Model‐free causal inference of binary experimental data

For binary experimental data, we discuss randomization‐based inferential procedures that do not need to invoke any modeling assumptions. In addition to the classical method of moments, we also introduce model‐free likelihood and Bayesian methods based solely on the physical randomization without any hypothetical super population assumptions about the potential outcomes. These estimators have some properties superior to moment‐based ones such as only giving estimates in regions of feasible support. Due to the lack of identification of the causal model, we also propose a sensitivity analysis approach that allows for the characterization of the impact of the association between the potential outcomes on statistical inference.

[1]  Dylan S. Small,et al.  Randomization‐based instrumental variables methods for binary outcomes with an application to the ‘IMPROVE’ trial , 2017 .

[2]  P. Ding,et al.  General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference , 2016, 1610.04821.

[3]  P. Ding,et al.  Exact confidence intervals for the average causal effect on a binary outcome , 2015, Statistics in medicine.

[4]  David Allan,et al.  Complications in Causal Inference: Incorporating Information Observed After Treatment is Assigned , 2016 .

[5]  Weizhen Wang.  Exact Optimal Confidence Intervals for Hypergeometric Parameters , 2015 .

[6]  M. Hudgens,et al.  Exact Confidence Intervals in the Presence of Interference. , 2015, Statistics & probability letters.

[7]  Y. Chiba.  Exact Tests for the Weak Causal Null Hypothesis on a Binary Out come in Randomized Trials , 2015 .

[8]  D. Rubin,et al.  Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction , 2016 .

[9]  M. Hudgens,et al.  Randomization inference for treatment effects on a binary outcome , 2015, Statistics in medicine.

[10]  Tirthankar Dasgupta,et al.  A Potential Tale of Two-by-Two Tables From Completely Randomized Experiments , 2015, 1501.02389.

[11]  Dylan S. Small,et al.  Discrete Optimization for Interpretable Study Populations and Randomization Inference in an Observational Study of Severe Sepsis Mortality , 2014, 1411.4873.

[12]  D. A. Watson.  Complications in Causal Inference: Incorporating Information Observed After Treatment is Assigned , 2014 .

[13]  Donald K. K. Lee,et al.  SHARP BOUNDS ON THE VARIANCE IN RANDOMIZED EXPERIMENTS , 2014, 1405.6555.

[14]  P. Ding,et al.  A paradox from randomization-based causal inference , 2014, 1402.0142.

[15]  Michael G. Hudgens,et al.  Randomization-Based Inference Within Principal Strata , 2011, Journal of the American Statistical Association.

[16]  Alan Agresti,et al.  Categorical Data Analysis , 2003 .

[17]  Jake Bowers,et al.  Attributing Effects to a Cluster-Randomized Get-Out-the-Vote Campaign , 2009 .

[18]  P. Rosenbaum.  Interference Between Units in Randomized Experiments , 2007 .

[19]  D. Rubin.  Causal Inference Using Potential Outcomes , 2005 .

[20]  Paul R. Rosenbaum,et al.  Robust, accurate confidence intervals with a weak instrument: quarter of birth and education , 2005 .

[21]  Paul R. Rosenbaum,et al.  Effects attributable to treatment: Inference in experiments and observational studies with a discrete pivot , 2001 .

[22]  A. Winsor.  Sampling techniques. , 2000, Nursing times.

[23]  P. Rosenbaum,et al.  Reduced Sensitivity to Hidden Bias at Upper Quantiles in Observational Studies with Dilated Treatment Effects , 1999, Biometrics.

[24]  R. Nelsen.  An Introduction to Copulas , 1998 .

[25]  D B Rubin,et al.  More powerful randomization-based p-values in double-blind trials with non-compliance. , 1998, Statistics in medicine.

[26]  T. Shakespeare,et al.  Observational Studies , 2003 .

[27]  Sander Greenland,et al.  On the Logical Justification of Conditional Tests for Two-By-Two Contingency Tables , 1991 .

[28]  D. Rubin.  [On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9.] Comment: Neyman (1923) and Causal Inference in Experiments and Observational Studies , 1990 .

[29]  T. Speed,et al.  On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9 , 1990 .

[30]  J M Robins,et al.  Confidence intervals for causal parameters. , 1988, Statistics in medicine.

[31]  D. Rubin.  Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician , 1984 .

[32]  F. Yates,et al.  Tests of Significance for 2 × 2 Contingency Tables , 1984 .

[33]  D. Rubin.  Randomization Analysis of Experimental Data: The Fisher Randomization Test Comment , 1980 .

[34]  D. Basu.  Randomization Analysis of Experimental Data: The Fisher Randomization Test , 1980 .

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

[36]  J. Copas.  Randomization models for the matched and unmatched 2 × 2 tables , 1973 .

[37]  J. L. Hodges,et al.  Estimates of Location Based on Rank Tests , 1963 .

[38]  J. I.  The Design of Experiments , 1936, Nature.

[39]  R Fisher,et al.  Design of Experiments , 1936 .