I am designing a causal inference analysis using observational data and I am trying to determine the sensitivity of my study design given a fixed sample size.
Study Details:
Goal: Estimate the Average Treatment Effect (ATE).
Treatment (T): Binary (Patient received A1C test).
Outcome (Y): Binary (No hospital readmission).
Covariates (X): A mix of categorical and numeric variables.
Estimator: I plan to use a Linear Probability Model (OLS on binary outcome)
The Problem: Unlike an RCT, where I would calculate a required sample size (N), my N is fixed.
I want to calculate the Minimum Detectable Effect (MDE) to determine if my dataset is theoretically capable of detecting a meaningful effect size, or if the study is underpowered regardless of the findings.
My Questions:
MDE in Observational Settings:
Is calculating MDE a valid procedure for retrospective observational data if done as a sensitivity analysis (i.e., determining the smallest effect size detectable with 80% power given N)?
Or is this functionally equivalent to the criticized practice of "post-hoc power analysis"?
Impact of Estimator/Covariates: Does the formula for MDE need to change to account for the specific estimator (Linear Regression vs. Logistic) and the inclusion of covariates?
Specific concern: In an RCT, power is often based on simple proportions (p_1 vs p_2).
In my observational study, I assume the variance of the ATE estimator will be inflated due to correlations between Treatment and Covariates (collinearity/lack of overlap).
Recommended Approach: How should I analytically adjust the MDE calculation to account for this "variance inflation" or "design effect" caused by the non-randomized assignment?
