height z < -2 or oedema)
  14.9%   95% CI 11.1-18.7   n = 852   design effect 2.29   30 clusters
  IPC Phase 3 by point estimate; interval spans Phase 3 and Phase 4.

Severe acute malnutrition (z < -3 or oedema)
  3.8%    95% CI 2.3-5.2     n = 852   design effect 1.20

Plausibility: 4 of 6 SMART checks failed (SD 1.22, digit preference in one team,
age heaping 24%, team bias -0.42 to -1.09). Two of the four push the estimate
upward. Excluding the affected team gives 12.6% on 628 children.

Analysable denominator: 852 of 930 measured. 66 had no computable z-score
(32 missing weight or age, 30 outside the reference range, 4 heights in metres,
recoverable) and 12 were flagged by the WHO bounds.

Twelve lines. They carry the estimate, its interval, its design, its classification, its known biases and its denominator, and there is nothing left for a reviewer to ask that the block does not answer.

What comes next

The survey says what the situation is. The next unit asks what the programme did about it — CMAM performance against the Sphere standards, and the denominator that moves the cure rate by nine points.