Patient microsimulation
Explore individual trajectories and the simulation variability around a fixed state-transition model.
Concepts and reasoning
Turning probabilities into individual histories
A cohort model redistributes population fractions. A microsimulation instead creates individual records and samples what happens to each one. If a Stable patient has probabilities 0.85, 0.10, and 0.05 of remaining Stable, progressing, or dying, one uniform random draw can determine the next state. Draws below 0.85 select Stable; draws from 0.85 to below 0.95 select Progressed; the remaining draws select Dead.
Repeating this process creates a trajectory rather than a fractional patient. Costs, time in states, and quality-adjusted survival accumulate along that trajectory. Different patients can have different outcomes even under identical model parameters. The sample average estimates the expected outcome of the simulated population.
More detail requires more information
Individual simulation is useful when the model must remember history, such as time since a complication, previous treatments, or accumulated risk factors. But the simulation must actually include those variables and specify how they alter future events. A patient identifier alone does not create heterogeneity. A microsimulation using the same memoryless transitions and state rewards as a cohort model should approach the cohort expectation as simulated population size increases.
Three distinct ideas are often mixed together. Patient variability is variation in outcomes among individuals. Parameter uncertainty is uncertainty about probabilities, costs, or treatment effects. Monte Carlo error is numerical error from simulating only a finite number of individuals or parameter draws. These require different remedies. Krijkamp and colleagues’ tutorial explains the individual-simulation framework.
Mathematical foundations
Estimating a mean and its simulation error
For simulated outcomes
The sample standard deviation
For a difference between independently simulated strategies, the Monte Carlo variance is approximately
The square-root relationship is costly: reducing MCSE by half requires roughly four times as many independent simulated individuals. A fixed seed reproduces a particular realization; it does not establish that the realization is sufficiently accurate.
Worked example
Why a simulated count is not its expectation
Simulate 1000 Stable patients with a one-cycle progression probability of 0.10. The expected number progressing is 100, but the actual count is random. Under independent draws its standard deviation is
Suppose a simulation estimates mean cost at 12,000 and the patient-level standard deviation is 6000. With 10,000 simulated patients, the MCSE is
| Simulated patients | Patient-level SD | Approximate MCSE of mean cost |
|---|---|---|
| 2500 | 6000 | 120 |
| 10000 | 6000 | 60 |
| 40000 | 6000 | 30 |
Now compare two strategies whose true expected incremental cost is only 20. An MCSE of 60 for either strategy can make the simulated difference unstable in sign. Increasing the simulation size or using a justified variance-reduction design may matter more than displaying extra decimal places.
For a memoryless model, also calculate the deterministic cohort expectation. As the simulation size grows, repeated simulated means should fluctuate more tightly around that benchmark. Persistent disagreement suggests a timing, reward, transition, or discounting mismatch rather than mere random noise.
Interpreting the results
Distinguish variation among patients from uncertainty about the mean
A microsimulation generates individual trajectories and summarizes their outcomes. Patients can have very different costs or survival even when they share identical transition rules. That between-patient variation is different from Monte Carlo error, which describes how precisely a finite simulation estimates the model's expected outcome.
For fixed parameters, simulation standard errors generally shrink approximately with the square root of the number simulated. Four times as many patients therefore gives roughly half the error, not one quarter. A tight simulation interval only says the chosen model has been evaluated precisely.
Compare simulated means with the corresponding cohort expectations when both models use the same memoryless structure. Differences should be compatible with simulation error. Economic conclusions still depend on the transition probabilities, rewards, and structure; increasing the simulated population cannot resolve uncertainty in those inputs.
Assumptions and limitations
Individual simulation does not automatically add realism
A simulated patient has only the attributes and history represented in the model. Sampling individual state transitions from a common fixed matrix retains the same memoryless assumptions as a cohort model. History-dependent risks, heterogeneity, and treatment selection must be modeled explicitly if they matter.
Independent random streams for strategies generate separate artificial populations. They do not represent observed paired treatment outcomes for the same person. Common random numbers can reduce simulation variance in some implementations, but require deliberate design and appropriate uncertainty calculations.
State definitions, cycle length, reward timing, and discounting must remain consistent across strategies. Initial state probabilities describe a population distribution, so even starting counts vary in a finite simulated sample. Parameter uncertainty requires an outer sampling layer or other sensitivity analysis; it is not supplied by simulating more individual histories.
Diagnostics and sensitivity analysis
Establish numerical precision before comparing strategies
Run a small calculation to inspect behavior, then increase patient counts and compare simulated means, Monte Carlo standard errors, and the cohort benchmark. Large systematic discrepancies suggest a timing, reward, or transition problem rather than insufficient simulation size.
Repeat with different random seeds to check whether a decision near zero incremental net benefit is stable. A sign change driven only by simulation noise is a reason to improve precision, not evidence that the model contains parameter uncertainty. Compare the remaining numerical error with the size of the decision-relevant difference.
Use deterministic edge cases such as certain transitions and identical rewards to audit calculations. Check both rare costly events and common transitions; rare events may require substantially more patients to stabilize their contribution. The microsimulation tutorial explains individual trajectories and simulation error.
References and other material
Read the methodological references and supporting tutorials below. The examples in this lesson are original teaching calculations, not findings from these sources.
- Microsimulation modeling for health decision sciences — Free tutorial on simulating individual patient histories.