Vose SoftwareModelRisk example · Pharmaceuticals and biotech
Patient Recruitment and Trial Timelines
When will the last patient be enrolled — and how many sites does it take to be confident of the deadline?
From the model’s saved run
When will the last patient be enrolled?
Month of the last patient in, by number of sites. Highlighted: the options that meet the deadline as often as the Inputs ask.
| Option | Plan month | Median month | P80 month | Deadline chance met | By deadline patients, mean |
|---|---|---|---|---|---|
| Plan: 40 sites | 18.0 | 21.4 | 25.0 | 15% | 242 |
| More sites: 50 sites | 15.0 | 17.8 | 20.6 | 54% | 279 |
| Most sites: 60 sites | 13.0 | 15.3 | 17.6 | 83% | 295 |
| Fewest sites that meet the deadline 80% of the time | Most sites: 60 sites |
Deadline: the end of month 18. Plan: every site open at the most likely month, recruiting at the most likely rate.
S-curve (cumulative probability) of Plan, More sites, Most sites from the saved simulation.
The business question
A company is planning a Phase III trial that must enrol 300 patients. The last patient must be in within 18 months of the first site being ready, or the filing slips by a year.
The feasibility study counts on 40 sites recruiting half a patient a month each once they open, about three months after the start: 20 patients a month, and 300 patients in 18 months.
But in past trials in this indication the average rate per site ranged from 0.3 to 0.7, sites differed widely — some recruited three times the average — about one site in seven never enrolled anyone, and sites opened anywhere from one to eight months after the start. The company can open 50 or 60 sites instead, at a cost. How many should it open?
- Who it is for
- Clinical operations, feasibility and study start-up teams; programme leaders planning a filing date.
- Main outputs
- The month the last patient is enrolled for 40, 50 and 60 sites: plan, median, P80 and the chance of meeting the deadline · patients enrolled by the deadline · cumulative enrolment month by month against the plan.
How the model works
Four sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The patients to enrol and the deadline. The three numbers of sites to compare; the average recruitment rate per site (uncertain), the spread between sites, the share of sites that never recruit. The earliest, most likely and latest opening of a site.
Sites sheet
For each of sixty sites: VoseBernoulli decides whether it ever recruits, VoseGamma its rate relative to the average, VosePERT the month it opens. An option with 40 sites uses the first 40, so all options share the same sites.
Enrolment sheet
A grid of sites by months gives each site's expected patients in each month: its rate times the share of the month it is open. Each option adds up the grid over its sites (SUMIF on the site number). The actual number is Poisson with that mean. One uniform draw per month drives all three options.
The month the cumulative count crosses the target, interpolated within the month, is the month the last patient is enrolled.
Results sheet
For each option: the plan's completion month, the simulated median and the percentile the Inputs ask for, the chance of meeting the deadline and the patients enrolled by then. The fewest sites that meet the deadline that often; the fan of cumulative enrolment against the plan.
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The results in detail
The plan's sites, month by month
Cumulative enrolment against the plan and the target.
Line chart: 90th percentile, Median, Mean, 10th percentile, Target, Plan.
| Measure | Unit | Value |
|---|---|---|
| Patients a month with all sites open, on the plan | patients | 20.0 |
| …simulated mean | patients | 17.0 |
| …chance of falling short of the plan's rate | probability | 81% |
| Sites that never recruit, on average | sites | 6.0 |
| Patients enrolled by the deadline, mean | patients | 242 |
| …10th percentile | patients | 183 |
How to read these results
- The plan — 40 sites at half a patient a month, open from month 3 — enrols the 300th patient at the end of month 18, just in time. The simulation gives it a 15% chance of meeting the deadline: the median finish is month 21.4, and one trial in five is still enrolling after month 25.
- The plan leaves out three things. About six of the 40 sites never recruit. The others recruit at very different rates, around an average that is itself uncertain; and the sites open over several months. With all sites open, the 40 sites enrol about 17 patients a month on average, not 20, and fall short of the plan's rate in 81% of futures.
Opening 50 sites gives an even chance of the deadline (54%); 60 sites give 83%, with the P80 finish in month 17.6. The plan's arithmetic says 60 sites would finish five months early, in month 13: averages hide how often enrolment runs slow. Sixty is the fewest of the three that meets the deadline 80% of the time.
Change the confidence on the Inputs sheet and the line under the table follows.
- By the deadline the 40 sites have enrolled about 242 patients on average, and fewer than 183 one time in ten. Tracking actual enrolment against the fan chart shows early whether rescue sites are needed.
- Recruitment rates are the weakest assumption. Update them as the sites report: a Gamma prior on each site's rate and its Poisson counts give a Gamma posterior, and the forecast sharpens within a few months (PH-08 shows Bayesian updating).
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.
The trial 3 inputs
| Assumption | Unit | Value |
|---|---|---|
| Patients to enrolFrom the sample-size calculation. | patients | 300 |
| Last patient in by the end of monthLater, and the filing slips by a year. | month | 18 |
| How sure the company wants to be of the deadlineThe Results sheet highlights the options that meet the deadline this often. | probability | 80% |
Options 3 inputs
Numbers of sites to compare, in increasing order; each option uses the first sites on the Sites sheet.
| Assumption | Unit | Value |
|---|---|---|
| PlanThe feasibility study's plan. | sites | 40 |
| More sites | sites | 50 |
| Most sitesAt most 60: the sites listed. | sites | 60 |
Recruitment 3 inputs
Patients a site enrols a month once it is open.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Average rate of a recruiting sitePrevious trials in this indication: 0.3 to 0.7. Common to all sites in an iteration. | patients / month | PERT | 0.30 | 0.50 | 0.70 |
| Spread between sites (CV)Some sites recruit three times the average, others a fraction of it. | of the average | Fixed | 60% | ||
| Chance that a site ever recruitsAbout one site in seven never enrols a patient. | probability | Fixed | 85% | ||
Site openings 3 inputs
Month in which a site opens, counted from the start: a PERT for each site.
| Assumption | Unit | Value |
|---|---|---|
| Earliest | month | 1.0 |
| Most likelyContracts and ethics approval. | month | 3.0 |
| Latest | month | 8.0 |
Units and conventions
- Time
- Months from the start: the first site can open from month 1.
- Rates
- Patients a site enrols a month once it is open.
- Completion
- The month the target is reached, interpolated within the month: 17.5 = half way through month 18.
- Plan
- Every site recruits at the most likely average rate and opens at the most likely month.
Key assumptions and limitations
- Recruitment
- A Poisson process at each open site: patients arrive independently at the site's rate, which stays constant once the site is open.
- Sites
- Rates differ between sites (Gamma); the average rate is uncertain and common to all sites; sites open independently.
- Options
- The extra sites are like the first 40; screening capacity and drug supply never limit enrolment.
- Data
- The trial and all figures are invented for this example.
How to use it
- Enter your target, deadline and the numbers of sites to compare on the Inputs sheet.
- Enter recruitment rates from your feasibility work or previous trials: the average, the spread, the sites that never recruit.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Set how sure you need to be of the deadline on the Inputs sheet: the Results sheet highlights the options that meet it that often.
ModelRisk functions used
- VoseGamma
- Each site's rate relative to the average: a mean of 1 and the spread between sites.
- VoseBernoulli
- Whether a site ever recruits.
- VosePERT
- The average rate per site, and the month each site opens.
- VosePoisson
- Patients enrolled in a month, with a shared uniform draw (U argument) across the options.
- VoseUniform
- The month's uniform draw that drives all three options.
- VoseOutput, VoseSimMean, VoseSimPercentile
- Outputs and their statistics on the Results sheet.
Further reading
- Monte Carlo simulation explained (Vose guide)
- Anisimov, V. V. & Fedorov, V. V. (2007). Modelling, prediction and adaptive adjustment of recruitment in multicentre trials. Statistics in Medicine 26(27), 4958–4975.
- Tufts CSDD (2013). 89% of trials meet enrollment, but timelines slip. Impact Report 15(1).
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.