Principal Stratification -- Uses and Limitations

Pearl (2011) asked for the causal inference community to clarify the role of the principal stratification framework in the analysis of causal effects. Here, I argue that the notion of principal stratification has shed light on problems of non-compliance, censoring-by-death, and the analysis of post-infection outcomes; that it may be of use in considering problems of surrogacy but further development is needed; that it is of some use in assessing “direct effects”; but that it is not the appropriate tool for assessing “mediation.” There is nothing within the principal stratification framework that corresponds to a measure of an “indirect” or “mediated” effect.

[1]  Jack Cuzick,et al.  Estimating the effect of treatment in a proportional hazards model in the presence of non‐compliance and contamination , 2007 .

[2]  Bryan E Shepherd,et al.  Sensitivity Analyses Comparing Time-to-Event Outcomes Existing Only in a Subset Selected Postrandomization , 2007, Journal of the American Statistical Association.

[3]  L. Keele,et al.  A General Approach to Causal Mediation Analysis , 2010, Psychological methods.

[4]  D. Rubin,et al.  Bayesian inference for causal effects in randomized experiments with noncompliance , 1997 .

[5]  E. Mackenzie,et al.  On Estimation of the Survivor Average Causal Effect in Observational Studies When Important Confounders Are Missing Due to Death , 2009, Biometrics.

[6]  Glenn Shafer,et al.  Comments on "Causal Inference without Counterfactuals" by A.P. Dawid , 1999 .

[7]  R. Gallop,et al.  Mediation analysis with principal stratification , 2009, Statistics in medicine.

[8]  Tom Greene,et al.  Related Causal Frameworks for Surrogate Outcomes , 2009, Biometrics.

[9]  Donald B. Rubin,et al.  Estimation of Causal Effects via Principal Stratification When Some Outcomes are Truncated by “Death” , 2003 .

[10]  Michael R Elliott,et al.  A Bayesian Approach to Surrogacy Assessment Using Principal Stratification in Clinical Trials , 2010, Biometrics.

[11]  A. Rotnitzky,et al.  Semiparametric estimation of treatment effects given base‐line covariates on an outcome measured after a post‐randomization event occurs , 2007, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[12]  Judea Pearl,et al.  Direct and Indirect Effects , 2001, UAI.

[13]  D. Rubin,et al.  Principal Stratification in Causal Inference , 2002, Biometrics.

[14]  Corwin M Zigler,et al.  A Bayesian Approach to Improved Estimation of Causal Effect Predictiveness for a Principal Surrogate Endpoint , 2012, Biometrics.

[15]  Juni Palmgren,et al.  Sensitivity Analysis for Principal Stratum Direct Effects, with an Application to a Study of Physical Activity and Coronary Heart Disease , 2009, Biometrics.

[16]  Zhi Geng,et al.  Criteria for surrogate end points based on causal distributions , 2010 .

[17]  Andrea Rotnitzky,et al.  Sensitivity Analyses Comparing Outcomes Only Existing in a Subset Selected Post‐Randomization, Conditional on Covariates, with Application to HIV Vaccine Trials , 2006, Biometrics.

[18]  Kosuke Imai,et al.  Sharp bounds on the causal effects in randomized experiments with "truncation-by-death" , 2008 .

[19]  T. VanderWeele Simple relations between principal stratification and direct and indirect effects , 2008 .

[20]  D. Rubin Comment on "Causal inference without counterfactuals," by Dawid AP , 2000 .

[21]  A. Gupta,et al.  A Bayesian Approach to , 1997 .

[22]  J J Heckman,et al.  Local instrumental variables and latent variable models for identifying and bounding treatment effects. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Michael R Elliott,et al.  Bayesian inference for causal mediation effects using principal stratification with dichotomous mediators and outcomes. , 2010, Biostatistics.

[24]  James M. Robins,et al.  Transparent Parametrizations of Models for Potential Outcomes , 2012 .

[25]  P. Rosenbaum,et al.  Randomization Inference With Imperfect Compliance in the ACE-Inhibitor After Anthracycline Randomized Trial , 2004 .

[26]  Michael G Hudgens,et al.  Causal Vaccine Effects on Binary Postinfection Outcomes , 2006, Journal of the American Statistical Association.

[27]  James M. Robins,et al.  Principal stratification designs to estimate input data missing due to death - Discussion , 2007 .

[28]  J. Robins A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect , 1986 .

[29]  Zhi Geng,et al.  Criteria for surrogate end points , 2007 .

[30]  T. VanderWeele Bias Formulas for Sensitivity Analysis for Direct and Indirect Effects , 2010, Epidemiology.

[31]  Tyler J. VanderWeele,et al.  Bounding the Infectiousness Effect in Vaccine Trials , 2011, Epidemiology.

[32]  M. Hudgens,et al.  Sensitivity Analysis for the Assessment of Causal Vaccine Effects on Viral Load in HIV Vaccine Trials , 2003, Biometrics.

[33]  Tyler J VanderWeele,et al.  Statistical Applications in Genetics and Molecular Biology Epistatic Interactions , 2011 .

[34]  Tyler J VanderWeele,et al.  A simple method for principal strata effects when the outcome has been truncated due to death. , 2011, American journal of epidemiology.

[35]  J. Robins Correcting for non-compliance in randomized trials using structural nested mean models , 1994 .

[36]  Michael G Hudgens,et al.  Evaluating Candidate Principal Surrogate Endpoints , 2008, Biometrics.

[37]  Bias Analysis for The Principal Stratum Direct Effect in The Presence of Confounded Intermediate Variables , 2010 .

[38]  Hsin-Chieh Yeh,et al.  Effect of the 2011 vs 2003 duty hour regulation-compliant models on sleep duration, trainee education, and continuity of patient care among internal medicine house staff: a randomized trial. , 2013, JAMA internal medicine.

[39]  Dylan S. Small,et al.  Bounds on causal effects in three‐arm trials with non‐compliance , 2006 .

[40]  M. Hernán,et al.  Compound Treatments and Transportability of Causal Inference , 2011, Epidemiology.

[41]  Jan M. Rabaey,et al.  Comparison of Methods , 2004 .

[42]  Ellen MacKenzie,et al.  Principal Stratification Designs to Estimate Input Data Missing Due to Death , 2007, Biometrics.

[43]  Xihong Lin,et al.  A Comparison of Methods for Estimating the Causal Effect of a Treatment in Randomized Clinical Trials Subject to Noncompliance , 2009, Biometrics.

[44]  Stijn Vansteelandt,et al.  Odds ratios for mediation analysis for a dichotomous outcome. , 2010, American journal of epidemiology.

[45]  Julian Wolfson,et al.  Statistical Identifiability and the Surrogate Endpoint Problem, with Application to Vaccine Trials , 2010, Biometrics.

[46]  D. Rubin Estimating causal effects of treatments in randomized and nonrandomized studies. , 1974 .

[47]  D. Culler,et al.  Comparison of methods , 2000 .

[48]  J. Pearl,et al.  Bounds on Treatment Effects from Studies with Imperfect Compliance , 1997 .

[49]  James M. Robins,et al.  On the Validity of Covariate Adjustment for Estimating Causal Effects , 2010, UAI.

[50]  Michael G Hudgens,et al.  On the analysis of viral load endpoints in HIV vaccine trials , 2003, Statistics in medicine.

[51]  D. Rubin Causal Inference Through Potential Outcomes and Principal Stratification: Application to Studies with “Censoring” Due to Death , 2006, math/0612783.

[52]  James J. Heckman,et al.  Identification of Causal Effects Using Instrumental Variables: Comment , 1996 .

[53]  Tyler J. VanderWeele,et al.  Conceptual issues concerning mediation, interventions and composition , 2009 .