Identification of causal effects in the presence of nonignorable missing outcome values

We consider a new approach to identify the causal effects of a binary treatment when the outcome is missing on a subset of units and dependence of nonresponse on the outcome cannot be ruled out even after conditioning on observed covariates. We provide sufficient conditions under which the availability of a binary instrument for nonresponse allows us to derive tighter identification intervals for causal effects in the whole population and to partially identify causal effects in some latent subgroups of units, named Principal Strata, defined by the nonresponse behavior in all possible combinations of treatment and instrument. A simulation study is used to assess the benefits of the presence versus the absence of an instrument for nonresponse. The simulation design is based on real health data, coming from a randomized trial on breast self-examination (BSE) affected by a large proportion of missing outcome data. An instrument for nonresponse is simulated considering alternative scenarios to discuss the key role of the instrument for nonresponse in identifying average causal effects in presence of nonignorable missing outcomes. We also investigate the potential inferential gains from using an instrument for nonresponse adopting a Bayesian approach for inference. In virtue of our theoretical and empirical results, we provide some recommendations on study designs for causal inference.