Leveraging Time Series Data in Similarity Based Healthcare Predictive Models

Leveraging Time Series Data in Similarity
Based Healthcare Predictive Models:
The Case of Early ICU Mortality Prediction
Full Paper

Mohammad Amin Morid
David Eccles School of Business
University of Utah
amin.morid@business.utah.edu

Olivia R. Liu Sheng
David Eccles School of Business
University of Utah
olivia.sheng@business.utah.edu

Samir Abdelrahman
Department of Biomedical Informatics
University of Utah
samir.abdelrahman@utah.edu

Abstract
Patient time series classification faces challenges in high degrees of dimensionality and missingness. In
light of patient similarity theory, this study explores effective temporal feature engineering and reduction,
missing value imputation, and change point detection methods that can afford similarity-based
classification models with desirable accuracy enhancement. We select a piecewise aggregation
approximation method to extract fine-grain temporal features and propose a minimalist method to
impute missing values in temporal features. For dimensionality reduction, we adopt a gradient descent
search method for feature weight assignment. We propose new patient status and directional change
definitions based on medical knowledge or clinical guidelines about the value ranges for different patient
status levels, and develop a method to detect change points indicating positive or negative patient status
changes. We evaluate the effectiveness of the proposed methods in the context of early Intensive Care
Unit mortality prediction. The evaluation results show that the k-Nearest Neighbor algorithm that
incorporates methods we select and propose significantly outperform the relevant benchmarks for early
ICU mortality prediction. This study makes contributions to time series classification and early ICU
mortality prediction via identifying and enhancing temporal feature engineering and reduction methods
for similarity-based time series classification.
Keywords
time-series classification, similarity-based classification, mortality prediction, directional change point.

Introduction
Patient time series data are collected over time at varying time intervals to update patient status and to
support medical decisions, leading to a wide variety of patient time series data – e.g., vital signs, lab
results, diagnoses, prescriptions and billings in Electronic Health Records (EHRs) and other healthcare
information systems. Past studies have extracted and leveraged temporal patterns (e.g., temporal
statistics, trends, transitions and similarity) from time series data for patient event, (e.g., readmission or
mortality), risk (Johnson et al. 2012), cost prediction (Bertsimas et al. 2008), or performance prediction
(Cho et al. 2008). Some of the past studies have reduced such problems to one of classifying one or
multiple time series of the same entity into different outcome/decision classes, which is termed the time
series classification (TSC) problem (Lee et al. 2012). Time series classification can be tackled by
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Leveraging Time Series Data in Similarity Based Healthcare Predictive Models

engineering temporal features that provide meaningful representations of time series and predictive
power at reduced dimensionality for use with general-purposed classification methods (Hippisley-Cox et
al. 2009). The synergy between a certain temporal abstraction approach and classification algorithm
varies amongst the vast choice space, and hence must be properly considered. To diagnose new patients,
physicians are often influenced by previous similar cases with relevant clinical evidences, resulting in
patient similarity theory in the clinical decision support literature (Rouzbahman and Chignell 2014). In
light of this theory, this study focuses on enhancing similarity-based classification methods for patient
time series classification.
The challenges of time series data include high dimensionality and high degree of missingness. Temporal
abstraction of time series, missing value imputation and feature reduction approaches provide options to
address these challenges. In addition, changes or transitions in various contexts including time series
classification have provided essential predictive power (Lin et al. 2014). To explore effective temporal
abstraction, missing value imputation, feature weight assignment and change point detection methods
that can afford the k-Nearest-Neighbor (kNN) algorithm with desirable synergy, this study asks these
research questions:
“What are the effective temporal abstraction, missing value imputation and feature reduction methods
for similarity-based time series classification?"
“What is an effective approach to define and detect patient status change points for similarity-based
time series classification?”

Proposed Framework for Similarity-based Patient Time Series
Classification
In this section, we introduce the methods this study has selected or proposed for patient time series
classification and some background and justifications for these methods.

Similarity based classification
Similarity-based classifiers estimate the class label of a test or new sample based on the similarities
between the test sample and a set of labeled training samples, and the pairwise similarities between the
training samples (Chen et al. 2009). The most popular family of algorithms has grown out the k-NearestNeighbor (k-NN) algorithm where k is the number of training samples with maximal similarities to a test
sample. Many advancements of the original k-NN including ENN (two-way similarity) (Tang and He
2015), CNN (condensed nearest neighbors) (Hart 1968) and kernel-based approaches (e.g., SVM-KNN)
have been proposed (Chen et al. 2009) for similarity-based classification as well. To examine the
usefulness of temporal features and reduction, and their synergy with similarity-based classification
approaches, we made a conscientious decision to use the original k-NN in this study. The potentials of
advancing the methods for patient time-series classification based on other similarity-based classification
remain as future research directions.
Past research on similarity measure has led to a wide variety of time series distance functions such as
Dynamic Time Wrapping (DTW) (Berndt and Clifford 1994), Edit Distance with Real Penalty (ERP) (Chen
and Ng 2004) and Longest Common Subsequence (LCSS) (Vlachos et al. 2002) to measure dissimilarities
based on different considerations. Our empirical exploration of different distance functions shows that the
simplicity of the Manhattan distance function offers desirable flexibility to leverage the joint benefits of
distance function, PAA grain size and missing value imputation methods. We hence select the Manhattan
distance function in k-NN for patient time series classification.

Temporal abstraction
Temporal abstraction decides on how to transform time series data into the input features of a
classification model. The challenges of time series data include high dimensionality and high amount of
missing data amongst others. Extant temporal abstraction methods vary in their considerations to
address these challenges and the predictive power of the resulting temporal features (Fu 2011). One
commonly used simple temporal abstraction approach, called piecewise aggregation approximation
(PAA), segments a time series into a sequence of fixed-sized non-overlapping consecutive windows (or
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Leveraging Time Series Data in Similarity Based Healthcare Predictive Models

intervals) (Lin et al. 2003). Each window is represented by the average of all data values time-stamped
within the window. We regard the size of a PAA window as the grain size and divide the temporal features
produced by PAA into fine-grain features versus coarse grain features. Table 1 compares the
dimensionality, degrees of missingness and information loss of fine-grain versus coarse-grain features.
Fine-Grain

Coarse-Grain

Window size

Small

Large

Information loss

Low

High

Dimensionality

High

Low

Missingness

High

Low

Table 1. Comparison of fine-grain versus coarse-grain PAA temporal abstraction
The low information loss of fine-grain PAA could afford k-NN improved accuracy over coarse-grain PAA
features. Exploring effective grain-size, dimensionality reduction and missing value imputation methods
are necessary to realize additional predictive power of fine-grain PAA temporal features.
PAA grain decision
The optimal PAA grain decision is analytically intractable due to the apparent complexity of considering
the interrelated factors including missing value imputation, feature reduction and distance function.
Empirical comparison should be employed to decide on the grain size. To reduce the number of empirical
experiments, we only compare the classification accuracy resulting from different grain sizes while
holding other methods fixed at the selected or proposed settings for time series classification.
Missing value imputation (MVI)
Missing value handling methods such as propensity score imputation, predictive model–based imputation
and hot-deck imputation can be found from past literature (Penny and Chesney 2006). Some of the time
series distance functions such DTW also incorporates missing value imputation (Berndt and Clifford
1994). In particular, DTW considers prior and posterior values of a missing value at a time point when
deciding on the similarity between two time series. Motivated by DTW, we propose an adjacency-based
imputation method which replaces a missing value by its posterior value if its prior value is not available
or by its prior value if its posterior value is not available. If both prior and posterior values are available,
their average becomes the imputed value. The proposed imputation can be performed independent of the
distance function of choice.
Feature weighting (FW)
Feature reduction for classification can utilize a variety of approaches such as information gain, Gini
index and Chi-square metrics to calculate feature rankings or weights for feature selection or reduction
(Singh et al. 2010). Because of the well-tested ability to improve accuracy, we adopt the Gradient Descent
(GS) method (Modha and Spangler 2003; Wettschereck and Aha 1995) to assign weights to time series
features.

Change point detection (CPD)
Many change point detection methods focus on detecting changes in the mean, variance or trend in a time
series that follows a distribution – e.g., Gaussian, normal or regression (Hawkins and Zamba 2012). Such
methods are not appropriate for detecting change points in patient time series due to the underlying data
distribution assumptions. In addition, a change in the mean or variance of numeric patient time series, for
example, of blood pressure may not be a change in patient status if both the values before and after a
change point represent the same patient status – e.g. normal. Therefore, this paper uses a change point
detection method based on clinical domain knowledge.

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Leveraging Time Series Data in Similarity Based Healthcare Predictive Models

Directional change point detection method
Past research has emphasized the importance of change point in clinical guidelines and decision supports
(Assareh et al. 2011; La Rosa et al. 2008; Sawaya et al. 2011). Few or many change points of a patient’s
time series can easily differentiate a patient’s condition and outcomes. In this paper we propose to define
and detect change points based on changes in the health status according to categories of values in the
time series rather than measures like mean or variance. For instance, systolic blood pressure less than 120
is considered normal, while between 120 and 139 is considered Prehypertension (Le et al. 2013). A
directional change point is defined as a change in a patients’ status category.
We denote a directional change point of patient i for time series (TS) j as DCP(i, j). The input is the
status(i, j, k) that indicates the health status level of patient i during time window k based on TS j. The
status output is an integer, where the lowest value of status for a feature represents the worst category of
health status, while the highest value of status for this feature represents the best category of health
status. Status change of patient i at time window k in terms of TS j is computed as follow:

StatusChange(i, j, k) = Positive, if status(i, j, k) > status (i, j, m), m<k
= Negative, if status(i, j, k) < status (i, j, m), m<k
= Stable, if status(i, j, k) = status (i, j, m), m<k
where m is the time window of the most recent available status of the patient before window k. We
propose three change point features for patient i based on TS j - the number of directional change points
or 𝑁𝑢𝑚_𝑜𝑓_𝐷𝐶𝑃(𝑖, 𝑗), and the first and last status changes, or LastStatusChange(i,j), and
FirstStatusChange(i,j). The following determines the value of directional change point of patient i status
at time windows k in terms of TS j:

DCP(i, j, k)

= 1, If status(i, j, k) is opposite to status (i, j, r), r<k
= 0, if status(i, j, k) = is not opposite to status (i, j, r), r<k

where r is the most recent available status change of the patient before window k that is either positive or
negative (i.e., Stable is not counted). DCP(i,j,1) for the first window is set to zero. Assume W is the number
of time windows (e.g., 24), the number of directional change points is derived as:
𝑊

𝑁𝑢𝑚_𝑜𝑓_𝐷𝐶𝑃(𝑖, 𝑗) = ∑ 𝐷𝐶𝑃(𝑖, 𝑗, 𝑘)
𝑘=1

The most recent and most related study to this method is the change point detection method proposed by
Lin et al. (2014)(Lin et al. 2014) for time-to-event prediction of chronic conditions using EHR data. To
detect change in patients’ status, the numerical time series values are replaced by three nominal states
(i.e., high, medium, low) based on numerical trend and two nominal trends (i.e., decrease, increase,
stable) based on numerical value changes of each predictor. Their change point detection will be used as a
benchmark for evaluating our proposed domain based directional change point detection method.

kNN-TSC-FIWC
We refer to the proposed patient time series classification method that combines the kNN algorithm with
fine-grain temporal features (F), missing-value imputation (I), feature weight assignment (W) and change
point detection (C) methods we select or propose to enhance similarity-based time series classification as
kNN-TSC-FIWC. Figure 1 summarizes the flow of the training and testing phases of kNN-TSC-FIWC.
Another benchmark of kNN-TSC-FIWC is Lee et al. (2012)(Lee et al. 2012) which proposes a similarity
based time series classification algorithm - KNN-TSC to predict customer churn after 30 days. KNN-TSC
divides each feature’s time series data into 15 equal size intervals and adopts the Discrete Fourier
transform (DFT) technique for time series similarity calculation. It doesn’t assign feature weights. KNNTSC utilizes stratified average voting to estimate the churn decision of a test sample. In empirical
evaluation, we will compare the accuracy of kNN-TSC-FIWC to that of KNN-TSC.

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Leveraging Time Series Data in Similarity Based Healthcare Predictive Models

Figure 1: An overview of kNN-TSC-FIWC

Empirical Evaluation
To evaluate the effectiveness of kNN-TSC-FIWC and its enabling methods, we compare them to
benchmarks representing combinations of different temporal features, classification algorithms, similarity
functions and dimension reduction methods in the context of early Intensive Care Unit (ICU) mortality
prediction. Accurate ICU mortality prediction impacts medical therapy, triaging, end-of-life care, and
many other aspects of ICU care (Gartman et al. 2009). To enhance the performance of ICU mortality
prediction more sophisticated machine learning methods have been utilized recently. The
PhysioNet/Computing in Cardiology 2012 Challenge aimed to provide a benchmark environment for early
ICU mortality prediction (Silva et al. 2012). To the best of our knowledge, its winner (CCW hereafter) is
the best early ICU mortality prediction benchmark using patients’ first 48 hours of ICU time series data.
CCW utilizes a new Bayesian ensemble scheme comprising of 500 weak decision tree learners which
randomly assigns an intercept and gradient to a randomly selected single feature (Johnson et al. 2012).

Data and evaluation procedure
To compare our results with CCW, we use the same experimental setup in the competition where patients
were filtered to 22,561 patients who are younger than 16 years old and remained in the ICU for at least 48
hours. The data input consists of time series data of 36 variables (e.g., Glasgow Coma Score GCS)
extracted from patients’ ICU stay, plus four static features (i.e., age, gender, height, and initial weight).
The target variable is a binary feature showing whether or not the patient eventually dies in the hospital
before discharge. While almost half of the ICU patients have died eventually, most of the deaths happened
out of hospital. The problem we analyze in this study is the prediction of in hospital mortality, which has
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Leveraging Time Series Data in Similarity Based Healthcare Predictive Models

an imbalanced distribution of 18% positive against 82% negative as shown in Table 2. It is interesting to
observe that the difference in average ICU stays is very minor while the difference in outcomes is life
versus death. Early mortality prediction may be able to help decision makers find ways to improve an ICU
patient’s survival rate. For finding and tuning the parameters including finding the best k, 50% of the
data was used, while the rest remained unseen for validation. In all experiments, 20-fold cross validation
was used to evaluate the performance of each method based on the validation dataset. Classification
performance was measured according to the average precision, recall, and F-measure across 20 folds.
Number of Patients

Average Hospital Stay

Average ICU Stay

Alive

11977 (53%)

9.68

5.21

Died

10584 (47%)

13.87

5.53

Died out of Hospital (no)

6516 (29%)

13.39

4.86

Died in Hospital (yes)

4068 (18%)

13.5

6.6

Died in ICU (yes)

3240 (14%)

10.53

7.49

Table 2: Data distribution over the target variable (mortality)

Results
Table 3 shows that using two hours’ time windows for the proposed method outperforms the same
method with one, four and eight hours’ time windows. The performance of the smallest grain size suffers
from high missingness and the resulting noises in two patients’ common PAA temporal values, while high
loss of information details hurts the performance of large grain sizes. The best prediction performance is
reached when the effect of missing values and information loss is balanced at window size of 2. Hence, the
grain size chosen for the rest of the evaluations is 2 hours.

Without change point detection
(kNN-TSC-FIW)

With change point detection
(kNN-TSC-FIWC)

Window
size

Accuracy

F-Measure
(yes)

F-Measure
(no)

Accuracy

F-Measure
(yes)

F-Measure
(no)

1

0.72

0.56

0.81

0.80

0.69

0.91

2

0.78

0.66

0.89

0.82

0.77

0.93

4

0.75

0.63

0.76

0.80

0.69

0.91

8

0.74

0.61

0.83

0.75

0.63

0.86

12

0.66

0.48

0.75

0.64

0.45

0.74

24

0.55

0.30

0.7

0.55

0.30

0.70

48

0.44

0.19

0.62

0.43

0.16

0.60

Table 3. Window size (abstraction size effect) effect on performance
Table 4 compares the performance of kNN-TSC-FIW where a few benchmarking distance functions
replace the Manhattan distance function. Although the performance results are close, they do validate the
performance benefit the simple Manhattan distance function offers.

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Leveraging Time Series Data in Similarity Based Healthcare Predictive Models

Without Change Point (kNN-TSC-FIW)

With Change Point (kNN-TSC-FIWC)

Accuracy

F-Measure (yes)

F-Measure (no)

Accuracy

F-Measure (yes)

F-Measure (no)

Manhattan

0.78

0.66

0.89

0.82

0.77

0.93

Euclidean

0.75

0.62

0.84

0.81

0.73

0.92

DTW

0.71

0.59

0.81

0.8

0.7

0.91

EDR

0.69

0.53

0.77

0.79

0.68

0.9

ERP

0.68

0.52

0.77

0.75

0.63

0.86

DFT

0.64

0.46

0.74

0.7

0.58

0.81

TSC

0.64

0.46

0.74

0.7

0.58

0.81

LCSS

0.57

0.33

0.71

0.66

0.48

0.75

Table 4. Comparison of different time-series distance function
Table 5 compares the performance of kNN-FIW against some of the well-established data mining
methods, including support vector machine (SVM), the original kNN without feature weight assignment,
neural network (NN) and logistic regression (LR). The input features for these algorithms are derived
based on the fine-grain PAA of 2-hr window size. The comparison validates the performance advantage of
similarity-based classification over its non-similarity counter-parts for early ICU mortality prediction.
Table 6 compares the performance of kNN combined with the selected or proposed methods starting with
fine-grain time series abstraction (kNN-TSC-F), missing value imputation (kNN-TSC-FI), feature
weighting (kNN-TSC-FIW) and change point detection (kNN-TSC-FIWC). The features based on the
proposed fine-grain temporal abstraction, missing value imputation and feature weighting help the kNNTSC-FIW model outperform the CCW benchmark by increasing the F-measure of the “yes” class by 11%.
The proposed change point features also further double this performance improvement. The significance
and benefits of these performance improvements in early ICU mortality by the proposed classification
features cannot be underestimated.
Table 7 shows the significant effect of the proposed feature weighting technique on the proposed method
(without considering change point features) against well-established feature weighting techniques,
including Gini index, Chi-square and information gain, as well as the method proposed by Lee et al. (Lee
et al. 2012).
Without Change Point

With Change Point

Accuracy

F-Measure
(yes)

F-Measure
(no)

Accuracy

F-Measure
(yes)

F-Measure
(no)

kNN-TSC-FIW (left)
kNN-TSC-FIWC (right)

0.78

0.66

0.89

0.82

0.77

0.93

CCW

0.7

0.55

0.81

0.75

0.62

0.84

CCW on fine-grain
features

0.66

0.48

0.75

0.71

0.59

0.81

SVM

0.7

0.58

0.81

0.65

0.47

0.85

LR

0.61

0.42

0.74

0.72

0.56

0.81

kNN

0.68

0.5

0.77

0.68

0.52

0.77

NN

0.64

0.46

0.74

0.68

0.52

0.77

Table 5. Similarity based method against son-similarity based methods using fine-grain
abstraction

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Leveraging Time Series Data in Similarity Based Healthcare Predictive Models

Method

Grain

MVI

FW

CPD

Accuracy

F-Measure (yes)

F-Measure (no)

CCW

Coarse

No

No

No

0.70

0.55

0.81

kNN-TSC-F

Fine

No

No

No

0.55

0.29

0.71

kNN-TSC-FI

Fine

Yes

No

No

0.64

0.40

0.83

kNN-TSC-FIW

Fine

Yes

Yes

No

0.78

0.66

0.89

kNN-TSCFIWC

Fine

Yes

Yes

Yes

0.82

0.77

0.93

Table 6. Full performance results by class
Without Imputation

With Imputation

Accuracy

F-Measure
(yes)

F-Measure
(no)

Accuracy

F-Measure
(yes)

F-Measure
(no)

kNN-TSC-FW (left)
kNN-TSC-FIW (right)
Lee et al.

0.6

0.40

0.72

0.78

0.66

0.89

0.52

0.27

0.67

0.72

0.56

0.81

Manual weights

0.57

0.33

0.71

0.71

0.59

0.81

Chi Square

0.50

0.24

0.64

0.68

0.52

0.77

Information Gain

0.53

0.28

0.68

0.71

0.55

0.81

Gini Index

0.55

0.30

0.7

0.70

0.58

0.81

No Feature Weights

0.44

0.19

0.62

0.49

0.27

0.64

Table 7. Comparison of different feature weighting techniques on the proposed method
This table shows the advantage of the selected Gradient Descent FW over methods that assign weights
based on pre-calculated values as well as domain knowledge based weight assignment (i.e. Manual
weights). The performance of a model without the proposed adjacency-based imputation on the left-hand
side of Table 7 is significantly lower than the same model with imputation on the right-hand side,
providing evidences for the effectiveness of the proposed minimalist imputation method.
Table 8 compares the performance of kNN-TSC-FIWC using different change point detection (CPD)
methods including parametric (M-G and V-G) and non-parametric (L-NP, S-NP, and LS-NP) CPD
methods as well as the change point detection method proposed by Lin et al. (2014). Although nonparametric CPD approaches perform better than parametric CPD approaches, none of them nor the CPD
method proposed by Lin et al. [16] could outperform kNN-TSC-FIWC. The comparison provides
evidences that changes in patient time series cannot be detected without considering domain-based
patient status categories. In addition, our post process analysis shows that patients with higher number of
DCHP are more likely to die due to their unstable situation. Patients with negative last change points
which indicate declining health status dominate the early death class. These patterns show the importance
of the proposed change point detection features.
Change Point Detection Method

Accuracy

F-Measure (yes)

F-Measure (no)

kNN-TSC-FIWC

0.82

0.77

0.93

Lin et al.
L-NP
S-NP
LS-NP
M-G
V-G

0.75
0.79
0.75
0.8
0.75
0.75

0.63
0.68
0.63
0.7
0.62
0.62

0.86
0.9
0.76
0.91
0.84
0.84

Table 8. Comparison of kNN-TSC-FIWC using different Change Point Detection Methods
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Leveraging Time Series Data in Similarity Based Healthcare Predictive Models

Without Change Point

With Change Point

Window
Size

Num of
Patients

Died

Accuracy

F-Measure
(yes)

F-Measure
(no)

Accuracy

F-Measure
(yes)

F-Measure
(no)

24

33625

5102
(15%)

0.72

0.60

0.81

0.78

0.67

0.9

48

22561

4068
(18%)

0.78

0.66

0.89

0.82

0.77

0.93

72

15913

3389
(21%)

0.8

0.7

0.91

0.84

0.82

0.94

96

11976

2903
(24%)

0.75

0.63

0.86

0.82

0.75

0.92

12

9485

2647
(27%)

0.74

0.61

0.83

0.81

0.72

0.92

Table 9. Comparison of kNN-TSC-FIWC using different prediction windows

Contributions and Limitations
This study makes several contributions to the patient time series classification and the early ICU mortality
prediction research fields:
Based on the patient similarity theory, the study evaluates the effectiveness of the similarity-based patient
time series classification approach.
The study further evaluates and identifies effective fine-grain PAA temporal abstraction, similarity
functions and proposes necessary enhancements via adjacency-based missing value imputation. The
study also evaluates the effectiveness of the gradient decent feature weight assignment approach for
reducing temporal dimensions and improving accuracy.
To the best of our knowledge, the study is the first to propose directional patient status change point
detection to extract effective features for patient time series classification.
The study contributes to solutions to an important healthcare predictive problem – early ICU mortality
prediction by significantly improving prediction accuracy with a new framework that embeds effective
extant methods and new enhancements. Both intensive caregivers and patients’ families can benefit from
this framework with the crucial decision on aggressive or supportive treatment. Also, unexpected deaths,
which are still common despite evidence that patients often show signs of clinical deterioration hours in
advance, can be detected.
The main limitations of this study include the use of a single data set for evaluation, the difficulty of
explaining a kNN model, and the need to examine additional methods appropriate for time series
classification. Future research should pursue along the directions that could address these limitations.

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Twenty-third Americas Conference on Information Systems, Boston, 2017

