An example of Difference of Differences (D-I-D) causal methodology. As cited below (abadie) D-I-D is often used in comparisons of policy interventions
found a recent article in the NEJM, that adopts a "difference of difference" (D-I-D) methodology to assess effect of mask wearing in schools during the covid pandemic. While not clearly stated, the reasons the authors seem to have adopted D-I-D may be because of staggered policy implementationhttps://www.nejm.org/doi/full/10.1056/NEJMoa2211029
I will only give links to some of the technical details of "D-I-D" for causal estimation.
Abadie (an economist) describes some semi-parametric models and D-I-D. https://economics.mit.edu/sites/default/files/publications/Semiparametric.pdf
excerpting "The difference-in-differences (DID) estimator is one of the most popular tools for applied research
in economics to evaluate the effects of public interventions and other treatments of interest on some
relevant outcome variables.:" And Abadie refers to Heckman ( a Nobel prize winner in economics) and Heckmans "selection models"
HECKMAN, J. J. (1990), "Varieties of Selection Bias", American Economic Review, 80, 313–318.
HECKMAN, J. J., ICHIMURA, H., SMITH, J. and TODD, P. E. (1998), "Characterizing Selection Bias using
Experimental Data", Econometrica, 66, 1017–1098.
HECKMAN, J. J., ICHIMURA, H. and TODD, P. E. (1997), "Matching as an Econometric Evaluation
Estimator: Evidence from Evaluating a Job Training Programme", Review of Economic Studies, 64, 605–654.
There are some excellent recent examples of propensity scores in some complex innovative clinical trial designshttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4813540/
Descriptions of D-I-D
Some economists consider the paper by economists Drs Card and Krueger as an excellent example of D-I-D . Dr Card won the Nobel in economics.
Combining D-I-D with propensity scores is described here with considerable technical details such as SUTVA (Stable Unit Treatment Value Assumption)
Chris Barker, Ph.D.
2023 Chair Statistical Consulting Section
Adjunct Associate Professor of Biostatisticswww.barkerstats.com
"In composition you have all the time you want to decide what to say in 15 seconds, in improvisation you have 15 seconds."