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The disease progression dynamics observed in electronic health records often reflect patients’ health condition evolution, holding the promise of enabling the development of clinical predictive models. These dynamics, however, generally display significant variability among patients, due to some critical factors (e.g., gender and age) and patient-level heterogeneity. Moreover, future health state may not only depend on the current state, but also more distant history states due to the complicated disease progression. To capture this complex transition behavior and address mixed effects in clinical prediction problems, we propose a novel and flexible Bayesian Mixed-Effect Higher-Order Hidden Markov Model (MHOHMM), and develop a classifier based on MHOHMMs. A range of MHOHMMs are designed to capture different data structures and the optimal one is identified by using the k-fold cross-validation approach. An effective two-stage Markov chain Monte Carlo (MCMC) sampling algorithm is designed for model inference. A simulation study is conducted to evaluate the performance of the proposed sampling algorithm and the MHOHMM-based classification method. The practical utility of the proposed framework is demonstrated by a case study on the acute hypotensive episode prediction for intensive care unit patients. Our results show that the MHOHMM-based framework provides good prediction performance. 

In many scientific experiments, multiarmed bandits are used as an adaptive data collection method. However, this adaptive process can lead to a dependence that renders many commonly used statistical inference methods invalid. An example of this is the sample mean, which is a natural estimator of the mean parameter but can be biased. This can cause test statistics based on this estimator to have an inflated type I error rate, and the resulting confidence intervals may have significantly lower coverage probabilities than their nominal values. To address this issue, we propose an alternative approach called randomized multiarm bandits (rMAB). This combines a randomization step with a chosen MAB algorithm, and by selecting the randomization probability appropriately, optimal regret can be achieved asymptotically. Numerical evidence shows that the bias of the sample mean based on the rMAB is much smaller than that of other methods. The test statistic and confidence interval produced by this method also perform much better than its competitors.

 

We consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss functions. For one particular loss function, the resulting Bayes estimator relies on the marginal cumulative distribution function of the sample variances only. When replacing it with the empirical distribution function, we obtain an empirical Bayes version called the $F$-modelling-based empirical Bayes estimator of variances. We provide theoretical properties of this estimator, and further demonstrate its advantages through extensive simulations and real data analysis.