Principal Investigator:

Constantine E. Frangakis



Donald B. Rubin




Sponsoring Agency:

National Eye Institute



Progress Reports:


2003-2004 (doc)  

2004-2005 (doc)



This grant has been developing methods to evaluate treatment effects in studies with no direct control of these treatments, but with control of other factors useful to assess these effects. Original applications of interest include evaluating needle exchange using distance, and evaluating studies in ophthalmology, HIV, cancer, and orthopedics. The project has introduced the general framework of principal stratification for formulating and estimating effects of such partially controlled factors, and for better designing studies to estimate their effects.


Principal stratification has now been used in a broad range of areas, including surrogate endpoints, effects of vaccines for those infected, and noncompliance with missing outcomes in ophthalmology, HIV, cancer, orthopedics, mental health, and nephrology.



the grant

·       has produced > 40 peer-reviewed publications

·       has been used+cited by > 100 journal papers by other researchers

·       has been used in government documents

       (e.g., Supreme Court, Florida, school vouchers)

·       forms part of > 8 PhD theses (Hopkins, Harvard, UCLA)

·       forms part of courses at Hopkins, Harvard, Princeton, Emory, Beijin U, Karolinska


Framework of principal stratification for causal inference in partially controlled studies:
Frangakis, CE, and Rubin, DB (2002)  Principal stratification  in causal inference. Biometrics, 58, 21-29.

School Choice Voucher Evaluation using principal stratification:
Barnard, J, Frangakis, CE, Hill, JL, Rubin, DB.  (2003).  A principal stratification approach to broken randomized experiments: a case study of School Choice vouchers in New York City.  Journal of the American Statistical Association (with discussion) 98, 299-323. [ Full text - PDF]

Evaluation of needle exchange using principal stratification:
Frangakis, CE, Brookmeyer, RS, Varadhan, R, Mahboobeh, S,  Vlahov, D, and Strathdee, SA. (2004). Methodology for evaluating a partially controlled longitudinal treatment using principal stratification, with application to a Needle Exchange Program. Forthcoming in the Journal of the American Statistical Association . [ Full text - PDF]

Direct and indirect effects.
Rubin (2004). Direct and Indirect Causal Effects Via Potential Outcomes.  To appear in the Scandinavian Journal of Statistics, with discussion and reply.

Censoring by death.
Zhang, J. L. Rubin, D. 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.

Length Bias and Efficiency of case-crossover designs.

Varadhan, R, and Frangakis, C. E. (2004). Revealing and addressing length-bias and heterogeneous effects in frequency case-crossover studies. To appear in the  American Journal of Epidemiology. Available at :


Propensity scores.

Rubin, D.B. (2003). Taking causality seriously: propensity score methodology applied to estimate the effects of marking interventions.  Machine Learning: ECMC 2003.  14th European Conference on Machine Learning.  (N. Lavrae, D. Gamberger, H. Blockeel, and L. Todorovski (eds.)).  New York: Springer Verlag, pp. 16-22.  also in Knowledge Discovery in Databases: PKDD 2003.  7th European Conference on Principles and Practice of Knowledge Discovery in Databases.  (N. Lavrae, D. Gamberger, L. Todorovski and H. Blockeel (eds.)).  New York: Springer Verlag, pp. 16-22.


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