Topology of published referral counts among Saudi health clusters: an orientation-invariant audit of the 2024 Ministry of Health matrix

Abstract

Background: The Saudi Ministry of Health (MOH) publishes a cluster-by-cluster table of referrals including reverse referrals. Its two axis headings do not safely establish the direction of a particular cell, and the table does not define whether entries are unique people, requests or completed care. We described its topology using calculations unchanged by transposing the matrix.

Methods: We audited the official 2024 yearbook Table 4-63 as a complete 20 × 20 array. We verified all 400 cells and 40 marginal totals. We calculated diagonal and off-diagonal shares, then combined the two opposing positions for each of 190 unordered pairs of distinct cluster labels. The five largest pairs were an exploratory display cutoff; we also checked ranks one, six and ten and separately identified four pairs whose printed labels share a Riyadh or Jeddah city name. No patient, facility or population denominator was available.

Results: The 400 cells totalled 341,365 published counts. Diagonal cells contributed 301,968 (88.46%); off-diagonal cells contributed 39,397 (11.54%). The five largest unordered pairs contributed 17,496 (44.41% of the off-diagonal total). Fifth-ranked Madinah–Tabouk (1,724) exceeded sixth-ranked Eastern–Al-Ahsa (1,704) by 20; the top six contributed 48.73%. Four pairs between distinct clusters sharing a Riyadh or Jeddah city name contributed 15,772 (40.03% of off-diagonal counts); other off-diagonal counts totalled 23,625 (6.92% of N). These are positional descriptions, not travel or referral-fulfilment measures.

Conclusions: The MOH table permits a reproducible account of concentration among printed cluster labels, especially unordered pairs. It cannot show unique-patient movements, accepted or completed referrals, access, quality or clinical outcomes. Source-owner definitions and orientation are needed before directional or performance analysis.

Keywords

• Saudi Arabia
• health clusters
• referral matrix
• reverse referral
• administrative data
• source provenance
• descriptive analysis