Two Hospitals, One Crude Death Rate
Over one financial year, 4,200 patients were admitted across two public hospitals in a district. At Hospital A, a 900-bed tertiary centre, 9.1% of admitted patients died. At Hospital B, a 220-bed district hospital, 5.4% died. The district health officer concluded that A's clinical protocols are inferior and moved a proposal to transfer A's critical-care unit to B's management. A junior analyst placed four facts on record: (i) A receives every patient brought in by ambulance, while B diverts cardiac and trauma cases scoring above 7 on a severity scale to A; (ii) B's mean length of stay is 2.1 days against A's 6.8; (iii) 38% of A's admissions arrive after 8 p.m. against 12% at B; (iv) A's records were audited on a random sample of 240 discharges last year, while B's were not audited at all. The officer replied that both figures were 'taken from the same register, using the same definition of death'.
1. Identify the principal weakness in the officer's inference and say which of the four facts most directly exposes it. Explain why the officer's reply about the shared register misses the point.
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The weakness is confounding by case-mix. The officer compares two crude rates, but a crude rate is a weighted average of severity-specific rates, with the weights set by each hospital's patient population. If A treats a systematically sicker population, its crude rate can be higher even if its treatment is identical or better, at every level of severity. The inference from 'higher crude rate' to 'inferior protocols' therefore needs the populations to be comparable, and nothing in the setup shows that they are.
The fact that most directly exposes it is (i). Explicit diversion of high-severity cardiac and trauma cases means the two denominators are constructed differently by design. Fact (ii) is suggestive but ambiguous, since a longer stay can reflect either sickness or inefficiency; (iv) is a data-quality problem, not a confounding problem.
Why the register reply misses the point. The officer confuses measurement comparability with population comparability. Using one register and one definition of death makes the two rates consistently measured; it does not make the two patient groups alike. Consistent measurement of non-comparable groups yields a precisely estimated but meaningless comparison. The reply answers a criticism nobody made.
2. Given that patients cannot be randomly assigned to hospitals, what comparison would actually test whether the protocols differ?
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Randomisation is both infeasible and unethical here, since allocation is dictated by geography and severity. The substitute is risk adjustment, built on the severity score B already uses to divert patients.
- Stratified comparison. Compute mortality within severity bands (1-3, 4-6, 7-8, 9-10), separately by diagnosis group. If A's mortality is no worse within each band, the crude gap is composition, not care.
- Standardised mortality ratio. Apply A's band-specific rates to B's case-mix, and B's rates to A's case-mix. The resulting expected counts, compared with observed counts, give an SMR for each hospital on a common population.
- Matched comparison. Match each B patient to A patients on severity, age and diagnosis, then compare outcomes within matched sets, which is a propensity-style approach suited to small B.
- Process measures. Outcome comparison is blunt with 4,200 admissions. Time to antibiotics in sepsis, door-to-balloon time, unplanned readmissions and escalation-to-ICU rates compare what hospitals do, and are far less sensitive to case-mix than death.
- Fix the denominator first. Since B's records were never audited, some deaths may be misclassified or discharged moribund patients uncounted. An audit of B is a precondition for any comparison, not a side issue.
A properly risk-adjusted comparison cannot prove superiority of protocols, but it can defeat the officer's inference, which is all the proposal requires.
3. Does fact (iii), that 38% of A's admissions arrive after 8 p.m., support an alternative explanation? What evidence would distinguish it from the case-mix explanation?
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Yes, (iii) supports a genuine rival explanation, and it is important to see why it is not simply case-mix in disguise.
The rival explanation. Overnight arrival may be a marker of care quality rather than patient sickness: fewer senior clinicians on site, slower access to diagnostics, delayed escalation. On that account A's excess mortality is caused by staffing at night, a real and remediable protocol problem, which is exactly the officer's conclusion reached by a different route.
The competing reading. Night arrival may just be a proxy for severity. Road traffic crashes, late inter-hospital transfers and emergency presentations cluster after dark, so the 38% figure may be another way of saying 'A receives the ambulance cases', which is confounding again.
How to distinguish them.
- Stratify twice. Within narrow severity bands, compare night versus day mortality at each hospital separately. If the night penalty persists at A within severity bands but is absent at B, staffing time is doing independent work. If the night effect vanishes once severity is controlled, it was a proxy.
- Look for a dose-response. If mortality rises steadily with later arrival hour at A and not at B, a staffing mechanism is more plausible than a binary severity story.
- Check staffing records against arrival times. If the excess concentrates in the hours when the intensivist is off site, the case for a protocol/staffing cause is strong.
Neither explanation can be dismissed on the facts given, and the officer should be told that (iii) is the one fact that could rescue part of his case.