Use of State Sequence Analysis in Pharmacoepidemiology: A Tutorial

While state sequence analysis (SSA) has been long used in social sciences, its use in pharmacoepidemiology is still in its infancy. Indeed, this technique is relatively easy to use, and its intrinsic visual nature may help investigators to untangle the latent information within prescription data, facilitating the individuation of specific patterns and possible inappropriate use of medications. In this paper, we provide an educational primer of the most important learning concepts and methods of SSA, including measurement of dissimilarities between sequences, the application of clustering methods to identify sequence patterns, the use of complexity measures for sequence patterns, the graphical visualization of sequences, and the use of SSA in predictive models. As a worked example, we present an application of SSA to opioid prescription patterns in patients with non-cancer pain, using real-world data from Italy. We show how SSA allows the identification of patterns in prescriptions in these data that might not be evident using standard statistical approaches and how these patterns are associated with future discontinuation of opioid therapy.

Maximum-a-posteriori estimation of LTI state-space models via efficient Monte-Carlo sampling

This paper addresses Maximum-A-Posteriori (MAP) estimation of Linear Time-Invariant State-Space (LTI-SS) models. The joint posterior distribution of the model matrices and the unknown state sequence is approximated by using Rao-Blackwellized Monte-Carlo sampling algorithms. Specifically, the conditional distribution of the state sequence given the model parameters is derived analytically, while only the marginal posterior distribution of the model matrices is approximated using a Metropolis-Hastings Markov-Chain Monte-Carlo sampler. From the joint distribution, MAP estimates of the unknown model matrices as well as the state sequence are computed. The performance of the proposed algorithm is demonstrated on a numerical example and on a real laboratory benchmark dataset of a hair dryer process.

A Hybrid Hidden Markov Model for Pipeline Leakage Detection

In this paper, a deep neural network hidden Markov model (DNN-HMM) is proposed to detect pipeline leakage location. A long pipeline is divided into several sections and the leakage occurs in different section that is defined as different state of hidden Markov model (HMM). The hybrid HMM, i.e., DNN-HMM, consists of a deep neural network (DNN) with multiple layers to exploit the non-linear data. The DNN is initialized by using a deep belief network (DBN). The DBN is a pre-trained model built by stacking top-down restricted Boltzmann machines (RBM) that compute the emission probabilities for the HMM instead of Gaussian mixture model (GMM). Two comparative studies based on different numbers of states using Gaussian mixture model-hidden Markov model (GMM-HMM) and DNN-HMM are performed. The accuracy of the testing performance between detected state sequence and actual state sequence is measured by micro F1 score. The micro F1 score approaches 0.94 for GMM-HMM method and it is close to 0.95 for DNN-HMM method when the pipeline is divided into three sections. In the experiment that divides the pipeline as five sections, the micro F1 score for GMM-HMM is 0.69, while it approaches 0.96 with DNN-HMM method. The results demonstrate that the DNN-HMM can learn a better model of non-linear data and achieve better performance compared to GMM-HMM method.

Multiobjective Lightning Flash Algorithm Design and Its Convergence Analysis via Martingale Theory

In this paper, a novel multiobjective lightning flash algorithm (MOLFA) is proposed to solve the multiobjective optimization problem. The charge population state of the lightning flash algorithm is defined, and we prove that the charge population state sequence is a Markov chain. Since the convergence analysis of MOLFA is to investigate whether a Pareto optimal solution can be reached when the optimal charge population state is obtained, the development of a charge population state is analyzed to achieve the goal of this paper. Based on the martingale theory, the MOLFA convergence analysis is carried out in terms of the supermartingale convergence theorem, which shows that the MOLFA can reach the global optimum with probability one. Finally, the effectiveness of the proposed MOLFA is verified by a numerical simulation example.