Intention to treat

A key complication in drawing inference about causal effects in any trial is that compliance is rarely perfect. A standard approach is to estimate the intention-to-treat (ITT) effect. The ITT effect describes the benefit of being randomized to treatment. ITT can be used, for example, to determine the impact that
recommending (or encouraging; Hirano and others, 2000) a particular treatment over an alternative treatment would have, on average, in the population. However, one treatment might appear superior because it is better tolerated. For example, one could imagine a treatment that fewer people would comply with but that has superior results among those that do comply. If this information was known, the recommended
treatment could potentially be tailored to individual subjects. Thus, in addition to knowing the ITT effect, it would be useful to know which treatment would result in better outcomes among subjects who would comply with and receive either intervention and which characteristics are predictive of compliance.
In trials of an active treatment versus placebo (or no treatment), it is possible to recover causal effects under some reasonably mild assumptions. For all-or-none compliance situations, the method of instrumental variables can be particularly useful (Angrist and others, 1996). Causal effects among compliers (subjects who would take treatment if offered) are identifiable under the assumption that there are no
subjects who would take the active treatment if randomized to the control arm but not to the treatment arm (no defiers). This assumption is reasonable in trials where the control group does not have access to the active treatment. In such settings, the instrumental variables estimator is equivalent to the estimator from certain structural mean models (Robins, 1994; Goetghebeur and Lapp, 1997; Robins and Rotznitzky,(2004). Structural mean models can also be used when compliance is continuous and if there are interactions between the causal effect and the baseline covariates. However, if it is unreasonable to assume there are no defiers, the causal parameters are generally not identifiable without structural assumptions; several
authors have derived bounds on the causal effects (Robins, 1989; Manski, 1990; Balke and Pearl, 1997; Joffe, 2001). For comparisons of 2 active treatments, the principal stratification framework (Frangakis and Rubin, 2002) can be used to define and infer causal parameters of interest, such as the effect of the exercise intervention
compared with standard therapy among subjects who would comply with either intervention.
Direct implementation of the principal stratification approach has several limitations. First, causal effects of interest would not be point identified (Cheng and Small, 2006). Further, it would not provide information about characteristics of subjects in each subpopulation (stratum). To address these issues, we identify
causal parameters of interest, up to a sensitivity parameter, through the use of baseline covariates that are predictive of compliance. Including covariates in the model is not straightforward as care has to be taken to ensure the marginal compliance distributions are compatible with the joint distribution. In addition, our
model clearly separates parameters that can be identified from the data from those that cannot. Finally, we illustrate how a constraint on the joint distribution of the potential compliance variables can be integrated into the methodology. This approach provides investigators with additional useful information, beyond just the ITT effect.
Principal stratification with predictors of compliance for randomized trials with 2 active treatments, Biostatistics (2008), 9, 2, pp. 277–289, Oxford Univ Press Journals