Vital Sign Quality Assessment using Ordinal Regression of

Time Series Data

Risa B. MyersComp 600

September 30, 2013

Christopher M. Jermaine PhDRice University

Department of Computer Science

John C. Frenzel MDUniversity of Texas

MD Anderson Cancer Center

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

• Physiological Measures– Temperature– Blood Pressure– Heart Rate– Respiration Rate

What Vitals Signs Are

Vital signs vs. EKG

Seconds

Systolic BP

Minutes

✔

✗

Heart RateDiastolic BP

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

63, 66, 72, 79, 85, 90, 92, 93, 88, 81, 72, 65 Average monthly high temperatures in Houston

www.weather.com

Ordinal Regression

Ordinal Temperature Labels

Tempera-ture

0

20

40

60

80

100

120

Really HotHotNiceCool°

Fahr

enhe

it

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

63, 66, 72, 79, 85, 90, 92, 93, 88, 81, 72, 65

3, 6, 7, 6, 5, 2, 1, -5, -7, -9, -7

Average monthly high temperatures

Change in average monthly high temperatures

2. States via HMM

• Hidden Markov Model– States (hidden)– Emissions (visible)– Transition Matrix

2. State Assignment

Inference

2. Segmenting

41%25% 7%19%8%

State 1: State 2:State 3: State 4:State 5:

3. Regression

Generative ProcessK 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. Upper Bound – 2 experts predicting 12. AR-OR Model*3. 1NN-DTW 4. 1NN-Complexity-Invariant Distance5. Linear Regression on variance6. Guess the most common label

*My model

Results

Upper

Bound

AR-OR*

1NN-D

TW

1NN-C

ID

Linea

r Reg

ressio

n

Guess

30

1

2

3

AllOutliers

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

Pro-vider

Gold Stnd

AR-OR

1NN-DTW

1NN-CID

LR Guess 3

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

Pro-vider

Gold Stnd

AR-OR

1NN-DTW

1NN-CID

LR Guess 3

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

Pro-vider

Gold Stnd

AR-OR

1NN-DTW

1NN-CID

LR Guess 3

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

Pro-vider

Gold Stnd

AR-OR

1NN-DTW

1NN-CID

LR Guess 3

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

Indicator function

Length of time series i

State S

Ordinal Regression in the AR-OR Model

Real valued outcome

Number of states

State fraction function

Ordinal regression noise

Regression coefficient for state k

Autoregression

Observed data

Order of the regression

Regression coefficient

Constant

Noise

State Assignments

Bootstrapping

• Randomly sample test set with replacement– 30% of records

• Remaining records are training set• Repeat

• Alternative to k-fold cross-validation