Diagnostics for Confounding of Time-varying and Other Joint Exposures

The effects of joint exposures (or exposure regimes) include those of adhering to assigned treatment versus placebo in a randomized controlled trial, duration of exposure in a cohort study, interactions between exposures, and direct effects of exposure, among others. Unlike the setting of a single point exposure (e.g., propensity score matching), there are few tools to describe confounding for joint exposures or how well a method resolves it. Investigators need tools that describe confounding in ways that are conceptually grounded and intuitive for those who read, review, and use applied research to guide policy. We revisit the implications of exchangeability conditions that hold in sequentially randomized trials, and the bias structure that motivates the use of g-methods, such as marginal structural models. From these, we develop covariate balance diagnostics for joint exposures that can (1) describe time-varying confounding, (2) assess whether covariates are predicted by prior exposures given their past, the indication for g-methods, and (3) describe residual confounding after inverse probability weighting. For each diagnostic, we present time-specific metrics that encompass a wide class of joint exposures, including regimes of multivariate time-varying exposures in censored data, with multivariate point exposures as a special case. We outline how to estimate these directly or with regression and how to average them over person-time. Using a simulated example, we show how these metrics can be presented graphically. This conceptually grounded framework can potentially aid the transparent design, analysis, and reporting of studies that examine joint exposures. We provide easy-to-use tools to implement it.