A latent variable transformation model approach for exploring dysphagia

Multiple outcomes are often collected in applications where the quantity of interest cannot be measured directly or is difficult or expensive to measure. In a head and neck cancer study conducted at Dana-Farber Cancer Institute, the investigators wanted to determine the effect of clinical and treatment factors on unobservable dysphagia through collected multiple outcomes of mixed types. Latent variable models are commonly adopted in this setting. These models stipulate that multiple collected outcomes are conditionally independent given the latent factor. Mixed types of outcomes (e.g., continuous vs. ordinal) and censored outcomes present statistical challenges, however, as a natural analog of the multivariate normal distribution does not exist for mixed data. Recently, Lin et al. proposed a semiparametric latent variable transformation model for mixed outcome data; however, it may not readily accommodate event time outcomes where censoring is present. In this paper, we extend the work of Lin et al. by proposing both semiparametric and parametric latent variable models that allow for the estimation of the latent factor in the presence of measurable outcomes of mixed types, including censored outcomes. Both approaches allow for a direct estimate of the treatment (or other covariate) effect on the unobserved latent variable, greatly enhancing the interpretability of the models. The semiparametric approach has the added advantage of allowing the relationship between the measurable outcomes and latent variables to be unspecified, rendering more robust inference. The parametric and semiparametric models can also be used together, providing a comprehensive modeling strategy for complicated latent variable problems.