Inferring Causal Effect of a Digital Communication Strategy under a Latent Sequential Ignorability Assumption and Treatment Noncompliance

Organizations are increasingly relying on digital communications, such as targeted e-mails and mobile notifications, to engage with their audiences. Despite the evident advantages like cost-effectiveness and customization, assessing the effectiveness of such communications from observational data poses various statistical challenges. An immediate challenge is to adjust for targeting rules used in these communications. When digital communications involve a sequence of e-mails or notifications, however, further adjustments are required to correct for selection bias arising from previous communications influencing the subsequent ones and to deal with noncompliance issues, for example, not opening the e-mail. This article addresses these challenges in a study of promotional e-mail sequences sent by a U.S. retailer. We use a Bayesian methodology for causal inference from longitudinal data, considering targeting, noncompliance, and sequential confounding with unmeasured variables. The methodology serves three objectives: to evaluate the average treatment effect of any deterministic e-mailing strategy, to compare the effectiveness of these strategies across varying compliance behaviors, and to infer optimal strategies for distinct customer segments. Our analysis finds, among other things, that certain promotional e-mails effectively maintain engagement among individuals who have regularly received such incentives, and individuals who consistently open their e-mails exhibit reduced sensitivity to promotional content. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.