Accounting for extent of non-compliance when estimating treatment effects on an ordinal outcome in randomized...

In randomized clinical trials (RCTs) with non-compliance, evaluating the causal effects of interventions would lead to a more precise estimation of treatment effect when the estimand of interest is the effect of treatment amongst compliers. While there is a large body of literature addressing the issue of non-compliance for continuous, binary, and time-to-event outcomes, this issue is seldom discussed for ordinal outcomes.

In this paper, we consider one-sided non-compliance. We introduce an extension of the inverse probability weighting (IPW) method for handling non-compliance involving an ordinal outcome by fully utilizing the information of non-compliance and defining it as a categorical variable to describe the extent of non-compliance. This is in contrast to the usual convention where compliance is regarded as a binary variable. We provide the identification and asymptotic distribution of the proposed method. We compare the proposed method (IPW_Dnew) with intention-to-treat (ITT), per protocol (PP), instrumental variable (IV), and IPW method via a simulation study and real-life data from the JOBS II intervention trial and the IMMACULATE trial.

Simulation results demonstrate that the proposed method performs better than other methods in terms of bias, coverage, mean squared error, power and Type I error under various scenarios, particularly in situations with selection bias and partial compliance. In the empirical study, a substantial estimate of partial compliance by IPW_Dnew implies that there may be a partial compliance effect.

For ordinal outcome in the presence of non-compliance, we suggest using the proposed method to estimate the causal effect of treatment amongst compliers and partial compliers, especially when there exists selection bias.