Strategies for Prospective Biosurveillance Using Multivariate Time Series Howard Burkom 1, Yevgeniy Elbert 2, Sean Murphy 1 1 Johns 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

Defining the Multivariate Temporal Surveillance Problem 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 Varying Nature of the Data: Trend, day-of-week, seasonal behavior depending on data type & grouping:

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

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

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 Univariate Alerting Methods

Parallel Hypotheses & Multiple Testing Adapting Standard Methods P-values p 1,…,p n with multiple null hypotheses desired type I error rate  : “no outbreak at any hospital j” j=1,…,N Bonferroni bound: error rate is achieved with test p j <  /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 if any P ( j* ) < j*  N –Reject null for j <= j* (or use more complex criteria)

Parallel Hypotheses: Criteria to Control False Alert Rate Simes-Seeger-Elkund criterion: Gives expected alert rate near desired  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

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

Consensus Monitoring: Multiple Univariate Methods Fisher’s combination rule (multiplicative) –Given p-values p 1, p 2,…,p n : –F is  2 with 2n degrees of freedom, for p j independent –Recommended as “stand-alone” method Edgington’s rule (additive) –Let S = sum of p-values p 1, p 2,…,p n –Resultant p-value: ( stop when (S-j) <= 0 ) –Normal curve approximation formula for large n –“Consensus” method: sensitive to multiple near-critical values

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

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 934 days of EMS Data Multiple Testing Problem!Add’l Consensus AlertsStand-Alone Method

Multivariate Control Charts T 2 statistic: (X-  S -1 (X-  –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): “T 2 particularly bad at distinguishing location shifts from scale shifts” –T 2 nondirectional –Directional statistic: (   -  S -1 (X- , where   –  is direction of change

MSPC Example: 2 Data Streams

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 , modeled overdispersion with   = k  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 ) ( sensitivity ) ROC: Both as a function of threshold injectedsignals# alertedsignals# )ectionPr(det 

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

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

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

Backups

References 1 Testing Multiple Null Hypotheses Simes, R. J., (1986) "An improved Bonferroni procedure for multiple tests of significance", Biometrika 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, Hommel, G. (1988). "A stagewise rejective multiple test procedure based on a modified Bonferroni test “, Biometrika 75, 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 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 Edgington, E.S. (1972). "A normal curve method for combining probability values from independent experiments. “, Journal of Psychology, Vol. 82, pp Bauer P. and Kohne K. (1994), “Evaluation of Experiments with Adaptive Interim Analyses”, Biometrics 50,

References 2 Statistical Process Control Hawkins, D. (1991). “Mulitivariate Quality Control Based on Regression-Adjusted Variables “, Technometrics 33, 1: 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 Dec 15;18(23): Lowry, C.A., Woodall, W.H., A Multivariate Exponentially Weighted Moving Average Control Chart, Technometrics, February 1992, Vol. 34, No. 1, Point-Source Epidemic Curves & Simulation Sartwell, P.E., The Distribution of Incubation Periods of Infectious Disease, Am. J. Hyg. 1950, Vol. 51, pp ; 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, 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)

MSPC 2-Stream Example: Detail of Aug. Peak

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

Bayes Belief Net (BBN) Umbrella 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

Flu SeasonGI AnomalyResp AnomalySensor Alarm Bayes Network Elements P(Flu | Evidence) P(Anthrax | Evidence) Flu SeasonGI AnomalyResp AnomalySensor AlarmFlu SeasonGI AnomalyResp AnomalySensor AlarmFlu SeasonGI AnomalyResp AnomalySensor Alarm Posterior probabilities Evidence FluAnthrax Flu SeasonGI AnomalyResp AnomalySensor Alarm >> > <

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

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