Ding, P., and Dasgupta, T. (2016), “A Potential Tale of Two-by-Two Tables From Completely Randomized Experiments,” Journal of the American Statistical Association, 111, 157–168, DOI: 10.1080/01621459.2014.995796.
The variance estimator in (8) is asymptotically equivalent to the ones derived by Robins (Citation1988) and Aronow et al. (Citation2014), although they have slightly different forms. Moreover, for binary outcomes from completely randomized experiments, Robins (Citation1988) first discussed the causal risk ratio measure using the potential outcomes framework, and he obtained a variance formula that is asymptotically equivalent to our variance estimator in (A.2). We thank Professor James M. Robins for bringing these issues to our attention.
References
- Aronow, P. A., Green, D. P., and Lee, D. K. K. (2014), “Sharp Bounds on the Variance in Randomized Experiments,” Annals of Statistics, 42, 850–871.
- Robins, J. M. (1988), “Confidence Intervals for Causal Parameters,” Statistics in Medicine, 7, 773–785.