A substantial proportion of participants who are offered internet-based psychological treatments in randomized trials do not adhere and may therefore not receive treatment. Despite the availability of justified statistical methods for causal inference in such situations, researchers often rely on analytical strategies that either ignore adherence altogether or fail to provide causal estimands. The objective of this paper is to provide a gentle nontechnical introduction to complier average causal effect (CACE) analysis, which, under clear assumptions, can provide a causal estimate of the effect of treatment for a subsample of compliers. The article begins with a brief review of the potential outcome model for causal inference. After clarifying assumptions and model specifications for CACE in the latent variable framework, data from a previously published trial of an internet-based psychological treatment for irritable bowel syndrome are used to demonstrate CACE-analysis. Several model extensions are then briefly reviewed. The paper offers practical recommendations on how to analyze randomized trials of internet interventions in the context of nonadherence. It is argued that CACE-analysis, whenever it is considered appropriate, should be carried out as a complement to the standard intention-to-treat analysis and that the format of internet-based treatments is particularly well suited to such an analytical approach.
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