Longitudinal patient data has the potential to improve clinical risk stratification models for disease. However, chronic diseases that progress slowly over time are often heterogeneous in their clinical presentation. Patients may progress through disease stages at varying rates. This leads to pathophysiological misalignment over time, making it difficult to consistently compare patients in a clinically meaningful way. Furthermore, patients present clinically for the first time at different stages of disease. This eliminates the possibility of simply aligning patients based on their initial presentation. Finally, patient data may be sampled at different rates due to differences in schedules or missed visits. To address these challenges, we propose a robust measure of patient similarity based on subsequence alignment. Compared to global alignment techniques that do not account for pathophysiological misalignment, focusing on the most relevant subsequences allows for an accurate measure of similarity between patients. We demonstrate the utility of our approach in settings where longitudinal data, while useful, are limited and lack a clear temporal alignment for comparison. Applied to the task of stratifying patients for risk of progression to probable Alzheimer's Disease, our approach outperforms models that use only snapshot data (AUROC of 0.839 vs. 0.812) and models that use global alignment techniques (AUROC of 0.822). Our results support the hypothesis that patients' trajectories are useful for quantifying inter-patient similarities and that using subsequence matching and can help account for heterogeneity and misalignment in longitudinal data.
In the last decade, Dynamic Time Warping (DTW) has emerged as the distance measure of choice for virtually all time series data mining applications. This is the result of significant progress in improving DTW’s efficiency, and multiple empirical studies showing that DTW-based classifiers at least equal the accuracy of all their rivals across dozens of datasets. Thus far, most of the research has considered only the one-dimensional case, with practitioners generalizing to the multi-dimensional case in one of two ways. In general, it appears the community believes either that the two ways are equivalent, or that the choice is irrelevant. In this work, we show that this is not the case. The two most commonly used multidimensional DTW methods can produce different classifications, and neither one dominates over the other. This seems to suggest that one should learn the best method for a particular application. However, we will show that this is not necessary; a simple, principled rule can be used on a case-by-case basis to predict which of the two methods we should give credence to. Our method allows us to ensure that classification results are at least as accurate as the better of the two rival methods, and in many cases, our method is strictly more accurate. We demonstrate our ideas with the most extensive set of multi-dimensional time series classification experiments ever attempted. Keywords—Dynamic Time Warping; Classification With the advances and increasing sophistication in data collection techniques, we are facing with large amounts of data collected from multiple heterogeneous sources in many applications. For example, in the study of Alzheimer's Disease (AD), different types of measurements such as neuroimages, gene protein expression data, genetic data etc. are often collected and analyzed together for improved predictive power. It is believed that a joint learning of multiple data sources is beneficial as different data sources may contain complementary information, and feature-pruning and data source selection are critical for learning interpretable models from high-dimensional data. Very often the collected data comes with block-wise missing entries; for example, a patient without the MRI scan will have no information in the MRI data block, making his her overall record incomplete. There has been a growing interest in the data mining community on expanding traditional techniques for single-source complete data analysis to the study of multi-source incomplete data. The key challenge is how to effectively integrate information from multiple heterogeneous sources in the presence of block-wise missing data. In this paper we first investigate the situation of complete data and present a unified bi-level" learning model for multi-source data. Then we give a natural extension of this model to the more challenging case with incomplete data. Our major contributions are threefold: (1) the proposed models handle both feature-level and source-level analysis in a unified formulation and include several existing feature learning approaches as special cases; (2) the model for incomplete data avoids direct imputation of the missing elements and thus provides superior performances. Moreover, it can be easily generalized to other applications with block-wise missing data sources; (3) efficient optimization algorithms are presented for both the complete and incomplete models. We have performed comprehensive evaluations of the proposed models on the application of AD diagnosis. Our proposed models compare favorably against existing approaches. Missing values are a common problem when applying classification algorithms to real-world medical data. This is especially true for trauma patients, where the emergent nature of the cases makes it difficult to collect all of the relevant data for each patient. Standard methods for handling missingness first learn a model to estimate missing data values, and subsequently train and evaluate a classifier using data imputed with this model. Recently, several proposed methods have demonstrated the benefits of jointly estimating the imputation model and classifier parameters. However, these methods make assumptions that limit their utility with many real-world medical datasets. For example, the assumption that data elements are missing at random is often invalid.We address this situation by exploring a novel approach for jointly learning the imputation model and classifier. Unlike previous algorithms, our approach makes no assumptions about the missingness of the data, can be used with arbitrary probabilistic data models and classification loss functions, and can be used when both the training and testing data have missing values. We investigate the utility of this approach on the prediction of several patient outcomes in a large national registry of trauma patients, and find that it significantly outperforms standard sequential methods.