In many healthcare settings, intuitive decision rules for risk stratification can help effective hospital resource allocation. This paper introduces a novel variant of decision tree algorithms that produces a chain of decisions, not a general tree. Our algorithm, $\alpha$-Carving Decision Chain (ACDC), sequentially carves out ``pure'' subsets of the majority class examples. The resulting chain of decision rules yields a pure subset of the minority class examples. Our approach is particularly effective in exploring large and class-imbalanced health datasets. Moreover, ACDC provides an interactive interpretation in conjunction with visual performance metrics such as Receiver Operating Characteristics curve and Lift chart.

1. ACDC: Alpha-Carving Decision
Chain for Risk Stratification
Yubin Park, Accordion Health, Inc.
Joyce Ho, Emory University
JoydeepGhosh, The University of Texas at Austin
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2. What is Decision Chain (DC)?
• Also known as Rule Lists (Wang & Rudin, 2015)
• A sequence of rules, applied to one after another, where the ratio of
positive class increases over the sequence of rules
• Toy Example: A decision chain for predicting the likelihood of being a
Longhorn fan,
• If Tom lives in Austin, TX à 25% chance of being a Longhorn fan
• And Tom likes to watch football games à 50% chance
• And Tom goes out for a tail gate on every Saturday à 75% chance
• And Tom wears burnt orange t-shirts all the time à 95% chance
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3. Conceptually, something like this
3
+ +
+
✓A ✓B
S1
S1
S0
S0
S2
S2
+ +
+
✓A ✓B
S1
S1
S0
S0
S2
S2
Decision Tree Decision Chain
ICML WHI 2016

4. Is DC More Interpretable than DT?
• In Decision Chain (DC),
• Risk is proportional to the number of rules
• Less to memorize for filtering out low-risk population (or samples)
• More to memorize for capturing high-risk population
• Using DC, one can implement an economically efficient business process
based on job maturity-level
• While in Decision Tree (DT),
• The number of rules is agnostic to risk
• Low-risk can be captured with one rule as well as hundreds of rules
• Thus, DC may be helpful for some applications
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5. In Healthcare Applications,
• Class imbalance problems are prevalent
• Majority class examples can be often carved out (or filtered out) with
a simple conjunction of if-else statements
• An implementation strategy
• Filter out majority class with rules à Obtain a less imbalanced dataset à
Apply a fancy machine learning algorithm
• One question:How many majority examples should I filter out?
• A possible solution:If we build a decision chain, then we can streamline grid-
search much easily
• DC can be more interpretable as well as more efficient (sometimes)
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6. Question is How
• We will use a greedy approach
• Note that decision tree is also a greedy algorithm
• Pick a splitting feature that maximizes {information gain, purity score, etc.}
• Split the dataset into parts based on the value of the splitting feature
• Repeat from the beginning for each dataset
• We will grow a decision chain as follows
• Pick a splitting feature that carves out the most amount of majority samples
• Split the dataset into parts based on the value of the splitting feature
• Repeat from the beginning on only one partition that has more positive class
examples
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7. More Details on How
• Selecting the best splitting feature
• We will use Alpha-Divergence
• Alpha-Divergence is the same as KL-Divergence when Alpha=1
• Alpha-Divergence is the same as Hellingerdistance when Alpha=0.5
• Alpha-Divergence can be a lot of different things based on the value of Alpha
• We will change the value of Alpha adaptively (with a simple strategy)
to achieve our goal
• More details are in the paper
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8. Effect of Different Alphas
• High Alpha
• Pure partitions
• Low Alpha
• Balanced partitions
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α = 1
α = 16
α = 48
α = 64
0
25
50
75
50 100 150
nbp.systolic
count
Shock F T
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9. Experiments: Septic Shock
• Alpha-Carving Decision
Chain (ACDC) shows
comparable performance
with other decision tree
algorithms
• ATree(a=1): C4.5
• ATree(a=2): CART
• ATree(a=x): other alpha-
trees
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●
●
0.5
0.6
0.7
0.8
ATree(a=1)
ATree(a=2)
ATree(a=4)
ATree(a=16)
ATree(a=64)
ATree(a=128)
ACDC
Model
AUC
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10. Experiments: Septic Shock
• Since ACDC is a decision chain,
we can make this cool
visualization
• Put decision rules and
performance metrics in a single
chart
• Risk is proportional to the
number of rules applied
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L1: nbp.systolic<=132
L2: nbp.systolic<=98.4
L3: min.nbp.systolic<=90.4
L4: nbp.diastolic<=46
0
1
2
3
0.00 0.25 0.50 0.75 1.00
Coverage
Lift
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11. Experiments: Cardiac Arrest
• Another example: Asystole
• Again, comparable to other
decision trees
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0.5
0.6
0.7
0.8
ATree(a=1)
ATree(a=2)
ATree(a=4)
ATree(a=16)
ATree(a=64)
ATree(a=128)
ACDC
Model
AUC
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12. Experiments: Cardiac Arrest
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L1: min.nbp.diastolic<=48.767L2: min.nbp.systolic<=104
L3: min.spo2<=90
L4: spo2<=93.6
L5: min.spo2<=78
L6: avg.pp>57.495
L7: hr<=90.9
0.0
2.5
5.0
7.5
10.0
0.00 0.25 0.50 0.75 1.00
Coverage
Lift
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L1: min.nbp.diastolic<=48.
L2: min.nbp.systolic<=104
L3: min.spo2<=90
L4: spo2<=93.6
L5: min.spo2<=78
L6: avg.pp>57.495
L7: hr<=90.9
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
FPR
TPR
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13. Experiments: Cardiac Arrest
• You also can make a risk
pyramid
13
min.diastolic < 48 mmHg
min.systolic < 104 mmHg
min.spo2 < 90 %
spo2 < 93 %
Baseline Risk
1.3 times higher
1.5 times higher
3.7 x
5.8 x
Asystole !
Risk Stratification !
Decision Chain
Higher risk
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14. Contacts
• Yubin Park
• yubin [at] accordionhealth[dot] com
• Joyce Ho
• joyce [dot] c [dot] ho [at] emory [dot] edu
• Joydeep Ghosh
• jghosh [at] utexas [dot] edu
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