Principal stratification

Principal stratification is a statistical technique used in causal inference when adjusting results for post-treatment covariates. The idea is to identify underlying strata and then compute causal effects only within strata. It is a generalization of the Local Average Treatment Effect (LATE).

Example

An example of principal stratification is where there is attrition in a randomized controlled trial. With a binary post-treatment covariate (e.g. attrition) and a binary treatment (e.g. "treatment" and "control") there are four possible strata in which subjects could be:

1. those who always stay in the study regardless of which treatment they were assigned
2. those who would always drop-out of the study regardless of which treatment they were assigned
3. those who only drop-out if assigned to the treatment group
4. those who only drop-out if assigned to the control group

If the researcher knew the stratum for each subject then the researcher could compare outcomes only within the first stratum and estimate a valid causal effect for that population. The researcher does not know this information, however, so modelling assumptions are required to use this approach.

An alternative to principal stratification, common in situations of attrition, is to provide bounds for the estimated effect under different bounding assumptions.

See also

• Rubin causal model
• Instrumental variable

References

• Frangakis, Constantine E.; Rubin, Donald B. (March 2002). "Principal stratification in causal inference". Biometrics 58 (1): 21–9. doi:10.1111/j.0006-341X.2002.00021.x. PMID 11890317.  Preprint
• Zhang, Junni L.; Rubin, Donald B. (2003) "Estimation of Causal Effects via Principal Stratification When Some Outcomes are Truncated by “Death”", Journal of Educational and Behavioral Statistics, 28: 353–368 doi:10.3102/10769986028004353
• Barnard, John; Frangakis, Constantine E.; Hill, Jennifer L.; Rubin, Donald B. (2003) "Principal Stratification Approach to Broken Randomized Experiments", Journal of the American Statistical Association, 98, 299–323 doi:10.1198/016214503000071
• Roy, Jason; Hogan, Joseph W.; Marcus, Bess H. (2008) "Principal stratification with predictors of compliance for randomized trials with 2 active treatments", Biostatistics, 9 (2), 277–289. doi:10.1093/biostatistics/kxm027
• Egleston, Brian L.; Cropsey, Karen L.; Lazev, Amy B.; Heckman, Carolyn J.; (2010) "A tutorial on principal stratification-based sensitivity analysis: application to smoking cessation studies", Clinical Trials, 7 (3), 286–298. doi:10.1177/1740774510367811