## Department of Biostatistics Seminar/Workshop Series

# Joint Models using Latent Variables with Time Series Data

### Chris Slaughter, PhD

Associate Professor
Department of Biostatistics, Vanderbilt University School of Medicine
Structural time series models, also called unobserved components models, can be used to represent the observed series as a sum of suitably chosen components such as trend, seasonal, cyclical, and regression effects.

Such models can be used to formulate comprehensive models that bring out all the salient features of the series under consideration. This presentation will address how structural time series models can be used to flexibly summarize a high dimensional predictor of interest for use in a joint model with a future outcome. We can also identity latent classes of subjects who may be at increased risk of outcomes.
The model will be demonstrated using an example of patient-report symptoms and gastroesophegeal reflux measured over time. Interest lies in using 48 hours of acidity and symptom information to summarize a subject's reflux status, the degree to which symptoms are associated with reflux, and the association of these predictors with disease progression. I will discuss the current approaches for summarizing reflux and symptoms in this field, and describe why they are inadequate.
A structural time series model using latent variables is proposed as an alternative.