1. Columbia University, Department of Biostatistics
Using Published Prevalence estimates to perform difference-in-Difference Tests
Christine Mauro, PhD
Columbia University, Department of Biostatistics
JSM, July 30, 2018

2. Introduction
Colorado and Washington first two states with Recreational Marijuana Laws (RML)
enacted 2012, fully implemented 2014
Goal: Assess impact of RML on marijuana use in Washington and Colorado
Examine changes in the prevalence of past-month marijuana use from to using a difference-in-difference (DID) analysis.
Statistical Challenge:
Data limited to published two-year state-level prevalence estimates and confidence intervals (CIs).

3. Statistical Methods Derive standard errors from confidence intervals
For each state (and US) and year, simulate 10K observations from a normal distribution
mean=published prevalence, sd=derived standard error.
From simulated data,
Obtain 10K estimates of change (Δ) in use for CO, WA, and the US ( vs )
Obtain 10K diff-in-diff estimates (ΔCO - ΔUS; Δ WA - ΔUS)
95% CI: Extract 2.5th and 97.5th percentiles of 10K diff-in-diff estimates
CIs not crossing zero  statistically significant change post RML

4. Results Overall Trends in past-month marijuana use:
↓ among those aged 12-17
↑ among those and 26+.
After RML in Colorado:
No differential change for year olds or those
Significantly larger ↑ for those 26+, DID=+3.7% =
After RML in Washington:
No differential change for any age group.
Extracting standard errors from published CIs allows for testing of simple research hypotheses using simulation methods.