Unequal Randomization in Clinical Trials

This repository contains R scripts for simulating and analyzing different randomization schemes in two-arm clinical trials. The simulations focus on evaluating key performance metrics such as expected mean response, Type-I error rate, statistical power, and patient allocation across various trial designs.

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Table of Contents

• Project Overview
• Project Context
• Randomization Schemes Implemented
• Key Metrics Analyzed
• Files in this Repository
• Reproducibility
• Dependencies

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Project Overview

This project provides a simulation framework to compare the performance of various randomization strategies for two-arm clinical trials. It lets researchers investigate how different allocation rules impact trial outcomes under diverse data distributions and parameter settings.

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Project Context

The simulations in this repository are designed to generate data for specific tables and figures in a research study:

• Table 1: Results from simulations using binary outcomes (i.e., dist="bern" in sim_ER, sim_FR, sim_ERADE) are intended for Table 1.
• Table 2: Results from simulations using normal outcomes (i.e., dist="norm" in sim_ER, sim_FR, sim_ERADE), as shown in the examples below, are intended for Table 2.
• Figure 1: The allocation ratios (specifically, the mean proportion of patients allocated to the experimental arm, corresponding to column 6 of the simulation output) from all simulation types are relevant for illustrating patient distribution and are intended for Figure 1.

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Randomization Schemes Implemented

The simulations cover the following randomization methods:

1. Equal Randomization (ER): Patients are assigned to treatment arms with equal probability (e.g., 50/50).
2. Fixed Randomization (FR): Patients are assigned to treatment arms with a pre-specified fixed probability (e.g., 70% to arm 1, 30% to arm 2).
3. ERADE (Efficient Response Adaptive Design): An adaptive randomization method that adjusts allocation probabilities based on observed patient responses during the trial. This includes specific implementations like "RSHIR_Z0", "RSHIR_Z1", "Neyman_Z0", and "Neyman_Z1," which adapt based on different variance and mean estimators.

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Key Metrics Analyzed

For each simulation, we compute and evaluate the following metrics:

• Expected Mean Response (EMR): The overall average response observed across all patients in a trial, averaged over many simulations.
• Type-I Error Rate: The probability of incorrectly rejecting the null hypothesis (i.e., concluding there's a difference between arms when there is none). We assess this when there's no true difference between the experimental and control arms.
• Power: The probability of correctly rejecting the null hypothesis (i.e., detecting a true difference between arms when one exists). We assess this when a true difference is present.
• Allocation towards Experimental Arm: The average proportion of patients assigned to the experimental treatment arm.
• Proportion in Theoretically Superior Arm: For adaptive designs, this indicates how often patients were allocated to the arm that's truly better.

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Files in this Repository

• Data_Generator.R: Contains functions to simulate patient data based on specified distributions (e.g., Bernoulli, Normal) and parameters. It also likely includes the superior() function to determine which arm is theoretically superior based on the true parameters.
• WaldTest.R: Provides functions (wald.test, wald.test.binary) for performing Wald tests to compare outcomes between two arms.
• sim_ER.R: The main simulation function for Equal Randomization. It calls two_arm_ER.
• two_arm_ER.R: Implements a single trial simulation for Equal Randomization.
• sim_FR.R: The main simulation function for Fixed Randomization. It calls two_arm_FR.
• two_arm_FR.R: Implements a single trial simulation for Fixed Randomization.
• sim_ERADE.R: The main simulation function for ERADE (Adaptive Randomization). It calls two_arm_ERADE.
• two_arm_ERADE.R: Implements a single trial simulation for ERADE, including the logic for dynamic patient allocation.
• Helper Functions: The two_arm_ERADE script relies on helper functions like ERADE() (to calculate ERADE probabilities) and find_root() (for RSHIR_Z0 calculations), which are included in the same file or implicitly sourced.

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Reproducibility

All results presented in the associated paper can be generated using the respective simulation files and R code provided within this repository. This ensures full transparency and reproducibility of the research findings.

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Dependencies

This project requires the following R packages:

• BSDA
• rankFD
• lawstat

You can install them using:

install.packages(c("BSDA", "rankFD", "lawstat"))