I'm interested in using Propensity Score Matching (PSM) to create matched control vs treatment sample and estimate the treatment effect. But the problem with PSM is that the sample is matched based on observed covariates.
What are the sensitivity analyses for PSM, to assess its robustness to unobserved factors? I know there is Rosenbaum Bound analysis and M-H bound (rbounds and mhbounds in STATA, respectively,), any others?
there is also a simulation-based sensitivity analysis for matching estimators, which is described in Nannici (2007) and Ichino et al. (2008). In Stata, the program sensatt can perform this kind of analysis.
Moreover, you could imagine a binary unmeasured confounder and stratify on it as proposed by Greenland (1996) and discussed in the context of matching by Harding (2003). This idea can again be combined with simulation techniques, see e.g. Groenwold et al. (2010) or Liu et al. (2013). In general, the latter two papers provide a good overview about sensitivity analysis techniques.
Further approaches, which are not specific to matching but readily applicable to matching, are e.g. described in Arah et al. (2008), VanderWeele & Arah (2011), Blackwell (2013), Ding & VanderWeele (2016) and VanderWeele & Ding (2017).
If you want to work with a minimal set of assumptions, it might be interesting to have a look at the literature on non-parametric bounds for average treatment effects (e.g. Manski, 1990).
Here are doi references to most of the papers I mentioned:
https://doi.org/10.1086/379217
https://doi.org/10.1002/jae.998
https://doi.org/10.1093/ije/dyp332
https://doi.org/10.1007/s11121-012-0339-5
https://doi.org/10.1016/j.annepidem.2008.04.003
https://doi.org/10.1097/EDE.0b013e3181f74493
