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Multiple Endpoints - Patient Simulation

Anoop Singh Rawat, Gabriel Potvin

January 09, 2026

MEPPatientSimulation.Rmd

Introduction

This example illustrates how to integrate new patient outcome simulation (response) capabilities into East Horizon using R functions in the context of 2-arm clinical trials with multiple endpoints. The example combines time-to-event, binary, and continuous outcomes within a single response-generating function.

In the R directory of this example you will find the following R file:

  1. GenerateMEPResponse.R - This file contains the response-generation logic used to simulate patient-level outcomes across multiple endpoints.

Example 1 - Simulate Response for Multiple Endpoints

The function GenerateMEPResponse simulates patient-level outcomes for a two-arm clinical trial with an arbitrary number of endpoints. Each endpoint can independently be defined as continuous, binary, or time-to-event. All endpoints are generated within a single unified Response function. No user-defined parameters are used in this example.

Important inputs to the function include:

  • EndpointType: Defines the type of each endpoint (0 = Continuous, 1 = Binary, 2 = TTE).
  • EndpointName: Character vector containing endpoint names. These names are used as keys in RespParams and the returned response list.
  • RespParams: A list of endpoint-specific parameter lists. Each endpoint entry contains control and treatment parameters appropriate to its type.
  • Correlation: A correlation matrix of dimension (Number of Endpoints ×\times Number of Endpoints) used to induce correlation across all endpoints.

To model correlation between endpoints, the function:

  1. Generates independent standard normal variables for all patients and endpoints.
  2. Applies a Cholesky decomposition of the correlation matrix.
  3. Transforms the normal variables to obtain correlated latent responses.

These correlated latent variables are then mapped to endpoint-specific outcomes depending on the endpoint type.

Time-to-Event Endpoints

Time-to-event endpoints are generated using an exponential survival model. The function supports either of the three alternative parameterizations methods (Hazard rate, Cumulative survival percentages, Median survival times) as chosen in East Horizon.

Treatment effects are incorporated through a hazard ratio (HR) applied multiplicatively to the control hazard. For each patient, the survival time is generated by transforming the correlated normal variable into a uniform variable and applying the inverse exponential survival function. The resulting outcome represents the event time for each patient.

Binary Endpoints

Binary endpoints are generated using a latent normal threshold model using control and treatment response probabilities provided in RespParams. These probabilities are converted into probit-scale thresholds. Then, the correlated latent normal variable is compared against the arm-specific threshold to determine the binary outcome. With this approach, we ensure consistency between marginal response rates and the specified correlation structure.

Continuous Endpoints

Continuous endpoints are generated from normal distributions, with arm-specific mean and standard deviation parameters via the lists RespParams$Treatment and RespParams$Control. Each list contains two elements: the mean (e.g., RespParams$Treatment[1]) and the standard deviation (e.g., RespParams$Treatment[2]). The correlated latent normal variable is scaled and shifted according to the treatment assignment to produce the final outcome.

The final responses are returned for each endpoint and patient.

The figure below illustrates where this example fits within the R integration points of Cytel products, accompanied by a flowchart outlining the general steps performed by the R code.