The gap opens before the referral is made

Find the gate, not the total

An end-to-end completion rate of 43.8% tells you the pathway is leaking. It does not tell you where, and the four gates lose very different amounts.

import pandas as pd

referrals = pd.read_csv("protection-referrals-2024.v1.csv")

def cascade(frame):
    consented = frame[frame["consent_to_refer"]]
    made = consented[consented["referral_made"]]
    accepted = made[made["referral_accepted"]]
    reached = accepted[accepted["days_to_first_service"].notna()]
    return pd.Series({
        "n": len(frame), "consented": len(consented), "made": len(made),
        "accepted": len(accepted), "reached": len(reached),
    })

totals = cascade(referrals)
print(totals)
print("\nloss at each gate:")
print(f"  consent:  {1 - totals['consented'] / totals['n']:.1%}")
print(f"  referral: {1 - totals['made'] / totals['consented']:.1%}")
print(f"  accepted: {1 - totals['accepted'] / totals['made']:.1%}")
print(f"  service:  {1 - totals['reached'] / totals['accepted']:.1%}")

library(dplyr)

referrals |> summarise(
  n = n(),
  consented = sum(consent_to_refer),
  made = sum(consent_to_refer & referral_made),
  accepted = sum(referral_made & referral_accepted),
  reached = sum(referral_accepted & !is.na(days_to_first_service))
)

Gate	Lost here
Consent	11.5% — a decision, not a loss
Referral made	30.3%
Referral accepted	33.7%
Reached the service	5.3%

The two middle gates lose almost everything. Once a referral is accepted, 94.7% of cases reach the service — the receiving end works. The failure is upstream: a referral that is never made, and a referral that is made and refused.

Those are two different problems with two different owners. A single completion rate hides which one you have, and a programme reading 43.8% would reasonably invest in the service that is not the bottleneck.

Which service, and which area

by_service = referrals.groupby("service_requested").apply(cascade,
                                                          include_groups=False)
by_service["completion"] = by_service["reached"] / by_service["consented"]
print((by_service["completion"] * 100).round(1).sort_values())

referrals |>
  summarise(consented = sum(consent_to_refer),
            reached = sum(referral_accepted & !is.na(days_to_first_service)),
            .by = service_requested) |>
  mutate(completion = reached / consented) |> arrange(completion)

Service	Completion	Referral made	Accepted
Livelihood support	20.7%	49%	47%
Legal	30.0%	61%	50%
Safety and security	33.8%	61%	58%
Psychosocial	53.2%	77%	72%
Health	57.6%	81%	76%

Livelihood support completes at a third of the rate health does, and it fails at both middle gates equally — half the referrals are never made and half of those made are refused. That is the signature of a service that is known to be oversubscribed: caseworkers stop referring to it because they know the answer.

Areas range from 29.7% to 53.8%, a spread wide enough to act on and narrow enough that no area is fine.

The gap that matters

disability = referrals["disability_reported"].isin([True, "true", "Yes"])
no_disability = referrals["disability_reported"].isin([False, "false", "No"])

for label, mask in [("reported", disability), ("not reported", no_disability)]:
    row = cascade(referrals[mask])
    print(f"{label:14} n={row['n']:>5}  "
          f"consent {row['consented'] / row['n']:.1%}  "
          f"made {row['made'] / row['consented']:.1%}  "
          f"accepted {row['accepted'] / row['made']:.1%}  "
          f"→ {row['reached'] / row['consented']:.1%}")

referrals |>
  mutate(disability = disability_reported %in% c("true", "Yes")) |>
  summarise(n = n(), consented = sum(consent_to_refer),
            made = sum(consent_to_refer & referral_made),
            accepted = sum(referral_made & referral_accepted),
            reached = sum(referral_accepted & !is.na(days_to_first_service)),
            .by = disability)

	n	Consent	Referral made	Accepted	Completion
Disability reported	227	89.0%	54.5%	56.4%	26.7%
Not reported	1,623	88.5%	71.9%	67.3%	46.2%

Consent is identical — 89.0% against 88.5%. People with disabilities are exactly as willing to be referred.

The gap opens at the two gates the service system controls. A referral is made for 54.5% of them against 71.9%, and accepted for 56.4% against 67.3%. By the service door the difference has compounded to nineteen points.

Locating the gap at a specific gate turns an observation into an action. “Outcomes are worse for people with disabilities” is a finding nobody can act on. “Caseworkers make a referral for 55% of them against 72%, and receiving services accept 56% against 67%” names two conversations with two named parties.

Before publishing it

Three checks, and the first will change your numbers.

The disability column has four values. One area recorded Yes and No instead of true and false, so a naive grouping produces four categories, two of them too small to interpret and one of them silently dropped by a boolean filter.

print(referrals["disability_reported"].value_counts(dropna=False))

referrals |> count(disability_reported)

Disability is self-reported and under-reported. 227 of 1,850 is 12.3%, below most population estimates. The gap is real; the denominator is a group who disclosed, and people who did not disclose are counted in the comparison group. That biases the gap downward — so 19 points is a floor.

Check the cell sizes before disaggregating further. Disability by area by service is exactly the four-way table the last lesson refused to publish.

Report the gates, not the total

Referral pathway, 1,638 consenting cases

  Referral made                   69.7%
  Accepted, of those made         66.3%
  Reached service, of accepted    94.7%
  End to end, of consenting       43.8%

  The pathway fails upstream. Once a referral is accepted 94.7% of cases
  reach a service; the losses are at referral-making and acceptance.

  Cases reporting a disability: 26.7% complete against 46.2%. Consent is
  identical (89.0% and 88.5%); the gap is entirely at referral-making
  (54.5% against 71.9%) and acceptance (56.4% against 67.3%).

  Disability is self-reported by 12.3% of cases. Non-disclosure places some
  people in the comparison group, so the gap is a lower bound.

What comes next

The pathway ends when a case reaches a service. What happens after that is a case that someone has to carry, and the next unit is the register that records who is carrying how many.