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**Statistical Methods for Alerting Algorithms in Biosurveillance**

Howard S. Burkom The Johns Hopkins University Applied Physics Laboratory National Security Technology Department Washington Statistical Society Seminar February 3, 2006 National Center for Health Statistics Hyattsville, MD

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**ESSENCE Biosurveillance Systems**

ESSENCE: An Electronic Surveillance System for the Early Notification of Community-based Epidemics Monitoring health care data from ~800 military treatment facilities since Sept. 2001 Evaluating data sources Civilian physician visits OTC pharmacy sales Prescription sales Nurse hotline/EMS data Absentee rate data Developing & implementing alerting algorithms In the ESSENCE system, outpatient visit and emergent care data are collected from about 800 MTFs worldwide. We get syndromic counts from these sites on a daily basis, so we’re looking at data streams with a daily sample rate, which in some cases is increasing Put remarks in context of multiple streams of syndromic counts/rates each day

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Outline of Talk Prospective Syndromic Surveillance: introduction, challenges Algorithm Evaluation Approaches Statistical Quality Control in Health Surveillance Data Modeling and Process Control Regression Modeling Approach Generalized Exponential Smoothing Comparison Study Summary & Research Directions

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**Required Disciplines: Medical/Epi**

Medical/Epidemiological filtering/classifying clinical records => syndromes interpretation/response to system output coding/chief complaint interpretation

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**Required Disciplines: Informatics**

Information Technology surveillance system architecture data ingestion/cleaning interface between health monitors and system

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**Required Disciplines: Analytics**

Analytical Statistical hypothesis tests Data mining/automated learning Adaptation of methodology to background data behavior

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**Essential Task Interaction in Volatile Data Background**

Medical/Epidemiological filtering/classifying clinical records => syndromes interpretation/response to system output coding/chief complaint interpretation Information Technology surveillance system architecture data ingestion/cleaning interface between health monitors and system Analytical Statistical hypothesis tests Data mining/automated learning Adaptation of methodology to background data behavior

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**The Multivariate Temporal Surveillance Problem**

Varying Nature of the Data: Scale, trend, day-of-week, seasonal behavior depending on 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

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**Data issues affecting monitoring**

Most suitable for modeling without data-specific information Statistical properties Scale and random dispersion Periodic effects Day-of-week effects, seasonality Delayed (often variably) availability in monitoring system Trends: long/short term: many causes, incl. changes in: Population distribution or demographic composition Data provider participation Consumer health care behavior Coding or billing practices Prolonged data drop-outs, sometimes with catch-ups Outliers unrelated to infectious disease levels Often due to problems in data chain Inclement weather Media reports (example: the “Clinton effect”)

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**Forming the Outcome Variable: Binning by Diagnosis Code**

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**Rash Syndrome Grouping of Diagnosis Codes**

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Chief Complaint Query Simulated Data

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Dynamic Detection Dynamic Detection Simulated Data

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**Example with Detection Statistic Plot**

Threshold Injected Cases Presumed Attributable to Outbreak Event

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**Comparing Alerting Algorithms Criteria:**

Sensitivity Probability of detecting an outbreak signal Depends on effect of outbreak in data Specificity ( 1 – false alert rate ) Probability(no alert | no outbreak ) May be difficult to prove no outbreak exists Timeliness Once the effects of an outbreak appear in the data, how soon is an alert expected?

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**Modeling the Signal as Epicurve of Primary Cases**

Need “data epicurve”: time series of attributable counts above background Plausible to assume proportional to epidemic curve of infected Sartwell lognormal model gives idealized shape for a given disease type Epicurve: plot of number of symptomatic cases by day Canonical idea of a bioterrorist attack is a localized, point-source outbreak, such as the 1979 accident at Sverdlovsk where weaponized anthrax spores were released in aerosol form, an unknown number infected, and about 70 died Magenta dotted curve shows actual epicurve we constructed from plot in 1992 Meselson paper We’ve taken data such as this to calculate zeta and sigma for disease-specific lognormal dist. Can then plot the “maximum likelihood epicurve” Modal day is exp(zeta + 2*sigma); in constructing a test signal, we set the modal number of cases to a multiple of the estimated standard deviation of the time series of interest, then divide by the modal probability to get the total number infected, and we add the resulting counts to the authentic data Sartwell, PE. The distribution of incubation periods of infectious disease. Am J Hyg 1950; 51:310:318

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**Signal Modeling: Realizations of Smallpox Epicurve**

Each symptomatic case a random draw “maximum likelihood” epicurve However, we don’t assume the maximum likelihood epicurve in our simulation; we form a stochastic signal using the calculated N, zeta, and sigma For each of the N simulated cases, we take a random draw from the lognormal with params, zeta & sigma, just as each individual’s incubation period could be seen as a random draw from distributions of dosage and susceptibility Each trial is then a set of N such random draws, giving a large set of random signals These signals are what we add to the noise background of authentic data

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**Assessing Algorithm Performance**

Summary processing: measure dependence of sensitivity or timeliness on false alert rate (ROC or AMOC curves or key sample values at practical rates) Sensitivity/Specificity as a function of threshold: Receiver Operating Characteristic (ROC) Detection Probability (sensitivity) threshold False Alert Rate (1 – specificity) Actual false alert rate of interest depends on: resources of public health dept using the system “prior” likelihood of an outbreak (DHS threat level) However, we do NOT look at area under the curve, but at PD at alert rates of interest Timeliness/Specificity as a function of threshold: Activity Monitor Operating Characteristic (AMOC) Timeliness Score (e.g. Mean or Median Time to Alert) threshold False Alert Rate (1 – specificity)

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**Detection Performance Comparison**

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**Quality Control Charts and Health Surveillance**

Benneyan JC, Statistical Quality Control Methods in Infection Control and Hospital Epidemiology, Infection and Hospital Epidemiology, Vol. 19, (3) Part I: Introduction and Basic Theory Part II: Chart use, statistical properties, and research issues 1998 Survey article gives 135 references Many applications: monitoring surgical wound infections, treatment effectiveness, general nosocomial infection rate, … Monitoring process for “special causes” of variation Organize data into fixed-size groups of observations Look for out-of-control conditions by monitoring mean, standard deviation,… General 2-phase procedure: Phase I: Determine mean m, standard deviation s of process from historical “in-control” data; control limits often set to m 3s Phase II: Apply control limits prospectively to monitor process graphically

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**Adaptation of Traditional Process Control to Early Outbreak Detection**

On adapting statistical quality control to biosurveillance: Woodall , W.H. (2000). “Controversies and Communications in Statistical Process Control”, Journal of Quality Technology 32, pp “Researchers rarely…put their narrow contributions into the context of an overall SPC strategy. There is a role for theory, but theory is not the primary ingredient in most successful applications.” Woodall , W.H. (2006, in press). “The Use of Control Charts in Health Care Monitoring and Public Health Surveillance” “In industrial quality control it has been beneficial to carefully distinguish between the Phase I analysis of historical data and the Phase II monitoring stage” “It is recommended that a clearer distinction be made in health-related SPC between Phase I and Phase II…” Does infectious disease surveillance require an “ongoing Phase I” strategy to maintain robust performance?

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**Statistical Process Control in Advanced Disease Surveillance**

Key application issues: Background data characteristics change over time Hospital/clinic visits, consumer purchases not governed by physical science, engineering But monitoring requires robust performance: algorithms must be adaptive Target signal: effect of infectious disease outbreak Transient signal, not a mean shift May be sudden or gradual

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**The Challenge of Data Modeling for Daily Health Surveillance**

Conventional scientific application of regression Do covariates such as age, gender affect treatment? Does treatment success of differ among sites if we control for covariates? Studies use static data sets with exploratory analysis In surveillance, we model to predict data levels in the absence of the signal of interest Need reliable estimates of expected levels to recognize abnormal levels Data sets dynamic—covariate relationships change

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**The Challenge of Data Modeling for Daily Health Surveillance, cont’d**

Modeling to generate expected data levels Predictive accuracy matters, not just strength of association or overall goodness-of-fit For a gradual outbreak, recent data can “train” model to predict abnormal levels Alerting decisions based on model residuals Residual = observed value – modeled value Conventional approach: assume residuals fit a known distribution (normal, Poisson,…) hypothesis test for membership in that distribution For surveillance, can also apply control-chart methods to residuals

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**Monitoring Data Series with Systematic Features**

Problem: How to account for short-term trends, cyclic data features in alerting decisions? Approaches Data Modeling Regression: GLM, ARIMA, others & combinations Signal Processing LMS filters and wavelets Exponential Smoothing: generalizes EWMA

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**Example: OTC Purchasing Behavior Influenced by Many Factors**

Loglinear Regression Example: Tracking Daily Sales of Flu Remedies Log(Y) = b0 + b1-6d + b7t + b8-9h +b10w + b11p + e daily count of anti-flu sales day of week (6 indicators) linear trend harmonic (seasonal) weather (temp.) sales promotion (indicator) deviation (Poisson dist.) 2a. The black curve on this plot shows daily sales of flu remedies from a large urban region. 2b. The blue curve gives the fitted values from a single regression model over the entire interval on all data features shown except for sales promotions; will discuss model specifics on next slides. 2c. The drop called “unusual weather” was during a heatwave.

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**Recent Surveillance Method Based on Loglinear Regression**

Modeling emergency department visit patterns for infectious disease complaints: results and application to disease surveillance Judith C Brillman , Tom Burr , David Forslund , Edward Joyce , Rick Picard and Edith Umland BMC Medical Informatics and Decision Making 2005, 5:4, pp 1-14 Modeling visit counts on day d: Let S(d) = log ( visits(day d) + 1 ), the “started log” S(d) = [Σi ci × Ii(d)] + [c8 + c9 × d] + [c10 × cos(kd) + c11 × sin(kd)], k = 2π / c1-c7 day-of-week effects c9 long-term trend c10-c11 seasonal harmonic terms Training period: 3036 days ~ 8.33 years Test period: 1 year 2a. The black curve on this plot shows daily sales of flu remedies from a large urban region. 2b. The blue curve gives the fitted values from a single regression model over the entire interval on all data features shown except for sales promotions; will discuss model specifics on next slides. 2c. The drop called “unusual weather” was during a heatwave.

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Brillman et. al. Figure 1 2a. The black curve on this plot shows daily sales of flu remedies from a large urban region. 2b. The blue curve gives the fitted values from a single regression model over the entire interval on all data features shown except for sales promotions; will discuss model specifics on next slides. 2c. The drop called “unusual weather” was during a heatwave.

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**EWMA Monitoring Exponential Weighted Moving Average**

Average with most weight on recent Xk: Sk = wS k-1 + (1-w)Xk, where 0 < w < 1 Test statistic: Sk compared to expectation from sliding baseline Basic idea: monitor (Sk – mk) / sk Added sensitivity for gradual events Larger w means less smoothing

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**EWMA Concept & Smoothing Constant**

Brown, R.G. and Meyer, R.F. (1961), "The Fundamental Theorem of Exponential Smoothing," Operations Research, 9, Exponential smoothing represents “an elementary model of how a person learns”: xk = xk-1 + w (xk - xk-1) where 0 < w < 1 For the smoothed value Sk, Sk = wS k-1 + (1-w)Xk , The variance of Sk is sS = [w / (2 - w)] sX So a smaller w is preferred because it gives a more stable Sk; values between 0.1 and 0.3 often used But Chatfield: changes in global behavior will result in a larger optimal w

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**Generalized Exponential Smoothing**

Holt-Winters Method: modeling level, trend, and seasonality Annex_B_The_Holt-Winters_forecasting_method.pdf Forecast Function: where: mj = level at time j, bj = trend at time j, cj = periodic multiplier at time j s = periodic interval k = number of steps ahead and mj, bj, cj are updated by exponential smoothing

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**Holt-Winters Updating Equations**

Updating Equations, multiplicative method: Level at time t: Slope at time t: Periodic multiplier at time t: And choice of initial values m0, b0, c0,…cs-1 should be calculated from available data

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**Forecasting Local Linearity: Automatic vs Nonautomatic Methods**

Chatfield, C. (1978), "The Holt-Winters Forecasting Procedure," Applied Statistics, 27, Chatfield, C.and Yar, M. (1988), "Holt-Winters Forecasting: Some Practical Issues, " The Statistician, 37, “Modern thinking favors local linearity rather than global linear regression in time…” “Local linearity is also implicit in ARIMA modelling…” Simple EWMA ~ ARIMA(0,1,1) EWMA + trend ~ ARIMA(0,2,2) Multiplicative Holt-Winters has no ARIMA equivalent “Practical considerations rule out [Box-Jenkins] if there are insufficient observations or …expertise available” “Box-Jenkins… requires the user to identify an appropriate… [ARIMA] model” For “fair” comparison of H-W to B-J, have both automatic or nonautomatic. Assertion: The simplicity of H-W permits easier classification, requiring less historic data. Can an automatic B-J give robust forecasting over a range of input series types?

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**Regression vs Holt-Winters**

Ongoing study with Galit Shmueli, U. of MD Sean Murphy, JHU/APL 30 time series, 700 days’ data 5 cities 3 data types 2 syndromes Respiratory: seasonal & day-of-week behavior Gastrointestinal: day-of-week effects

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**Temporal Aggregation for Adaptive Alerting**

Data stream(s) to monitor in time: Counts to be tested for anomaly Nominally 1 day Longer to reduce noise, test for epicurve shape Will shorten as data acquisition improves test interval baseline interval Used to get some estimate of normal data behavior Mean, variance Regression coefficients Expected covariate distrib. -- spatial -- age category -- % of claims/syndrome guardband Avoids contamination of baseline with outbreak signal

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**Candidate Methods 1. Global loglinear regression of Brillman et. al.**

2. Holt-Winters exponential smoothing fixed sets of smoothing parameters for data: with both day-of-week & seasonal behavior with only day-of-week behavior 3. Adaptive Regression Log(Y) = b0 + b1-6d + b7t + b8hol + b9posthol + e 56-day baseline, 2-day guardband b1-6 = day-of-week indicator coefficient b7 = centered ramp coefficient b8 = coefficient for holiday indicator b9 = coefficient for post-holiday indicator 1-day ahead and 7-day-ahead predictions

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**Respiratory Visit Count Data**

--- Holt-Winters --- Regression --- Adaptive Regr. All series display this autocorrelation; good test for published regression model

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**GI Visit Count Data --- Data --- Holt-Winters --- Regression**

--- Adaptive Regr.

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**Stratified Residual Comparisons**

--- Data --- Holt-Winters --- Regression --- Adaptive Regr.

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**Mean Residual Comparison**

When mean residuals favor regression, difference is small, and this difference results from largest residuals If the holiday terms in adaptive regression are removed, H-W means uniformly smaller

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**Median Residual Comparison**

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**Residual Autocorrelation Comparison**

--- Data --- Holt-Winters --- Regression --- Adaptive Regr.

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**Residual Autocorrelation Comparison 1-Day Ahead Predictions**

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**Residual Autocorrelation Comparison 7-Day Ahead Predictions**

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Summary Data-adaptive methods are required for robust prospective surveillance Appropriate algorithm selection requires an automated data classification methodology, often with little data history Statistical expertise is required to manage practical issues to maintain required detection performance as datasets evolve: stationarity (causes rooted in population behavior, evolving informatics, others) late reporting data dropouts

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Research Directions Classification of time series for automatic forecasting Easier for Holt-Winters than for Box-Jenkins? Determining reliable discriminants: Autocorrelation coefficients Simple means/medians Goodness-of-fit measures How little startup data history required? Most effective alerting algorithm using residuals, given signal of interest Apply control chart to residuals? Need to detect both sudden, gradual signals Detection performance constraints: Minimum detection sensitivity Maximum background alert rate

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