Hospital Mortality Risk Analysis
A hospital's 30-day mortality rate (3.2%) sits well above the national benchmark (2.1%). Before launching a mortality reduction programme, the Chief Medical Officer needed a statistically rigorous answer to one question: is this gap a genuine patient safety problem, or statistical noise from a riskier patient case mix?
Dataset
Synthetic hospital administrative data (200 patients, 12 months) merged from patient demographics, surgical records, and 30-day outcomes exports, calibrated to NHS SHMI-style mortality benchmarks
Key Questions
- Is the 3.2% vs 2.1% national benchmark gap a genuine patient safety problem or statistical noise?
- Which departments and patient groups carry the highest mortality risk?
- Is there a time trend — is the rate getting worse or improving?
- How much of the gap is explained by patient case mix versus genuine underperformance?
Methods
- Merged three separate hospital administrative exports (patient demographics, surgical records, 30-day outcomes) into a single 200-patient master dataset
- Data quality and frequency profiling by department, age group, and risk category before any statistical testing
- Indirect standardisation (risk-adjusted expected deaths by risk category) to compute a Standardised Mortality Ratio (SMR)
- Chi-square goodness-of-fit test comparing observed vs risk-adjusted expected deaths, with 95% confidence intervals
- Funnel plot with volume-adjusted control limits to compare department-level mortality without penalising low-volume departments
- Pivot tables and PivotCharts breaking mortality down by department, age group, emergency status, and year
- Intervention scenario projections (current rate vs national benchmark vs targeted departmental improvement) extrapolated to 2,000 annual surgical patients
- 1,000-iteration Monte Carlo simulation of overall mortality rate from risk-tier proportions and risk-specific mortality assumptions, with an interactive what-if control panel
- KPI monitoring framework with red/amber/green thresholds, escalation triggers, and named owners for each metric
Results
Across the 200-patient sample, 8 patients died (4.0% crude mortality). All 8 deaths occurred in patients aged 75+ (19.5% mortality in that age group vs 0% in every group under 75) — age, not department, was the dominant risk factor. Cardiac Surgery had the highest crude departmental rate (11.6%, 5/43), driven largely by CABG procedures (14.8%, 4/27), while General Surgery, Neurosurgery, and Orthopedics each sat around 2.4-2.5% and Urology recorded zero deaths. The year-over-year breakdown answers the CMO's trend question directly: mortality fell from 4.84% in 2023 to 2.63% in 2024 — an improving trend, not a worsening one. After indirect standardisation for risk category, the hospital's expected death count was 7.6 against 8 observed (SMR ≈ 1.05), and a chi-square test comparing observed to risk-adjusted expected deaths returned χ² = 0.02, p = 0.89 — nowhere near statistical significance. Funnel-plot control limits (±2SD by department volume) were wide enough that even Cardiac Surgery's elevated rate stayed inside statistical control. A 1,000-iteration Monte Carlo simulation built purely from the hospital's risk-tier case mix (30% low / 35% medium / 20% high / 15% very-high risk) and standard risk-specific mortality rates produced a mean simulated mortality rate of 3.6% (SD 0.43%, 90% range 3.0-4.4%) — and exceeded the 2.1% national benchmark in 100% of simulated runs. Together, the evidence points toward the gap being substantially explained by this hospital's riskier patient case mix and an improving trajectory, rather than a standalone, worsening quality-of-care signal — though the 200-patient sample is too small to rule out a real effect entirely. The most consequential finding, however, surfaced in the KPI dashboard itself: it reports Emergency surgery mortality at 4.5%, but the underlying pivot data shows emergency-flagged patients actually died at 21.9% (vs 0.6% for non-emergency patients) — a five-fold understatement on the one metric most likely to trigger clinical escalation.
Dashboard Visualisations
Mortality by Department
Mortality by Age Group
Mortality by Emergency Status
Mortality Trend by Year
Patient Distribution
By Department
By Risk Category
By Age Group
Scenario Comparison
The workbook's own Scenario Comparison chart plots mortality rate, projected deaths, and SMR (values of 45 and 76 — see Limitations) on one percentage axis, producing a 0-9000% scale. Rate and projected annual deaths are shown here on separate, correctly scaled charts instead.
Projected Mortality Rate
Projected Annual Deaths
Scenario Comparison (Dynamic) — What-If Control Panel
The workbook's own dynamic chart, driven by the Monte Carlo sheet's interactive What-If panel: National Benchmark vs Current Hospital vs the What-If scenario (Cardiac Surgery rate 10%, 500 annual patients, 10% high/very-high risk). Bar height is annual deaths; the label above each bar is the mortality rate.
Funnel Plot & Monte Carlo Distribution
Department Mortality vs Volume
±2SD control limits narrow as department volume grows — every department, including Cardiac Surgery, falls inside the funnel.
Monte Carlo Mortality Rate Distribution
True per-bin histogram computed directly from the 1,000 simulated iterations (mean 3.64%, exceeds the 2.1% national benchmark in 100% of runs). The workbook's own chart plots a cumulative count instead, which reads as a rising curve rather than a distribution.
Dashboard Breakdown
By Department
By Age Group
By Emergency Status
By Year
KPI Monitoring Framework
| KPI | Current | Target | Escalation | Owner | Status |
|---|---|---|---|---|---|
| Overall 30-day mortality rate | 3.2% | ≤2.1% | >3.0% | CMO | Escalation breach |
| Cardiac Surgery mortality rate Dashboard value (5.8%) matches neither the crude rate (11.6%) nor its own 6-month trend (3.1-3.5%) | 5.8% | <3.5% | >5.0% | Head of Cardiac Surgery | Escalation breach |
| Standardized Mortality Ratio (SMR) Disagrees with the Modelling sheet's own SMR calculation of ≈1.05 | 1.35 | <1.0 | >1.2 | Analytical team | Escalation breach |
| Emergency surgery mortality rate Underlying pivot data shows the real figure is 21.9%, not 4.5% | 4.5% | <3.0% | >4.0% | Emergency Dept | Escalation breach |
| High-risk patient mortality rate | 8.0% | <5% | >7% | Risk Manager | Escalation breach |
Monte Carlo Simulation (1,000 iterations)
Simulation Parameters
- Annualised patient volume: 2,000
- Risk-tier case mix: Low 30% / Medium 35% / High 20% / Very High 15%
- Risk-specific mortality assumptions: Low 0.5%, Medium 2%, High 5%, Very High 12%
Simulation Summary
What-If Control Panel
Scenario Comparison
Recommendations
- Correct the Emergency surgery mortality KPI immediately — the dashboard shows 4.5% while the underlying outcomes data shows 21.9% for emergency-flagged patients; this is the highest-priority fix since it understates real risk on a metric feeding CMO escalation decisions
- Do not treat the 3.2% vs 2.1% gap alone as proof of a safety problem — the risk-adjusted analysis (SMR ≈ 1.05, p = 0.89) does not support that conclusion on this sample, and the trend is improving (4.84% in 2023 to 2.63% in 2024)
- Prioritise reviewing outcomes in patients aged 75+, since every observed death in the sample fell in that age group — a case-mix and frailty question, not a departmental one
- Investigate CABG-specific outcomes in Cardiac Surgery given its crude rate is roughly 5x other departments, even though it stayed within funnel-plot control limits
- Reconcile the SMR figure before it reaches the CMO dashboard — the Monitoring KPI sheet reports SMR = 1.35 while the underlying risk-adjustment calculation on the Modelling sheet computes SMR ≈ 1.05, and the Projection sheet's scenario table shows SMR values of 45 and 76 for two other scenarios; these should not disagree
- Track the five defined KPIs monthly against their escalation thresholds, and re-run the chi-square/SMR analysis quarterly as the sample grows past 200 patients, since statistical power at n=200 is limited
Limitations
The dataset is a 200-patient, 12-month administrative sample (synthetic, modelled on real hospital data structures) drawn from three merged export systems with no clinical chart review or comorbidity detail, so risk adjustment relies on a coarse four-tier risk category rather than true case-mix indices. At n=200 and only 8 deaths, statistical power is limited — a genuine moderate effect could exist without reaching significance. The workbook has internal inconsistencies worth flagging: the KPI dashboard's Emergency surgery mortality figure (4.5%) does not match the underlying pivot data (21.9%); the Modelling sheet's risk-adjusted SMR (≈1.05) disagrees with the Monitoring dashboard (1.35) and the Projection sheet's scenario table (45 and 76); and the Cardiac Surgery KPI's "current value" (5.8%) matches neither the crude departmental rate (11.6%) nor its own displayed 6-month trend (3.1-3.5%). These should be reconciled to single, traceable formulas before presentation to a Chief Medical Officer. Findings are for a single hospital and should not be generalised.