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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 Patient Monitoring http://ak4.picdn.net/shutterstock/videos/1240198/preview/stock-footage-looping-animation-of-a-medicalhospital-monitor-of-normal-vital-signs-hd.jpg What Vitals Signs Are • Physiological Measures – Temperature – Blood Pressure – Heart Rate – Respiration Rate Vital signs vs. EKG Systolic BP ✔ Heart Rate Diastolic BP Minutes ✗ Seconds Volatility • New term, wrt vital signs • Changes • Not just variance Anesthesia Vital Signs 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 Goals • Interpret vital sign data in a patient chart • Assign a volatility label • Mimic an expert’s assessment • Predict outcome 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 Terms Vital Sign Quality Assessment using Ordinal Regression of Time Series Data 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 Ordinal Regression Ordinal Temperature Labels 120 ° Fahrenheit 100 80 Really Hot Hot Nice Cool 60 40 20 0 Temperature Ordinal Regression Classification vs. Ordinal Regression Classes have order Labeled Vital Signs 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 … 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. 1NN-DTW Complexity Invariance G. Batista, X. Wang, and E. J. Keogh, “A complexity-invariant distance measure for time series,” SIAM Conf Data Mining, 2011. 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. 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 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 AR-OR Model Components 1. Autoregression – Time series representation 2. Segmenting – State assignment 3. Ordinal Regression – Integer valued output 1. Autoregression Linear combination of previous values + noise 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 2. States via HMM • Hidden Markov Model – States (hidden) – Emissions (visible) – Transition Matrix 2. State Assignment Inference 2. Segmenting State 1: 41% State 2: 25% State 3: 7% State 4: 19% State 5: 8% 3. Regression Generative Process K Number of states L Number of labels D Number of time series Φ Autoregression coefficients R Autoregressive order p State transition probabilities μ State means Σ State covariance matrices r Regression coefficients p0 Initial state probabilities ω Goalpost σ2ω Goalpost variance σ2r Regression variance Mi Time series length s State f Fraction of time in each state x Observations v’ Real valued label v Ordinal label 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, … Data • MD Anderson Cancer Center • Surgical vital sign – Systolic Blood Pressure • 3 anesthetists • 200 time series • Labels:1 (stable) to 5 (highly volatile) 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 Final Label • Assign label based on the mode of last n iterations Comparison 1. 2. 3. 4. 5. 6. 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 Results 3 2 1 0 All Outliers 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 Next Steps • Focus on feature selection • Solving a clinical problem • Expand model – History • Medications • Lab results 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. 1. 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. 2. 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 Decis Mak, 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). 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 Provider Labels Apply Bayes’ Theorem • To learn the model parameters • To learn the label for the test time series 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 MSE- All Test Cases Provider Gold Stnd AROR 1NNDTW 1NNCID LR Gues s3 1 0.52 0.50 1.38 0.65 0.63 0.61 2 0.81 0.94 1.25 1.39 1.20 1.01 3 0.58 0.58 1.10 0.89 0.80 0.76 TPR– All Test Cases Provider Gold Stnd AROR 1NNDTW 1NNCID LR Gues s3 1 0.57 0.58 0.35 0.50 0.55 0.55 2 0.44 0.35 0.42 0.30 0.35 0.39 3 0.52 0.53 0.39 0.46 0.41 0.41 MSE – Outliers Provider Gold Stnd AROR 1NNDTW 1NNCID LR Gues s3 1 2.71 2.08 4.81 2.51 4.00 4.00 2 2.32 1.99 2.20 1.80 3.49 4.00 3 1.68 1.16 3.54 2.15 3.55 4.00 TPR– Outliers Provider Gold Stnd AROR 1NNDTW 1NNCID LR Gues s3 1 0.01 0.11 0.05 0.05 0.00 0.00 2 0.00 0.06 0.28 0.41 0.00 0.00 3 0.04 0.06 0.01 0.06 0.00 0.00 State Fraction Equation • Time spent in state S States for time series i State S Indicator function Length of time series i Ordinal Regression in the AR-OR Model Real valued outcome Ordinal regression noise Number of states State fraction function Regression coefficient for state k Autoregression Observed data Constant Order of the regression Regression coefficient Noise States and mmHg State Assignments 150 100 50 0 50 100 150 200 Duration of Surgery (Minutes) 250 Bootstrapping • Randomly sample test set with replacement – 30% of records • Remaining records are training set • Repeat • Alternative to k-fold cross-validation