All Times ET
Keywords: distributed lag models, variational Bayesian inference, variational AIC, longitudinal data analysis, penalized splines
Distributed lag models or DLMs are commonly used methods for analyzing lagged effects of exposure on various outcomes. While much work exists on this class of models, data with more complex lag structures require additional methodological developments. Specifically, DLMs that handle lagged effects measured longitudinally, that is repeatedly over time, are largely limited to the random intercept case. However, longitudinally sampled lags may exhibit other forms of variability such that a random lag structure may be appropriate. Thus we propose a class of longitudinal DLMs for both Gaussian and Poisson outcome data where the lag structure can arise from longitudinally sampled lags, including crossover trials. Our models use penalized splines to estimate lagged effects and to model random lags. For computational efficiency in the model selection process, we perform estimation using variational Bayesian inference. We also derive variational AICs for our longitudinal DLMs and determine decision rules for model selection. We show in simulation that the variational AIC performs well in identifying the correctly specified model and that our models have good properties in terms of bias and mean integrated squared error. Finally, we demonstrate our models on a crossover trial that examines the lagged effect of depressed blood oxygen saturation during simulated flight conditions on post-flight heart rate and post-flight occurrence of supraventricular couplets.