Identification of complier and noncomplier average causal effects in the presence of latent missing-at-random (LMAR) outcomes: a unifying view and choices of assumptions.

The study of treatment effects is often complicated by noncompliance and missing data. In the one-sided noncompliance setting where of interest are the complier and noncomplier average causal effects, we address outcome missingness of the latent missing at random type (LMAR, also known as latent ignorability). That is, conditional on covariates and treatment assigned, the missingness may depend on compliance type. Within the instrumental variable (IV) approach to noncompliance, methods have been proposed for handling LMAR outcome that additionally invoke an exclusion restriction-type assumption on missingness, but no solution has been proposed for when a non-IV approach is used. This article focuses on effect identification in the presence of LMAR outcomes, with a view to flexibly accommodate different principal identification approaches. We show that under treatment assignment ignorability and LMAR only, effect nonidentifiability boils down to a set of two connected mixture equations involving unidentified stratum-specific response probabilities and outcome means. This clarifies that (except for a special case) effect identification generally requires two additional assumptions: a specific missingness mechanism assumption and a principal identification assumption. This provides a template for identifying effects based on separate choices of these assumptions. We consider a range of specific missingness assumptions, including those that have appeared in the literature and some new ones. Incidentally, we find an issue in the existing assumptions, and propose a modification of the assumptions to avoid the issue. Results under different assumptions are illustrated using data from the Baltimore Experience Corps Trial.

Sensitivity analysis for principal ignorability violation in estimating complier and noncomplier average causal effects.

An important strategy for identifying principal causal effects (popular estimands in settings with noncompliance) is to invoke the principal ignorability (PI) assumption. As PI is untestable, it is important to gauge how sensitive effect estimates are to its violation. We focus on this task for the common one-sided noncompliance setting where there are two principal strata, compliers and noncompliers. Under PI, compliers and noncompliers share the same outcome-mean-given-covariates function under the control condition. For sensitivity analysis, we allow this function to differ between compliers and noncompliers in several ways, indexed by an odds ratio, a generalized odds ratio, a mean ratio, or a standardized mean difference sensitivity parameter. We tailor sensitivity analysis techniques (with any sensitivity parameter choice) to several types of PI-based main analysis methods, including outcome regression, influence function (IF) based and weighting methods. We discuss range selection for the sensitivity parameter. We illustrate the sensitivity analyses with several outcome types from the JOBS II study. This application estimates nuisance functions parametrically - for simplicity and accessibility. In addition, we establish rate conditions on nonparametric nuisance estimation for IF-based estimators to be asymptotically normal - with a view to inform nonparametric inference.

Principal quantile treatment effect estimation using principal scores.

Intercurrent events and estimands play a key role in defining the treatment effects of interest precisely. Sometimes the median or other quantiles of outcomes in a principal stratum according to potential occurrence of intercurrent events are of interest in randomized clinical trials. Naïve analyses such as those based on the observed occurrence of the intercurrent events lead to biased results. Therefore, we propose principal quantile treatment effect estimators that can nonparametrically estimate the distribution of potential outcomes by principal score weighting without relying on the exclusion restriction assumption. Our simulation studies show that the proposed method works in situations where the median or quantiles may be regarded as the preferred population-level summary over the mean. We illustrate our proposed method by using data from a randomized controlled trial conducted on patients with nonerosive reflux disease.

Performance of principal scores to estimate the marginal compliers causal effect of an intervention.

We examine the properties of principal scores methods to estimate the causal marginal odds ratio of an intervention for compliers in the context of a randomized controlled trial with non-compliers. The two-stage estimation approach has been proposed for a linear model by Jo and Stuart (Statistics in Medicine 2009; 28:2857-2875) under a principal ignorability (PI) assumption. Using a Monte Carlo simulation study, we compared the performance of several strategies to build and use principal score models and the robustness of the method to violations of underlying assumptions, in particular PI. Results showed that the principal score approach yielded unbiased estimates of the causal marginal log odds ratio under PI but that the method was sensitive to violations of PI, which occurs in particular when confounders are omitted from the analysis. For principal score analysis, probability weighting performed slightly better than full matching or 1:1 matching. Concerning the variables to be included in principal score models, the lowest mean squared error was generally obtained when using the true confounders. Using variables associated with the outcome only but not compliance however yielded very similar performance.