10:17:54 Modeling of seasonal baseline in influenza data using HMMs Al Ozonoff ∗ , Paola Sebastiani Boston University School of Public Health Department of Biostatistics aozonoff@bu.edu 1/27/06 Al Ozonoff 1/27/06 DIMACS Influenza – 1 / 30
10:17:54 Motivation • Old and new • National P+I mortality Approach Results Motivation Al Ozonoff 1/27/06 DIMACS Influenza – 2 / 30
10:17:54 Old motivation Motivation Originally motivated to improve performance of “syndromic • • Old and new surveillance” to detect outbreaks of disease, e.g. bioterrorist • National P+I mortality attack. Approach Paradigm: Establish what is “normal”, then be vigilant for Results • deviations from normal behavior. Some model is used for baseline; one-step-ahead prediction tells us what is expected; departure from this prediction (one-step-ahead residual) forms basis for test statistic. Typical approach is to model respiratory illness as sinusoid (i.e. • Serfling’s method) and look for additional outbreak signal on top of baseline. Problem with this approach: sinusoid fits data poorly during • influenza epidemic periods. Implication for prospective surveillance is decreased performance (i.e. lower power for detection of outbreaks) during epidemic periods. Al Ozonoff 1/27/06 DIMACS Influenza – 3 / 30
10:17:54 Old motivation Motivation Originally motivated to improve performance of “syndromic • • Old and new surveillance” to detect outbreaks of disease, e.g. bioterrorist • National P+I mortality attack. Approach Paradigm: Establish what is “normal”, then be vigilant for Results • deviations from normal behavior. Some model is used for baseline; one-step-ahead prediction tells us what is expected; departure from this prediction (one-step-ahead residual) forms basis for test statistic. Typical approach is to model respiratory illness as sinusoid (i.e. • Serfling’s method) and look for additional outbreak signal on top of baseline. Problem with this approach: sinusoid fits data poorly during • influenza epidemic periods. Implication for prospective surveillance is decreased performance (i.e. lower power for detection of outbreaks) during epidemic periods. Al Ozonoff 1/27/06 DIMACS Influenza – 3 / 30
10:17:54 Old motivation Motivation Originally motivated to improve performance of “syndromic • • Old and new surveillance” to detect outbreaks of disease, e.g. bioterrorist • National P+I mortality attack. Approach Paradigm: Establish what is “normal”, then be vigilant for Results • deviations from normal behavior. Some model is used for baseline; one-step-ahead prediction tells us what is expected; departure from this prediction (one-step-ahead residual) forms basis for test statistic. Typical approach is to model respiratory illness as sinusoid (i.e. • Serfling’s method) and look for additional outbreak signal on top of baseline. Problem with this approach: sinusoid fits data poorly during • influenza epidemic periods. Implication for prospective surveillance is decreased performance (i.e. lower power for detection of outbreaks) during epidemic periods. Al Ozonoff 1/27/06 DIMACS Influenza – 3 / 30
10:17:54 Old motivation Motivation Originally motivated to improve performance of “syndromic • • Old and new surveillance” to detect outbreaks of disease, e.g. bioterrorist • National P+I mortality attack. Approach Paradigm: Establish what is “normal”, then be vigilant for Results • deviations from normal behavior. Some model is used for baseline; one-step-ahead prediction tells us what is expected; departure from this prediction (one-step-ahead residual) forms basis for test statistic. Typical approach is to model respiratory illness as sinusoid (i.e. • Serfling’s method) and look for additional outbreak signal on top of baseline. Problem with this approach: sinusoid fits data poorly during • influenza epidemic periods. Implication for prospective surveillance is decreased performance (i.e. lower power for detection of outbreaks) during epidemic periods. Al Ozonoff 1/27/06 DIMACS Influenza – 3 / 30
10:17:54 New motivation Motivation Recent interest in influenza spurred by prospects of novel strain • • Old and new emerging to cause pandemic illness. Renewed effort to • National P+I mortality understand historical record of influenza epidemics; to model Approach spread of disease in space and time; to prepare for possibility Results (eventuality?) of pandemic. Seasonality of influenza not completely understood. Difficult to • model spatio-temporal patterns of disease. Data sources beyond traditional influenza surveillance data are increasingly becoming available. Improved modeling of several time series (dispersed across a • geographic area) may start with model for a single time series. Better temporal models ⇒ better spatio-temporal models. Al Ozonoff 1/27/06 DIMACS Influenza – 4 / 30
10:17:54 New motivation Motivation Recent interest in influenza spurred by prospects of novel strain • • Old and new emerging to cause pandemic illness. Renewed effort to • National P+I mortality understand historical record of influenza epidemics; to model Approach spread of disease in space and time; to prepare for possibility Results (eventuality?) of pandemic. Seasonality of influenza not completely understood. Difficult to • model spatio-temporal patterns of disease. Data sources beyond traditional influenza surveillance data are increasingly becoming available. Improved modeling of several time series (dispersed across a • geographic area) may start with model for a single time series. Better temporal models ⇒ better spatio-temporal models. Al Ozonoff 1/27/06 DIMACS Influenza – 4 / 30
10:17:54 New motivation Motivation Recent interest in influenza spurred by prospects of novel strain • • Old and new emerging to cause pandemic illness. Renewed effort to • National P+I mortality understand historical record of influenza epidemics; to model Approach spread of disease in space and time; to prepare for possibility Results (eventuality?) of pandemic. Seasonality of influenza not completely understood. Difficult to • model spatio-temporal patterns of disease. Data sources beyond traditional influenza surveillance data are increasingly becoming available. Improved modeling of several time series (dispersed across a • geographic area) may start with model for a single time series. Better temporal models ⇒ better spatio-temporal models. Al Ozonoff 1/27/06 DIMACS Influenza – 4 / 30
10:17:54 National P+I mortality Motivation • Old and new Weekly P&I mortality • National P+I mortality 1990−1996 Approach Results 1200 1000 Count 800 600 1990 1991 1992 1993 1994 1995 1996 Year (starting Sep 1) Al Ozonoff 1/27/06 DIMACS Influenza – 5 / 30
10:17:54 National P+I mortality Motivation • Old and new Weekly P&I mortality • National P+I mortality 1990−1996 Approach Results 1200 1000 Count 800 600 1990 1991 1992 1993 1994 1995 1996 Year (starting Sep 1) Al Ozonoff 1/27/06 DIMACS Influenza – 6 / 30
10:17:54 National P+I mortality Motivation • Old and new Residuals from sinusoidal model • National P+I mortality Approach 400 Results 300 200 100 Residual 0 −100 −200 1990 1991 1992 1993 1994 1995 1996 Year (starting Sep 1) Al Ozonoff 1/27/06 DIMACS Influenza – 7 / 30
10:17:54 Motivation Approach • Classical approach • Other approaches • HMMs • Evaluation Results Approach Al Ozonoff 1/27/06 DIMACS Influenza – 8 / 30
10:17:54 Classical approach Motivation Serfling’s model based upon observation that underlying • Approach seasonal baseline is roughly sinusoidal (also true for mortality of • Classical approach some diseases besides influenza). May be driven by temp; • Other approaches • HMMs annual patterns (e.g. school year); dynamics of disease. • Evaluation Results Y t = α 0 + α 1 t + β 1 sin (2 πt 52 ) + β 2 cos (2 πt 52 ) + ǫ t Because Serfling’s model reflects seasonal baseline, large • deviations above this baseline indicate epidemic state. Integrating residuals allows calculation of “excess mortality” i.e. mortality attributed to influenza above what would be expected, accounting for seasonal variation. Model performs well for what it is asked to do. However, not well • suited to making one -step-ahead predictions, since model fit is poor during epidemic state. Al Ozonoff 1/27/06 DIMACS Influenza – 9 / 30
10:17:54 Classical approach Motivation Serfling’s model based upon observation that underlying • Approach seasonal baseline is roughly sinusoidal (also true for mortality of • Classical approach some diseases besides influenza). May be driven by temp; • Other approaches • HMMs annual patterns (e.g. school year); dynamics of disease. • Evaluation Results Y t = α 0 + α 1 t + β 1 sin (2 πt 52 ) + β 2 cos (2 πt 52 ) + ǫ t Because Serfling’s model reflects seasonal baseline, large • deviations above this baseline indicate epidemic state. Integrating residuals allows calculation of “excess mortality” i.e. mortality attributed to influenza above what would be expected, accounting for seasonal variation. Model performs well for what it is asked to do. However, not well • suited to making one -step-ahead predictions, since model fit is poor during epidemic state. Al Ozonoff 1/27/06 DIMACS Influenza – 9 / 30
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