Dose-Finding Study: Optimal Design & MED Identification using R

A full end-to-end dose-finding analysis pipeline in R, covering optimal study design, exploratory analysis, MED identification, and PK/PD modelling — from sample size calculation to a safety-adjusted minimum effective dose.

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Overview

This project simulates and analyses a Phase II dose-finding clinical trial for a hypothetical drug tested at four dose levels (0, 10, 100, and 200 mg). The goal is to identify the Minimum Effective Dose (MED) — the lowest dose that produces a clinically meaningful change in pharmacodynamic effect relative to placebo — while accounting for exposure variability and side-effect risk.

The analysis is structured into four tasks, each building on the last.

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Tasks

Task 1 — Sample Size & Optimal Dose Design

• Cohen's d-based sample size calculation using pwr
• Built a sigmoidal Emax (Hill) model in PopED to characterise the dose–response relationship
• Optimised active dose levels using Adaptive Random Search (ARS) + Local Search (LS)
• Generated model predictions with and without prediction intervals
• Quantified parameter uncertainty via Monte Carlo sampling from the Fisher Information Matrix (FIM)
• Explored sensitivity of dose–response shape across variations in Emax, ED50, and Hill coefficient

Task 2 — Exploratory Data Analysis

• Loaded and tidied real-format clinical trial data (data_7.csv) using dplyr and tidyr
• Stratified sampling of 200 subjects across four dose groups
• Computed summary statistics: mean, SD, median, trimmed mean, Hodges-Lehmann estimate
• Visualisations: boxplots, histograms, spaghetti plots of effect over time, and a full pairwise correlation matrix with significance annotation (GGally)

Task 3 — Statistical Testing & MED Identification

• Pairwise dose vs. placebo comparisons using:
  • Welch's t-test (one-sided, µ = 75, α = 0.05)
  • Hodges-Lehmann (Wilcoxon) robust estimator
• Multiple comparison correction via Holm's method
• MED defined as the lowest dose whose 95% lower confidence bound exceeds the target effect (Δ = 75)
• Side-effect analysis using Fisher's Exact Test at each dose level

Task 4 — PK/PD Modelling & Exposure-Response

• Fitted 12 models total across three exposure metrics (Dose, AUC, Cmax):
  • Simple linear regression
  • Multiple linear regression (with covariates: age, weight, sex, height, side effects)
  • Hyperbolic Emax (no Hill coefficient)
  • Sigmoidal Emax (Hill equation) using nlsLM
• Model selection via AIC and BIC
• Best model: Sigmoidal Emax (AUC-based) — supported by lowest AIC/BIC
• Diagnostic plots: observed vs. predicted, residuals vs. fitted, histogram of residuals, QQ-plot
• MED via Monte Carlo simulation: parametric bootstrap (B = 10,000) from the multivariate parameter distribution to identify the critical AUC where the 95% lower bound of predicted effect exceeds Δ = 75
• Converted AUC threshold to dose using a linear PK bridge model
• Safety analysis: logistic regression modelling side-effect probability at MED vs. placebo

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Files

File	Description
Dose finding study.R	Full analysis script — all 4 tasks
data_7.csv	Simulated clinical trial dataset (200 subjects, 4 dose groups)

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Key Results

• Optimal dose levels identified via PopED differ from naive equal-spacing assumptions
• Welch t-test and Hodges-Lehmann agree on MED identification
• Sigmoidal Emax (AUC) outperforms all linear models on AIC/BIC
• MED dose is computed with an explicit 95% confidence guarantee, not just a point estimate
• Side-effect risk at MED is quantified and benchmarked against placebo

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Dependencies

install.packages(c(
  "pwr", "readr", "dplyr", "tidyr", "ggplot2",
  "PopED", "minpack.lm", "mvtnorm", "patchwork",
  "DoseFinding", "DescTools", "boot", "GGally", "MASS"
))

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How to Run

1. Clone the repo
2. Place data_7.csv in your working directory (or update the setwd() path in Task 2)
3. Source or run Dose finding study.R section by section — each task is clearly delimited with # Task N---- comments

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Context

This analysis was completed as part of the Preclinical and Clinical Data Analysis course in the MSc Pharmaceutical Modelling programme at Uppsala University.

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Part of my pharmacometrics portfolio — see my GitHub profile for more.