Vital Sign Quality Assessment using Ordinal Regression of Time Series Data

1. Vital Sign Quality Assessment using Ordinal Regression of Time Series Data Risa B. Myers Comp 600 September 30, 2013 Christopher M. Jermaine PhD Rice University Department of Computer Science John C. Frenzel MD University of Texas MD Anderson Cancer Center

2. Patient Monitoring http://ak4.picdn.net/shutterstock/videos/1240198/preview/stock-footage-looping-animation-of-a-medical-hospital-monitor-of-normal-vital-signs-hd.jpg

3. What Vitals Signs Are • Physiological Measures • Temperature • Blood Pressure • Heart Rate • Respiration Rate

4. Vital signs vs. EKG Systolic BP ✔ Heart Rate Diastolic BP Minutes ✗ Seconds

5. Volatility • New term, wrt vital signs • Changes • Not just variance

6. Anesthesia Vital Signs

7. Motivation • Computer Science • Learn to interpret pattern-less signals • Biomedical • Assess quality of care • Clinical Decision Support • Interpret patient data • Discover underlying causes • Predict outcomes and events #7

8. Goals • Interpret vital sign data in a patient chart • Assign a volatility label • Mimic an expert’s assessment • Predict outcome

9. Contributions • Novel approach to ordinal regression for time series data lacking characteristic patterns • Ability to identify outlier time series • Model that can mimic expert assessment

10. Terms Vital Sign Quality Assessment using Ordinal Regression of Time Series Data

11. Time Series • Ordered series of data • Some relationship exists Average monthly high temperatures in Houston 63, 66, 72, 79, 85, 90, 92, 93, 88, 81, 72, 65 www.weather.com

12. Ordinal Regression

13. Ordinal Temperature Labels

14. Ordinal Regression

15. Classification vs. Ordinal Regression Classes have order

16. Labeled Vital Signs

17. State of the Art • Bayesian modeling of time series • Sykacek & Roberts – Hierarchical Bayesian model to perform feature extraction and classify time segments using a latent feature space • Small # of real examples • Time Series • kNN – DTW • Complexity-invariant classification • Shapelets • …

18. kNN-DTW C. Cassisi, P. Montalto, M. Aliotta, A. Cannata, and A. Pulvirenti, “Similarity Measures and Dimensionality Reduction Techniques for Time Series Data Mining,” no. 3, InTech, 2012.

19. 1NN-DTW

20. Complexity Invariance G. Batista, X. Wang, and E. J. Keogh, “A complexity-invariant distance measure for time series,” SIAM Conf Data Mining, 2011.

21. Shapelets L. Ye and E. Keogh, “Time series shapelets,” presented at the the 15th ACM SIGKDD international conference, New York, New York, USA, 2009, p. 947.

22. Biomedical Labeling • Vital sign analysis • Yang et al. – Classification of anesthesia time series segments • Patterns, durations, frequencies and sequences of patterns defined by an anesthesiologist • (Ordinal) regression • Meyfroidt et al. – Length of stay prediction after cardiac surgery • Vital signs derived values + additional patient and case data • Off-the-shelf classifiers • Regression problem, but use RMSE for evaluation • Best result: better than nurses, better than standard risk model, comparable to physicians’ predictions

23. The AR-OR Model • Autoregressive – Ordinal Regression Model • Generates ordinal labels using statistical properties of time series • Assumes patients with the same volatility label have similar state profiles

24. AR-OR Model Components • Autoregression– Time series representation • Segmenting – State assignment • Ordinal Regression – Integer valued output

25. 1. Autoregression Linear combination of previous values + noise

26. Autoregression in AR-OR • Order = 1 • Coefficients = 1 Average monthly high temperatures 63, 66, 72, 79, 85, 90, 92, 93, 88, 81, 72, 65 Change in average monthly high temperatures 3, 6, 7, 6, 5, 2, 1, -5, -7, -9, -7

27. 2. States via HMM • Hidden Markov Model • States (hidden) • Emissions (visible) • Transition Matrix

28. 2. State Assignment Inference

29. 2. Segmenting State 1: State 2: State 3: State 4: State5: 41% 25% 7% 19% 8%

30. 3. Regression

31. Generative Process

32. Bayesian Approach • Probability Density Function of the form • X - training data set • Observed values • Y - hidden variables • States, hidden label, … • Θ - model parameters • State means, co-variances, transition matrix, …

33. Data • MD Anderson Cancer Center • Surgical vital sign • Systolic Blood Pressure • 3 anesthetists • 200 time series • Labels:1 (stable) to 5 (highly volatile)

35. Implementation • Markov chain Monte Carlo • Iterative process • Sampling from probability distributions • Gibbs Sampling • Conjugate priors • Rejection Sampling • Two phases • Learning model parameters • Labeling unknown series

36. Final Label • Assign label based on the mode of last n iterations

37. Comparison • Upper Bound – 2 experts predicting 1 • AR-OR Model* • 1NN-DTW • 1NN-Complexity-Invariant Distance • Linear Regression on variance • Guess the most common label *My model

38. Results

39. Current Work • Other time series without patterns • ICU • Expanded model • Demographics • Time series features • Multiple time series • Direct comparisons • Demographic data only • Demographics + 1st and 2nd order features • Demographics + times series features + time series • More objective labels • Length of stay • Expiration

40. Next Steps • Focus on feature selection • Solving a clinical problem • Expand model • History • Medications • Lab results

41. References and Acknowledgements • P. Sykacek and S. Roberts, “Bayesian time series classification,” presented at the Advances in Neural Information Processing 14, Boston, MA, 2002, pp. 937–944. • P. Yang, G. Dumont, and J. M. Ansermino, “Online pattern recognition based on a generalized hidden Markov model for intraoperative vital sign monitoring,” Int. J. Adapt. Control Signal Process., vol. 24, 2010. • G. Meyfroidt, F. Güiza, D. Cottem, W. De Becker, K. Van Loon, J.-M. Aerts, D. Berckmans, J. Ramon, M. Bruynooghe, and G. Van Den Berghe, “Computerized prediction of intensive care unit discharge after cardiac surgery: development and validation of a Gaussian processes model.,” BMC Med Inform DecisMak, vol. 11, p. 64, 2011. Supported in part by by the NSF under grant number 0964526 and by a training fellowship from the Keck Center of the Gulf Coast Consortia, on Rice University’s NLM Training Program in Biomedical Informatics (NLM Grant No. T15LM007093).

42. Take-aways • Time series data are difficult to analyze • Using time series data produces better results than approaches like Linear Regression • Machine learning approaches can approximate expert assessments • Opportunity & need for clinical decision support

43. Provider Labels

44. Apply Bayes’ Theorem • To learn the model parameters • To learn the label for the test time series

45. Autoregression in the AR-OR Model • Time series values used to determine the state means and variances • Each state has a set of AR coefficients • Simplified • AR(1) • Coefficients = 1 • Values are the differences between points

46. MSE- All Test Cases

47. TPR– All Test Cases

48. MSE – Outliers

49. TPR– Outliers

50. State Fraction Equation • Time spent in state S States for time series i State S Indicator function Length of time series i