The denominator that moves the cure rate nine points

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What this lesson covers

• Four outcomes and a standard
• The three candidate denominators
• Which one Sphere means
• Break it down by site
• The cause is usually distance, not compliance
• Weight gain, and the entries that cannot be right
• The performance table to publish
• What comes next

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Four outcomes and a standard

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Four outcomes and a standard

• Every one of those is a proportion, and the argument is always the denominator

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The three candidate denominators — In Python

import pandas as pd

cmam = pd.read_csv("cmam-admissions-2024.v1.csv")

print(f"admissions:            {len(cmam):>5}")
print(f"with an outcome:       {cmam['outcome'].notna().sum():>5}")
print(f"excluding transfers:   "
      f"{(cmam['outcome'].notna() & (cmam['outcome'] != 'transferred')).sum():>5}")

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The three candidate denominators — In R

cmam |> summarise(
  admissions = n(),
  with_outcome = sum(!is.na(outcome)),
  excluding_transfers = sum(!is.na(outcome) & outcome != "transferred")
)

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The three candidate denominators

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The three candidate denominators — In Python

cured = (cmam["outcome"] == "cured").sum()
for label, n in [("all admissions", 1100), ("with an outcome", 1029),
                 ("excluding transfers", 984)]:
    print(f"cure rate on {label:22} {cured / n:.1%}")

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The three candidate denominators — In R

cured <- sum(cmam$outcome == "cured", na.rm = TRUE)
c(all = cured / 1100, outcome = cured / 1029, sphere = cured / 984)

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The three candidate denominators

• 73.6%, 78.7%, 82.3% — One numerator, three denominators, nine points

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Which one Sphere means

• Children who reached a treatment outcome, excluding transfers — 984 here
• Children still in treatment are not an outcome — Seventy-one children were admitted late enough that they had not been…
• Transfers are somebody else's outcome — Forty-five children moved between programmes — outpatient to inpatient, or the…

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Which one Sphere means — In Python

performance = cmam[cmam["outcome"].notna() & (cmam["outcome"] != "transferred")]

rates = performance["outcome"].value_counts(normalize=True)
print((rates * 100).round(1))
print(f"n = {len(performance)}")

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Which one Sphere means — In R

performance <- cmam |> filter(!is.na(outcome), outcome != "transferred")

performance |> count(outcome) |> mutate(rate = n / sum(n))

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Which one Sphere means

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Break it down by site — In Python

by_site = (
    performance.assign(**{o: performance["outcome"] == o
                          for o in ["cured", "defaulted", "died", "non-response"]})
    .groupby("site_id")
    .agg(n=("outcome", "size"), cured=("cured", "mean"),
         defaulted=("defaulted", "mean"), died=("died", "mean"))
)
print((by_site[["cured", "defaulted", "died"]] * 100).round(1))

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Break it down by site — In R

performance |>
  summarise(n = n(),
            cured = mean(outcome == "cured"),
            defaulted = mean(outcome == "defaulted"),
            died = mean(outcome == "died"),
            .by = site_id) |>
  arrange(desc(defaulted))

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Break it down by site

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Break it down by site

• The programme defaults at 13.7% and one site defaults at 20.5% — The district figure is inside the Sphere maximum and…

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Break it down by site — In Python

flagged = by_site[(by_site["defaulted"] > 0.15) | (by_site["cured"] < 0.75)]
print(f"{len(flagged)} of {len(by_site)} sites outside a Sphere standard")

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Break it down by site — In R

performance |>
  summarise(cured = mean(outcome == "cured"),
            defaulted = mean(outcome == "defaulted"), .by = site_id) |>
  filter(defaulted > 0.15 | cured < 0.75)

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The cause is usually distance, not compliance — In Python

length_of_stay = (
    pd.to_datetime(performance["discharge_date"])
    - pd.to_datetime(performance["admission_date"])
).dt.days

print(performance.assign(stay=length_of_stay)
      .groupby("outcome")["stay"].median().round(0))

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The cause is usually distance, not compliance — In R

performance |>
  mutate(stay = as.integer(as.Date(discharge_date) - as.Date(admission_date))) |>
  summarise(median_stay = median(stay), .by = outcome)

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Weight gain, and the entries that cannot be right — In Python

gain = (
    (performance["weight_discharge_kg"] - performance["weight_admission_kg"])
    / performance["weight_admission_kg"]
    / length_of_stay * 1000
)
print(gain.describe().round(1))
print(f"{(gain < 0).sum()} discharges with weight loss")

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Weight gain, and the entries that cannot be right — In R

performance |>
  mutate(gain = (weight_discharge_kg - weight_admission_kg) /
                weight_admission_kg / as.integer(as.Date(discharge_date) -
                as.Date(admission_date)) * 1000) |>
  summarise(median = median(gain, na.rm = TRUE), negative = sum(gain < 0, na.rm = TRUE))

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The performance table to publish — Example

CMAM performance, 2024

  Admissions                        1,100
  Still in treatment at cut-off        71    excluded: not an outcome
  Transferred                          45    excluded: outcome recorded elsewhere
  Performance denominator             984

  Cured           82.3%   Sphere >75%    pass
  Defaulted       13.7%   Sphere <15%    pass
  Died             1.0%   Sphere <10%    pass
  Non-response     2.9%

  One site (SITE-03, n=156) defaults at 20.5%, outside the Sphere maximum.
  Median stay for defaulters is 24 days against 58 for cured children,
  consistent with distance rather than non-response to treatment.

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What comes next

• The programme cures the children it admits.

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Where this goes next

Read the full lesson, with runnable code Back to the lesson