Estimating the Marginal Effect of a Continuous Exposure on an Ordinal Outcome using Data Subject to Covariate-Driven Treatment and Visit Processes

In the statistical literature, a number of methods have been proposed to ensure valid inference about marginal effects of variables on a longitudinal outcome in settings with irregular monitoring times. However, the potential biases due to covariate-driven monitoring times and confounding have rarely been considered simultaneously, and never in a setting with an ordinal outcome and a continuous exposure. In this work, we propose and demonstrate a methodology for causal inference in such a setting, relying on a proportional odds model to study the effect of the exposure on the outcome. Irregular observation times are considered via a proportional rate model, and a generalization of inverse probability of treatment weights is used to account for the continuous exposure. We motivate our methodology by the estimation of the marginal (causal) effect of the time spent on video or computer games on suicide attempts in the Add Health study, a longitudinal study in the United States. Although in the Add Health data, observation times are pre-specified, our proposed approach is applicable even in more general settings such as when analyzing data from electronic health records where observations are highly irregular. In simulation studies, we let observation times vary across individuals and demonstrate that not accounting for biasing imbalances due to the monitoring and the exposure schemes can bias the estimate for the marginal odds ratio of exposure.