Primary Submission Category: Design of Experiments
Causal Inference for Ordinal Outcomes with Temporal Structure in Randomized Experiments
Authors: Rituparna Dey, Tirthankar Dasgupta, Rituparna Dey,
Presenting Author: *
Randomized experiments involving sequentially collected ordinal outcomes over time, have been largely unexplored in causal inference. While most causal inference studies focus on continuous outcomes, standard causal parameters like the average treatment effect (ATE) lose their meaning when applied to ordinal data. This study introduces novel nonparametric causal estimands for randomized experiments, addressing both the ordinal nature and temporal structure of the data. A motivating industrial experiment illustrates these challenges, where treatment effects evolve over multiple time points. Our approach extends the potential outcomes framework and the distributional causal estimands and their sharp bounds within the temporal context. Furthermore, we propose time-adjusted estimands utilizing past outcomes for sharper inference. Estimation is performed using a matching-based imputation approach, ensuring that the missing potential outcomes are imputed while preserving the ordinal structure. A simulation study, employing a latent variable model, demonstrates the advantages of our approach, showing improved estimation accuracy over traditional methods. This work has broad applicability in fields such as clinical trials, user experience research, and social sciences.