Neymans causal model with stochastic potential outcomes: implications for the completely randomized design

 
 
 
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  • Abstract


    In Neymans causal model (NCM), each subject participating in a two-arm randomized trial has a pair of potential outcomes one outcome would be observed under treatment and another under control. In the stochastic version of NCM the two potential outcomes are viewed as possibly non-degenerate random variables with finite expectations and variances. The subject-level treatment effect is the expected outcome under treatment minus that under control, and the average treatment effect is the arithmetic mean of the subject-level effects. In the present paper properties of the ordinary difference of means estimator and its associated variance estimator are examined in the completely randomized design with stochastic potential outcomes. Estimation theory is developed under randomization distribution without commitment to any particular probability model for enrollment, because in real trials subjects are not enrolled by a sampling mechanism with known selection probabilities. It is shown that in this theoretical framework, the difference of means estimator is asymptotically normal and consistent for the average treatment effect in the study cohort, while its associated variance estimator is conservative, producing confidence intervals with at least nominal asymptotic coverage. The proofs are not trivial because in the randomization framework sample means under treatment and control are correlated random variables.

    Keywords: Causality; Clinical Trials; Internal Validity; Neymans Causal Model; Randomization-Based Inference; Stochastic Potential Outcomes.


  • References


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Article ID: 2895
 
DOI: 10.14419/ijasp.v2i2.2895




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