Strategies for Prospective Biosurveillance Using Multivariate Time Series

1. Strategies for Prospective Biosurveillance Using Multivariate Time Series Howard Burkom1, Yevgeniy Elbert2, Sean Murphy1 1Johns Hopkins Applied Physics Laboratory National Security Technology Department 2 Walter Reed Army Institute for Research Tenth Biennial CDC and ATSDR Symposium on Statistical Methods Panelist: Statistical Issues in Public Health Surveillance for Bioterrorism Using Multiple Data Streams Bethesda, MD March 2, 2005

2. Defining the Multivariate Temporal Surveillance Problem Varying Nature of the Data: • Trend, day-of-week, seasonal behavior depending on data type & grouping: Multivariate Nature of Problem: • Many locations • Multiple syndromes • Stratification by age, gender, other covariates Surveillance Challenges: • Defining anomalous behavior(s) • Hypothesis tests--both appropriate and timely • Avoiding excessive alerting due to multiple testing • Correlation among data streams • Varying noise backgrounds • Communication with/among users at different levels • Data reduction and visualization

3. Problem: to combine multiple evidence sources for increased sensitivity at manageable alert rates height of outbreak Recent Respiratory Syndrome Data early cases

4. Multivariate Hypothesis Testing • Parallel monitoring: • Null hypothesis: “no outbreak of unspecified infection in any of hospitals 1…N” (or counties, zipcodes, …) • FDR-based methods (modified Bonferroni) • Consensus monitoring: • Null hypothesis: “no respiratory outbreak infection based on hosp. syndrome counts, clinic visits, OTC sales, absentees” • Multiple univariate methods: “combining p-values” • Fully multivariate: MSPC charts • General solution: system-engineered blend of these • Scan statistics paradigm useful when data permit

5. Univariate Alerting Methods • Data modeling: regression controls for weekly, holiday, seasonal effects • Outlier removal procedure avoids training on exceptional counts • Baseline chosen to capture recent seasonal behavior • Standardized residuals used as detection statistics • Process control method adapted for daily surveillance • Combines EWMA, Shewhart methods for sensitivity to gradual or sudden signals • Parameters modified adaptively for changing data behavior • Adaptively scaled to compute 1-sided probabilities for detection statistics • Small-count corrections for scale-independent alert rates • Outputs expressed as p-values for comparison, visualization

6. Parallel Hypotheses & Multiple TestingAdapting Standard Methods • P-values p1,…,pnwith multiple null hypotheses desired type I error rate a : “no outbreak at any hospital j” j=1,…,N • Bonferroni bound: error rate is achieved with test pj < a /N, all j (conservative) • Simes’ 1986 enhancement (after Seeger, Elkund): • Put p-values in ascending order: P(1),…,P(n) • Reject intersection of null hypotheses ifany P(j*) < j* a / N • Reject null for j <= j* (or use more complex criteria)

7. Simes-Seeger-Elkund criterion: Gives expected alert rate near desired a for independent signals Applied to control the false discovery rate (FDR) for many common multivariate distributions (Benjamini & Hochberg, 1995) FDR = Exp( # false alerts / all alerts ) Increased power over methods controlling Pr( single false alert ) Numerous FDR applications, incl. UK health surveillance in (Marshall et al, 2003) Criterion: reject combined null hypothesis if any p-value falls below line Parallel Hypotheses: Criteria to Control False Alert Rate

8. Stratification and Multiple Testing … Counts unstratified by age Counts ages 0-4 Counts ages 5-11 Counts ages 71+ EWMA- Shewhart EWMA- Shewhart EWMA- Shewhart EWMA- Shewhart … p-value, ages 0-4 p-value, ages 5-11 p-value, ages 71+ aggregate p-value Modified Bonferroni (FDR) composite p-value MIN resultant p-value

9. Consensus Monitoring:Multiple Univariate Methods • Fisher’s combination rule (multiplicative) • Given p-values p1, p2,…,pn: • F is c2 with 2n degrees of freedom, for pj independent • Recommended as “stand-alone” method • Edgington’s rule (additive) • Let S = sum of p-values p1, p2,…,pn • Resultant p-value: ( stop when (S-j) <= 0 ) • Normal curve approximation formula for large n • “Consensus” method: sensitive to multiple near-critical values

10. Multiple Univariate Criteria: 2D Visualization Nominal univariate criteria Edgington Fisher

11. Add’l Consensus Alerts Stand-Alone Method Multiple Testing Problem! 934 days of EMS Data • 12 time series: separate syndrome groups of ambulance calls • Poisson-like counts: negligible day-of-week, seasonal effects • EWMA-Shewhart algorithm applied to derive p-values • Each row is mean over ALL combinations

12. Multivariate Control Charts • T2 statistic: (X-m) S-1(X-m) • X = multivariate time series: syndromic claims, OTC sales, etc. • S = estimate of covariance matrix from baseline interval • Alert based on empirical distribution to alert rate • MCUSUM, MEWMA methods “filter” X seeking shorter average run length • Hawkins (1993): “T2 particularly bad at distinguishing location shifts from scale shifts” • T2nondirectional • Directional statistic: (mA - m) S-1(X- m), where mA – m is direction of change

13. MSPC Example: 2 Data Streams

14. ROC: Both as a function of threshold Evaluation: Injection in Authentic and Simulated Backgrounds • Background: • Authentic: 2-8 correlated streams of daily resp syndrome data (23 mo.) • Simulated: negative binomial data with authentic m, modeled overdispersion with s2 = km • Injections (additional attributable cases): • Each case stochastic draw from point-source epicurve dist. (Sartwell lognormal model) • 100 Monte Carlo trials; single outbreak effect per trial • With and without time delays between effects across streams • ( 1-specificity ) # signals alerted = Pr(det ection ) # signals injected • ( sensitivity )

15. Data correlation tends to degrade alert rate of multiple, univariate methods Cross correlation can greatly improve multivariate method performance (if consistent), or can degrade it! PD=PFA (random) Multivariate Comparison Example: faint, 1-s peak signal with in 4 independent data streams, with differential effect delays

16. ROC Effects of Data Correlation Example: faint, 2-s peak signal with 2 of 6 highly correlated data streams, with differential effect delays Degradation of multiple, univariate methods Detection Probability Effect of strong, consistent correlation on multivariate methods Daily False Alarm Probability

17. Conclusions • Comprehensive biosurveillance requires an interweaving of parallel and consensus monitoring • Adapted hypothesis tests can help maintain sensitivity at practical false alarm rates • But background data and cross-correlation must be understood • Parallel monitoring: FDR-like methods required according to scope, jurisdiction of surveillance • Multiple univariate • Fisher rule useful as stand-alone combination method • Edgington rule gives sensitivity to consensus of tests • Multivariate • MSPC T2-based charts offer promise when correlation is consistent & significant, but their niche in routine, robust, prospective monitoring must be clarified

18. Backups

19. References 1 Testing Multiple Null Hypotheses • Simes, R. J., (1986) "An improved Bonferroni procedure for multiple tests of significance", Biometrika 73 751-754. • Benjamini, Y., Hochberg, Y. (1995). " Controlling the False Discovery Rate: a Practical and Powerful Approach to Multiple Testing ", Journal of the Royal Statistical Society B, 57 289-300. • Hommel, G. (1988). "A stagewise rejective multiple test procedure based on a modified Bonferroni test “, Biometrika 75,383-386. • Miller C.J., Genovese C., Nichol R.C., Wasserman L., Connolly A., Reichart D., Hopkins A., Schneider J., and Moore A. , “Controlling the False Discovery Rate in Astrophysical Data Analysis”, 2001, Astronomical Journal , 122, 3492 • Marshall C, Best N, Bottle A, and Aylin P, “Statistical Issues in Prospective Monitoring of Health Outcomes Across Multiple Units”, J. Royal Statist. Soc. A (2004), 167 Pt. 3, pp. 541-559. Testing Single Null Hypotheses with multiple evidence • Edgington, E.S. (1972). "An Additive Method for Combining Probability Values from Independent Experiments. “, Journal of Psychology , Vol. 80, pp. 351-363. • Edgington, E.S. (1972). "A normal curve method for combining probability values from independent experiments. “, Journal of Psychology , Vol. 82, pp. 85-89. • Bauer P. and Kohne K. (1994), “Evaluation of Experiments with Adaptive Interim Analyses”, Biometrics 50, 1029-1041

20. References 2 Statistical Process Control • Hawkins, D. (1991). “Mulitivariate Quality Control Based on Regression-Adjusted Variables “, Technometrics 33, 1:61-75. • Mandel, B.J, “The Regression Control Chart”, J. Quality Technology (1) (1969) 1:1-9. • Wiliamson G.D. and VanBrackle, G. (1999). "A study of the average run length characteristics of the National Notifiable Diseases Surveillance System”, Stat Med. 1999 Dec 15;18(23):3309-19. • Lowry, C.A., Woodall, W.H., A Multivariate Exponentially Weighted Moving Average Control Chart, Technometrics, February 1992, Vol. 34, No. 1, 46-53 Point-Source Epidemic Curves & Simulation • Sartwell, P.E., The Distribution of Incubation Periods of Infectious Disease, Am. J. Hyg. 1950, Vol. 51, pp. 310-318; reprinted in Am. J. Epidemiol., Vol. 141, No. 5, 1995 • Philippe, P., Sartwell’s Incubation Period Model Revisited in the Light of Dynamic Modeling, J. Clin, Epidemiol., Vol. 47, No. 4, 419-433. • Burkom H and Rodriguez R, “Using Point-Source Epidemic Curves to Evaluate Alerting Algorithms for Biosurveillance”, 2004 Proceedings of the American Statistical Association, Statistics in Government Section [CD-ROM], Toronto: American Statistical Association (to appear)

21. MSPC 2-Stream Example: Detail of Aug. Peak

22. Effect of Combining Evidence Algorithm P-values height of outbreak secondary event early cases

23. To include evidence from disparate evidence types Continuous/discrete data Derived algorithm output or probabilities Expert/heuristic knowledge Graphical representation of conditional dependencies Can weight statistical hypothesis test evidence using heuristics – not restricted to fixed p-value thresholds Can exploit advances in data modeling, multivariate anomaly detection Can model Heuristic weighting of evidence Lags in data availability or reporting Missing data Bayes Belief Net (BBN) Umbrella

24. Flu Season Flu Season Flu Season Flu Season GI Anomaly GI Anomaly GI Anomaly GI Anomaly Resp Anomaly Resp Anomaly Resp Anomaly Resp Anomaly Sensor Alarm Sensor Alarm Sensor Alarm Sensor Alarm Bayes Network Elements Flu Anthrax Flu Season GI Anomaly Resp Anomaly Sensor Alarm Posterior probabilities Evidence >> >> > <

25. Structure of BBN Model for Asthma Flare-ups Syndromic Asthma Interaction Asthma Military RX Cold/Flu Season and Irritant Resp Anomaly SubFreezing Temp Cold/Flu Season Cold/Flu Season Start Resp Military OV Pollution Resp Military RX Resp Civilian OV Ozone Resp Civilian OTC PM 2.5 AQI Season Allergen Mold Spores Grass Pollen Tree Pollen Weed Pollen Level Season Level Season Level Season Level Season

26. BBN Application to Asthma Flare-ups • Availability of practical, verifiable data: • For “truth data”: daily clinical diagnosis counts • For “evidence”: daily environmental, syndromic data • Known asthma triggers with complex interaction • Air quality (EPA data) • Concentration of particulate matter, allergens • Ozone levels • Temperature (NOAA data) • Viral infections (Syndromic data) • Evidence from combination of expert knowledge, historical data