STA 610 Case Study: Diazepam Street Pricing Analysis

Author: Zixiao Tan

Overview

This project analyzes street pricing data for Diazepam (a benzodiazepine) using hierarchical modeling techniques. The analysis explores factors associated with price per milligram (ppm) and investigates geographic heterogeneity in pricing across different U.S. states.

Research Questions

1. Which variables are associated with pricing per milligram of Diazepam?
2. Is there heterogeneity in pricing of Diazepam by location?

Data

The analysis uses the StreetRx dataset, which contains crowdsourced street drug pricing information. Key variables include:

• ppm: Price per milligram (outcome variable)
• mgstr: Dosage strength (2mg, 4mg, 5mg, 10mg)
• bulk_purchase: Indicator for purchases of 10+ units
• source: Source of information (Heard of, Internet, Personal)
• state: U.S. state where purchased
• year: Year of purchase

Methodology

Statistical Approach

• Model Type: Hierarchical linear mixed model with random intercepts by state
• Response Transformation: Log transformation of ppm to meet normality assumptions
• Fixed Effects: Dosage strength (mgstr), bulk purchase indicator, source of information
• Random Effects: State-level intercepts to capture geographic variation
• Model Selection: Exhaustive search with BIC criterion across 1,024 candidate models

Analysis Framework

• Frequentist Approach: Maximum likelihood estimation using lme4
• Bayesian Approach: MCMC sampling using brms with non-informative priors
• Model Diagnostics: Residual analysis, influential group detection, assumption checks

Key Findings

• Dosage Effects: Pricing per mg varies significantly across dosage strengths
• Bulk Discounts: Bulk purchases are approximately 12.4% cheaper per mg
• Source Differences: Internet sources show 33% lower prices compared to word-of-mouth, while personal reports are 10% lower
• Geographic Variation: Significant heterogeneity in baseline pricing across states
• Model Convergence: Frequentist and Bayesian estimates are nearly identical

Project Structure

.
├── case_study.Rmd              # Main analysis R Markdown file
├── case_study_report.Rmd       # Report version
├── streetrx.RData              # Dataset
├── presentation/               # Presentation materials
└── README.md                   # This file

Requirements

R Packages

tidyverse, lme4, rstan, brms, knitr, kableExtra,
patchwork, lubridate, gridExtra, influence.ME

Usage

To reproduce the analysis:

1. Load the required R packages
2. Open case_study.Rmd in RStudio
3. Knit the document to generate the PDF report

# In R console
rmarkdown::render("case_study.Rmd")

Presentation Video

Watch the project presentation on YouTube:

STA 610 Case Study Presentation

Limitations

• High within-state variance remains unexplained
• Normality assumption shows deviations in residual tails
• Some influential groups (e.g., Texas) detected but retained due to large sample sizes
• Missing data in primary_reason variable excluded from analysis

License

This project was completed as part of Duke University's STA 610 course.