Generating Virtual Trial Participants

From a Trial Scenario to Virtual Participants

A trial-level simulation needs more than an efficacy model: it needs a set of participants to whom that model can be applied. Each virtual participant should represent a plausible person from the scenario’s target population, meet the protocol’s eligibility criteria, receive treatment according to the planned randomization, and have an outcome generated according to the specified outcome model. If any of these steps is misrepresented, the simulated trial may answer a different question from the one intended.

The goal here is to translate specified population distributions and trial rules into participant-level records. Treat the distributions and model parameters as fixed inputs for each scenario. This tutorial does not address uncertainty in those parameters or elaborate joint models for correlated characteristics; those require additional specification. Any independence assumption used here must be stated as part of the scenario, not silently imposed by the simulation code.

A useful sequence is: generate candidate characteristics from the target population; apply eligibility rules; continue until the planned number of eligible participants is enrolled; randomize those participants; and generate outcomes conditional on their characteristics and assigned treatment. When the scenario instead asks how many people must be screened to enroll a target number, the screening process itself is part of the quantity being simulated. These are different questions and should not be conflated.

Generating Participants Who Meet Eligibility Criteria

Let \(X\) denote the baseline characteristics of a candidate drawn from the specified target-population distribution \(f(x)\). Let \(E\) denote the event that the candidate meets every eligibility criterion. If candidates are generated from \(f(x)\) and retained only when eligible, their distribution is the population distribution conditional on eligibility:

Here \(I(x\in E)\) equals 1 for an eligible candidate and 0 otherwise. The formula says that the retained distribution has zero probability outside the eligible region and is renormalized within it. Under independent candidate generation and a fixed eligibility rule, each retained candidate has this conditional distribution. Drawing until \(n\) eligible participants have been obtained therefore produces the planned number of participants from the eligible population.

This is rejection sampling: draw a candidate, evaluate the protocol criteria, retain an eligible candidate, and discard an ineligible one. It is simple and faithful to the specified population distribution, but can be inefficient if eligibility is rare. If the eligible fraction is \(q=P(E)\), then the expected number of candidates screened to enroll \(n\) people is \(n/q\), assuming independent candidate draws and a constant eligibility probability. A direct draw from the conditional distribution can be more efficient when it is available and correctly implemented.

Do not replace conditioning by clipping. For example, drawing a normally distributed laboratory value and changing every value below the eligibility threshold to that threshold creates an artificial pile-up at the cutoff. The result is not the original population conditional on eligibility. If a protocol criterion is based on several characteristics, apply the complete rule to each candidate; passing one criterion does not establish overall eligibility.

Randomization and Planned Enrollment

Randomization is a separate step from eligibility. First identify the enrolled eligible participants; then assign treatments using the design’s stated allocation procedure. For a fixed total \(n\) and exact allocation counts, one implementation is to create the required number of treatment labels, randomly permute them, and assign the permuted labels to the enrolled participants. This preserves the planned arm sizes while making assignments random. If the design instead uses independent assignment with probability \(r\) to one arm, arm sizes can vary across simulated trials; that is not equivalent to fixed allocation.

Randomization should not depend on a participant’s simulated outcome. Nor should an implementation quietly assign the first half of the participant records to one arm and the remainder to another: record order is not randomization. If a scenario specifies strata or blocks, the assignment algorithm must reflect them. The essential requirement is to implement the design that was specified, rather than a convenient substitute.

Generating Outcomes From the Specified Model

Once treatment is assigned, generate each participant’s outcome from the specified outcome distribution conditional on the inputs in that model. For example, a continuous outcome might follow a normal distribution with a mean depending on treatment and baseline, and a residual standard deviation that is specified for the scenario. The model’s assumptions must be explicit: for instance, whether residuals are independent across participants and whether the residual variance is constant. Generate an outcome draw, not just the model-predicted mean, unless the scenario explicitly calls for deterministic predictions.

The following example uses a simple specified model. Its numerical inputs are hypothetical and are used only to demonstrate the calculation.

Justification, Checks, and Failure Modes

The conditional distribution result follows directly from the definition of conditional probability. For any set \(B\) of baseline values,

Thus an accepted candidate has density \(f(x)/P(E)\) within the eligible region and density zero outside it. Repeated independent candidate draws followed by the same eligibility rule yield repeated draws from this conditional distribution. Stopping after the \(n\)th accepted candidate fixes enrollment without changing the distribution of the accepted values.

Several checks can reveal mistakes before trial summaries are interpreted. Confirm that the enrolled count is exactly the planned \(n\), that every retained participant meets every criterion, and that the arm counts match the specified allocation when it is fixed. Check that generated baseline values are on the intended scale and that the eligible sample does not contain values outside the permitted range. For outcomes, verify that the calculation uses the correct treatment indicator, baseline units, and residual scale.

A mismatch between the simulated eligible distribution and the intended conditional distribution can indicate a coding error, a mistaken eligibility rule, or a very small accepted sample. A pile-up at a boundary may indicate clipping. An arm-count discrepancy may indicate that independent Bernoulli assignment was used where exact allocation was intended. Identical outcomes across participants may indicate that the model mean was used without residual draws. These checks diagnose implementation; they do not establish that the chosen population distributions or outcome model are scientifically adequate.

The main alternatives depend on which part of the process is fixed. Rejection sampling is transparent and generally easy to check; direct conditional sampling can be faster but requires a correct method for the conditional distribution. Exact allocation preserves arm counts, whereas independent treatment assignment permits those counts to vary. A fixed-enrollment simulation answers questions conditional on reaching the planned eligible sample; simulating a fixed screening cohort can address recruitment yield instead. These approaches are not interchangeable, and none can correct an incorrectly specified population or outcome model.