ModelRisk example · General techniques
A Step Change in the Event Rate (Projected Cures)
How many lives will a cure save if nobody knows when it will arrive? A step change at an uncertain time.
From the model’s saved run
Deaths and lives saved over 100 months
The same deaths without and with the cure.
| Measure | Unit | Value |
|---|---|---|
| Expected deaths without the cure | deaths | 15,365 |
| Mean deaths with the cure | deaths | 11,901 |
| Mean lives saved by the cure | deaths | 3,464 |
| Lives saved per month the cure comes earlier | deaths | 40.1 |
| Measure | Unit | 10th pct | Median | 90th pct | Mean |
|---|---|---|---|---|---|
| Lives saved | deaths | 2,954 | 3,475 | 3,943 | 3,464 |
| Deaths with the cure | deaths | 11,408 | 11,884 | 12,420 | 11,901 |
| Deaths without the cure | deaths | 15,205 | 15,366 | 15,521 | 15,365 |
| Measure | Unit | Value |
|---|---|---|
| Standard deviation, deaths with the cure | deaths | 374 |
| Standard deviation, deaths without the cure | deaths | 123 |
Line chart: Without the cure, With the cure.
Line chart: 90th percentile, Median, Mean, 10th percentile.
The business question
A disease kills about 88 people a month, and the number rises by about 1.3 a month. Researchers are close to a cure that would prevent 30% of the deaths. It will be available in a month somewhere between the 20th and the 50th, each equally likely.
A health service wants to plan for the next 100 months: deaths with and without the cure, the lives the cure will save, and how much faster development would be worth. Deaths happen at random, so each month's number is Poisson. Once the cure is available, each death is prevented with a 30% chance, so the deaths that still happen are binomial.
- Who it is for
- Anyone forecasting events whose rate changes at an uncertain time: a new treatment, a regulation, a competitor, a process improvement.
- Main outputs
- Deaths over 100 months with and without the cure · lives saved at P10 / median / P90 · lives saved per month of earlier availability · monthly bands.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The current monthly deaths and their monthly increase, the window in which the cure becomes available, and the fraction of deaths it prevents.
Months sheet
Each month's deaths without the cure are VosePoisson(88 + 1.3 × month). From the breakthrough month on, VoseBinomial(deaths, 1 − 30%) gives the deaths that still happen; before it, they all do. The difference is the lives saved.
Results sheet
The 100-month totals, the lives saved, the value of each month of earlier availability, and monthly bands of deaths with the cure.
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The results in detail
How to read these results
- Without the cure about 15,400 people would die over the 100 months. The cure saves about 3,500 of them on average, and between about 3,000 and 3,900 (10th to 90th percentile) depending on when it arrives.
- Each month the cure comes earlier saves about 40 lives: 30% of a month's deaths in the middle of the window. That is the number to set against the cost of faster development.
- The breakthrough month dominates the uncertainty: the total with the cure varies about three times as much as the total without it, which reflects only the randomness of deaths.
- The mean line drops gradually between months 20 and 50 because the breakthrough month differs between iterations. In any one iteration the drop is a single step.
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Deaths now 2 inputs
The current rate and its trend.
| Assumption | Unit | Value |
|---|---|---|
| Deaths per month now | deaths | 88 |
| Increase in deaths per month, each month | deaths | 1.3 |
The cure 3 inputs
When it becomes available, and what it does.
| Assumption | Unit | Value |
|---|---|---|
| Earliest month it becomes available | month | 20 |
| Latest month it becomes availableEach month in the window equally likely. | month | 50 |
| Fraction of deaths it prevents | probability | 30% |
Units and conventions
- Month
- Month 1 is the first month of the plan.
- Breakthrough month
- The first month in which the cure prevents deaths.
Key assumptions and limitations
- Poisson
- Deaths happen independently at a steady rate within a month.
- Cure
- From its first month the cure prevents each death with the same probability; there is no ramp-up.
- Trend
- Linear, as in the original example; it continues whether or not the cure arrives.
- Data
- The rates, the window and the effect are those of ModelRisk's earlier Projected Cures example.
How to use it
- Set the current rate, the trend and the cure on the Inputs sheet.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Compare the lives saved with the cost of bringing the cure forward by a month.
ModelRisk functions used
- VoseStepUniform
- The breakthrough month: each month from 20 to 50 equally likely.
- VosePoisson
- Each month's deaths without the cure.
- VoseBinomial
- The deaths that still happen once the cure is available.
- VoseOutput
- Monthly deaths with the cure as an output range, and the totals.
- VoseSimMean, VoseSimPercentile
- Statistics of the simulation, the monthly bands and means.
Further reading
- Monte Carlo simulation explained (Vose guide)
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley: forecasting random events with a change in rate.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.