A multilevel structural equation model for assessing a drug effect on a patient-reported outcome measure in on-demand medication data

We analyze data from a clinical trial investigating the effect of an on-demand drug for women with low sexual desire. These data consist of a varying number of measurements/events across patients of when the drug was taken, including data on a patient-reported outcome consisting of five items measuring an unobserved construct (latent variable). Traditionally, these data are aggregated prior to analysis by composing one sum score per event and averaging this sum score over all observed events. In this paper, we explain the drawbacks of this aggregating approach. One drawback is that these averages have different standard errors because the variance of the underlying events differs between patients and because the number of events per patient differs. Another drawback is the implicit assumption that all items have equal weight in relation to the latent variable being measured. We propose a multilevel structural equation model, treating the events (level 1) as nested observations within patients (level 2), as alternative analysis method to overcome these drawbacks. The model we apply includes a factor model measuring a latent variable at the level of the event and at the level of the patient. Then, in the same model, the latent variables are regressed on covariates to assess the drug effect. We discuss the inferences obtained about the efficacy of the on-demand drug using our proposed model. We further illustrate how to test for measurement invariance across grouping covariates and levels using the same model.