Likelihood inference for a semi-parametric causal model addressing partial compliance by continuous principal strata

We propose a semi-parametric model for causal inference in the presence of continuous principal strata. The context of application is that of clinical trials with partial compliance in both placebo and drug arms. In order to reduce the modelling assumptions, we link the observed marginal distributions of drug and placebo compliances by a Plackett copula, so that their association is modelled by a single parameter, whereas no restrictions are posed on the marginal distributions. A likelihood inference approach for this model is proposed. In particular, the association parameter between the two compliances is studied via profile likelihood. We apply the model to data previously analysed by Efron and Feldman (1991) and Jin and Rubin (2008), comparing assumptions and results.