A negative control outcome cannot plausibly be affected by the
exposure but shares its confounding structure, so its estimated
effect is an estimate of the bias. Both outcomes go through the same
doubly robust moment of Sant'Anna and Zhao (2020), equation (2.6);
the design is refuted when
|tau_neg| > qnorm(1 - alpha/2) se_neg, and
tau_adj = tau_main - tau_neg subtracts the estimated bias.
Usage
Drnpc(y_main, y_neg, D, X = NULL, alpha = 0.05)
Arguments
- y_main
Outcome change for the outcome of interest.
- y_neg
Outcome change for the negative control outcome.
- D
Binary treatment indicator.
- X
Optional baseline covariates.
- alpha
Two-sided level of the falsification test.
Value
List with estimate, tau_main, tau_neg,
se_main, se_neg, z_neg, crit,
falsified, tau_adj, n.
References
Lipsitch, M., Tchetgen Tchetgen, E. and Cohen, T. (2010).
Negative controls. Epidemiology 21(3), 383-388. Sant'Anna,
P. H. C. and Zhao, J. (2020). Journal of Econometrics 219(1),
101-122.
