Sharp nonparametric bounds and randomization inference for treatment effects on an ordinal outcome

Area of Science:

• Biostatistics
• Clinical Trial Methodology
• Causal Inference

Background:

• Investigating average causal effects is crucial in clinical research.
• Existing causal parameters for ordinal outcomes lack clear definitions and do not align with binary outcome measures.
• The need for a well-defined causal parameter for ordinal outcomes is evident.

Purpose of the Study:

• To propose a novel causal parameter for ordinal outcomes.
• To define this parameter as the proportion where a potential outcome under one treatment is not smaller than under another.
• To develop methods for identifying and analyzing this parameter, especially in the presence of confounding.

Main Methods:

• Proposed a new causal parameter for ordinal outcomes.
• Developed a numerical method to calculate sharp nonparametric bounds to address confounding.
• Presented exact tests and confidence intervals for relative treatment effects using a randomization-based approach.

Main Results:

• The proposed causal parameter for ordinal outcomes is defined and its relationship to binary outcomes is established.
• Numerical methods provide bounds for the causal parameter, accounting for confounding.
• Randomization combined with the independent potential outcomes assumption allows for parameter identification.
• Exact tests and confidence intervals extend existing binary outcome methods.

Conclusions:

• The study successfully defines a new causal parameter for ordinal outcomes.
• Methodologies are presented to handle confounding and enable identification under specific assumptions.
• The developed statistical tests and confidence intervals offer valuable tools for analyzing ordinal outcomes in clinical trials.