Propensity score matching is the best method to use.

Thank you so much for confirming my thought.

Hi Susie,

Propensity score (PS) matching is a more robust to balance baseline co-variates and adjust for confounding. The propensity score allows one to design and analyze an observational (nonrandomized) study so that it mimics some of the particular characteristics of a randomized controlled trial ("The "strongest" study design). However, there are some pitfalls for using PS:

1) It is important to match on PS as "closely" as possible, however, this may cause the loss of some individuals leading to reduced sample size and power. I put closely in quotations because there are two primary methods for this: nearest neighbor matching and nearest neighbor matching within a specified caliper distance (Rosenbaum & Rubin, 1985).

2)You cannot use co-variates that may be affected by the exposure of interest in the model that estimates the propensity scores.

3) Even though PS can balance observed baseline covariates between treatment groups, they MAY NOT balance unmeasured characteristics and confounders.

Peter Austin has done some great work in the field of propensity scores. I highly recommend reading some of his work if you decide on using propensity scores.

One article of his:

Austin, PC. An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies. Multivariate Behav Res. 2011 May;46(3):399-424.

Rosenbaum P.R., Rubin D.B. Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. The American Statistician. 1985; 39:33–38

Thank you very much Ahmed for your great/detailed suggestions. I've downloaded these two papers. We have about 300,000 controls so I would be okay with power and sample size (I hope).