Case Study
Quantifying Risk in Cancer Waiting-Time Decisions
Based on three years of longitudinal data, we are 90% confident that the probability of a 62-day target breach for Skin Cancer lies between 10% and 18%.
The Problem
Point estimates hide the true risk of failure.
In many environments, critical decisions are driven by ‘point estimates’ — single numbers that hide the true risk of failure. Leadership sees a breach rate of 14% and plans around it, but has no way of knowing whether the real rate is 10% or 18%.
This system, utilising Bayesian statistical methods, analyses three years of longitudinal data to explicitly model uncertainty. The model allows leadership to see not just what happened, but how much confidence they can have in what happens next.
Systemic Risk Profiles
Posterior probability distributions by cancer pathway (population average).
Cancer Wait Time Breaches
Posterior probability of 62-day target breach — calculated from 4,000 MCMC draws
Skin
Breast
Lower GI
Gynaecological
Urological
Lung
0%
20%
40%
60%
80%
Lines represent 90% credible intervals. Wider distributions indicate greater uncertainty in the breach probability.
The ‘Fair Score’ League Table
Trust-level performance after adjusting for case-mix and regional complexity.
Outperforming
Underperforming
REP
RJ1
RRK
RAL
RQW
RTD
RFS
RWF
REN
RWY
← Outperforming | Relative Breach Risk (Log-Odds Deviation from Average) | Underperforming →
The Fair Score isolates genuine performance gaps from environmental factors like case-mix and regional complexity.
Strategic Impact
Shifting from reactive responses to proactive, risk-based planning.
Proactive Planning
The system shifts decision-making from short-term reactive responses to proactive, risk-based capacity planning with quantified confidence.
Fair Comparison
By adjusting for structural drivers such as case-mix and regional complexity, the Fair Score isolates performance gaps rather than differences driven by environmental factors.
Targeted Intervention
Leadership can commit capacity with quantified confidence, targeting interventions where they have the highest probability of preventing a breach.
Methodology
Built on rigorous Bayesian inference and proper uncertainty quantification.
BAYESIAN
Hierarchical modelling with MCMC sampling to produce full posterior distributions — not just point estimates.
LONGITUDINAL
Three years of NHS waiting-time data analysed to capture trends, seasonality, and structural variation across providers.
CREDIBLE INTERVALS
90% credible intervals give leadership a calibrated range of outcomes — honest uncertainty, not false precision.
Industry: Healthcare • Data Source: www.nhs.com