This document discusses causal inference methods for uncertain time series data. It presents a method for analyzing time-stamped medical sensor data to determine causal relationships between variables like glucose levels, exercise, sleep, and insulin dosage. The method is applied to data from 17 subjects with Type 1 diabetes over 72 hours. The results suggest that very vigorous exercise leads to short-term hyperglycemia, which is supported by literature. Open problems discussed include handling latent variables, non-stationary data, real-time prediction and explanation, and simulation.

1. Causal Inference from Uncertain
Time Series Data
Samantha Kleinberg
Stevens Institute of Technology

3. http://discoverysedge.mayo.edu/artificial-pancreas/

4. insulindependence.orginfluxis.com gigaom.com
Nate Heintzman @ UCSD, Dexcom

5. Time
Blood
Glucose
Heart
Rate
Skin
Temp.
Energy
Use Weight
7:20
7:25 95.7 26.80 37.23
7:30 90.5 28.63 12.85
7:35 82.4 29.69 6.78
7:40 79.2 30.32 6.41
7:45 77.0 30.55 8.17
7:50 73.3 31.19 6.87 155
7:55 72.7 31.29 6.08
8:00 130.0 71.4 31.96 9.74
8:05 203.5 89.8 31.59 24.58
8:10 208.2 87.9 31.67 10.63
8:15 209.0 84.8 31.16 15.63
8:20 207.8 81.0 31.11 11.74
8:25 205.9 83.7 31.26 16.28
8:30 204.8 98.3 31.05 23.59
8:35 214.9 82.2 30.47 11.66
8:40 225.7 82.9 30.95 16.93
8:45 231.4 0.1
8:50 232.8 89.6 29.67 21.96
8:55 239.4 81.2 30.81 15.86

6. Time
Blood
Glucose
Heart
Rate
Skin
Temp.
Energy
Use Weight
7:20
7:25 95.7 26.80 37.23
7:30 90.5 28.63 12.85
7:35 82.4 29.69 6.78
7:40 79.2 30.32 6.41
7:45 77.0 30.55 8.17
7:50 73.3 31.19 6.87 155
7:55 72.7 31.29 6.08
8:00 130.0 71.4 31.96 9.74
8:05 203.5 89.8 31.59 24.58
8:10 208.2 87.9 31.67 10.63
8:15 209.0 84.8 31.16 15.63
8:20 207.8 81.0 31.11 11.74
8:25 205.9 83.7 31.26 16.28
8:30 204.8 98.3 31.05 23.59
8:35 214.9 82.2 30.47 11.66
8:40 225.7 82.9 30.95 16.93
8:45 231.4 0.1
8:50 232.8 89.6 29.67 21.96
8:55 239.4 81.2 30.81 15.86
Errors

7. Time
Blood
Glucose
Heart
Rate
Skin
Temp.
Energy
Use Weight
7:20
7:25 95.7 26.80 37.23
7:30 90.5 28.63 12.85
7:35 82.4 29.69 6.78
7:40 79.2 30.32 6.41
7:45 77.0 30.55 8.17
7:50 73.3 31.19 6.87 155
7:55 72.7 31.29 6.08
8:00 130.0 71.4 31.96 9.74
8:05 203.5 89.8 31.59 24.58
8:10 208.2 87.9 31.67 10.63
8:15 209.0 84.8 31.16 15.63
8:20 207.8 81.0 31.11 11.74
8:25 205.9 83.7 31.26 16.28
8:30 204.8 98.3 31.05 23.59
8:35 214.9 82.2 30.47 11.66
8:40 225.7 82.9 30.95 16.93
8:45 231.4 0.1
8:50 232.8 89.6 29.67 21.96
8:55 239.4 81.2 30.81 15.86
Errors
Missing Data

8. Time
Blood
Glucose
Heart
Rate
Skin
Temp.
Energy
Use Weight
7:20
7:25 95.7 26.80 37.23
7:30 90.5 28.63 12.85
7:35 82.4 29.69 6.78
7:40 79.2 30.32 6.41
7:45 77.0 30.55 8.17
7:50 73.3 31.19 6.87 155
7:55 72.7 31.29 6.08
8:00 130.0 71.4 31.96 9.74
8:05 203.5 89.8 31.59 24.58
8:10 208.2 87.9 31.67 10.63
8:15 209.0 84.8 31.16 15.63
8:20 207.8 81.0 31.11 11.74
8:25 205.9 83.7 31.26 16.28
8:30 204.8 98.3 31.05 23.59
8:35 214.9 82.2 30.47 11.66
8:40 225.7 82.9 30.95 16.93
8:45 231.4 0.1
8:50 232.8 89.6 29.67 21.96
8:55 239.4 81.2 30.81 15.86
Errors
Missing Data
Different timescales

9. Discretization
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201
hypo
eu
hyper

10. Logic-based causal inference
• Complex, temporal relationships
• Potential causes raise probability of and are
earlier than effects
Kleinberg, S. (2012) Causality, Probability, and Time.

11. Which causes are significant?
• Main idea: looking for better explanations for
the effect
• Assess average difference cause makes to
probability of effect
• Determine which ε are statistically significant

12. Causes from EHR data
8
9
17
17
18
11
10
22
22
21
0510152025
dx_urinary_symptoms
first_antihtn_combo
dx_overweight
dx_diabetes
dx_hypothyroidism
Months before CHF diagnosis
S. Kleinberg and N. Elhadad (2013) Lessons Learned in Replicating Data-Driven Experiments in
Multiple Medical Systems and Patient Populations. AMIA Annual Symposium.

13. Adding uncertainty
D. Hutchison and S. Kleinberg (2013) Causality and Experimentation in the Sciences.

14. Carb-heavy meal (c), vigorous exercise
(e), blood glucose (g)

15. Calculate:
What’s the effect of exercise on glucose?

16. Calculate:
Strict discretization:
What’s the effect of exercise on glucose?

17. Calculate:
Strict discretization:
Probabilistic discretization:
What’s the effect of exercise on glucose?

18. Validation
Simulated structures
• Randomly generated
relationships
• 6 levels of uncertainty
• 20K observations

19. Results on simulated data

20. Causes of changes in glucose
Cohort: 17 subjects with T1DM
Sensor data (collected for >72 hours)
– Glucose values
– Insulin dosage
– Activity
– Sleep stage
– Heart rate
– Temperature
With N. Heintzman (UCSD,Dexcom) http://dial.ucsd.edu/what-we-do.php

21. Results
very vigorous exercise leads to hyperglycemia
(fdr <.01) in 5-30 minutes
– Found using both HR (anaerobic activity zone) and
METs
• Not found with strict discretization
• Supported by literature
(Marliss and Vranic, 2002; Riddell and
Perkins, 2006)
S. Kleinberg and N. Heintzman. Inference of Causal Relationships from Uncertain Data and
Application to Type 1 Diabetes. (under review)

22. Open problems
• Latent variables
• Nonstationary time series
• Real-time prediction/explanation
• Simulation

23. Thanks!
• NSF/CRA Computing
Innovation fellowship
• NLM Computational
Thinking contract
• NLM R01
• Columbia
– Noemie Elhadad
– George Hripcsak
– Mitzi Morris
– Rimma Pivovarov
• Geisinger
– Buzz Stewart
– Craig Wood
• UCSD
– Nathaniel Heintzman
• Stevens
– Dylan Hutchison