Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds

• Published in: Journal of educational and behavioral statistics 2018-10, Vol.43 (5), p.540-567
• Main Authors: Lu, Jiannan, Ding, Peng, Dasgupta, Tirthankar
• Format: Article
• Language: English
• Subjects: Behavioral psychology; Behavioral Science Research; Causal Models; Control Groups; Educational psychology; Educational Research; Experimental Groups; Mathematical Applications; Outcomes of Treatment; Patient compliance; Probability; Statistical Inference; Statistics
• ISSN: 1076-9986; 1935-1054
• DOI: 10.3102/1076998618776435

Assessing the causal effects of interventions on ordinal outcomes is an important objective of many educational and behavioral studies. Under the potential outcomes framework, we can define causal effects as comparisons between the potential outcomes under treatment and control However, unfortunately, the average causal effect, often the parameter of interest, is difficult to interpret for ordinal outcomes. To address this challenge, we propose to use two causal parameters, which are defined as the probabilities that the treatment is beneficial and strictly beneficial for the experimental units. However, although welldefined for any outcomes and of particular interest for ordinal outcomes, the two aforementioned parameters depend on the association between the potential outcomes and are therefore not identifiable from the observed data without additional assumptions. Echoing recent advances in the econometrics and biostatistics literature, we present the sharp bounds of the aforementioned causal parameters for ordinal outcomes, under fixed marginal distributions of the potential outcomes. Because the causal estimands and their corresponding sharp bounds are based on the outcomes themselves, the proposed framework can be flexibly incorporated into any chosen models of the potential outcomes and is directly applicable to randomized experiments, unconfounded observational studies, and randomized experiments with noncompliance. We illustrate our methodology via numerical examples and three real-life applications related to educational and behavioral research.