Time series vs. point processes for space-time surveillance in - PowerPoint PPT Presentation

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References Time series vs. point processes for space-time surveillance in public health ohle 1 , 2 Thais Correa 3 Michael H¨ 1 Department of Statistics, Ludwig-Maximilians-Universit¨ at M¨ unchen, Germany 2 Munich Center of Health Sciences, Germany 3 Department of Mathematics, Universidade Federal de Ouro Preto, Brazil Joint workshop of 3 IBS German Region workgroups L¨ ubeck, 02-05 December, 2009 M. H¨ ohle 1/ 28

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References Outline Motivation 1 Case study: Invasive Meningococcal Disease 2 Temporal Monitoring 3 Spatio-temporal Monitoring 4 Discussion 5 M. H¨ ohle 2/ 28

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References Motivation Consider outbreak detection within the framework of statistical process control Contrast the count data time series approach in H. and Paul (2008) with the spatio-temporal point process approach in Assun¸ c´ ao and Correa (2009). Idea: extend the spatio-temporal method to a regression model based approach. Hence, no quantitative comparisons a few qualitative considerations Aim of the talk is thus more to introduce the two views on outbreak detection M. H¨ ohle 3/ 28

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References Invasive Meningococcal Disease (IMD) in Germany IMD is an infectious bacterial disease causing life-threatening meningitis and sepsis conditions. Co-operation with the German National Reference for Meningococci hosted at the Institute for Hygiene and Microbiology at the University of W¨ urzburg. Data consists of 336 cases of finetype B:P1.7-2,4:F1-5 (abbrv. B) and 300 cases of C:P1.5,2:F3-3 (abbrv. C) during 2002–2008 in Germany Research questions: Perform a temporal, spatial and spatio-temporal routine surveillance of disease cases to detect emerging clusters Quantify differences in the dynamics of the two finetypes M. H¨ ohle 4/ 28

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References IMD in Germany – Temporal Incidence Times series of monthly number of counts for each finetype aggregated for entire Germany: B C 15 15 10 10 No. infected No. infected 5 5 0 0 2002 2004 2006 2008 2002 2004 2006 2008 1 1 1 1 1 1 1 1 time time M. H¨ ohle 5/ 28

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References IMD in Germany – Spatial Incidence Spatial resolution at postcode level. Multiplicity indicated by the radius of the circles: ● ● ● ● ● ● ● ● ● ● ● ● 8000 8000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 7000 7000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 6000 ● ● ● ● ● ● ● ● ● 6000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 5000 5000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 4000 ● ● ● ● ● ● ● 4000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3000 ● ● 3000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 2000 ● 2000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1000 ● ● ● 1000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● (a) Finetype B (b) Finetype C Also shown are the population densities (persons per km 2 ) of the 413 administrative regions in Germany. M. H¨ ohle 6/ 28

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References CUSUM based Temporal Monitoring (1) Prospective change-point detection in GLMs using likelihood ratio cumulative sum (CUSUM) methods: f k ( X 1 , . . . , X n ) T A = min n ≥ 1 { r ( X n ) ≥ A } , r ( X n ) = max f ∞ ( X 1 , . . . , X n ) 1 ≤ k ≤ n The joint distribution f ∞ ( x n ) is modelled by independent variables given by a log-linear Poisson model, i.e. n � f ∞ ( x n ) = f ( x t ; β ) t =1 Null-hypothesis: The time varying mean is µ t = E ∞ ( X t ) e.g. modeled as S � � 2 π � � 2 π �� � log µ t = β 0 + β 1 · t + β 2 s sin + β 2 s +1 cos . 12 t 12 t s =1 M. H¨ ohle 7/ 28

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References CUSUM based Temporal Monitoring (2) Alternative-hypothesis: The mean in the model for f k ( x ) is specified as E k ( X t ) = µ t · κ I ( t ≥ k ) , with I ( · ) being the indicator function and κ > 1 the prespecified relative change to detect optimal against. Historic data are used to estimate the regression parameters β under the null-model. In the subsequent monitoring the resulting estimation uncertainty is ignored. In case of fixed β and κ the loglikelihood ratio monitoring can be performed by the recursive form � f n ( x n ) � �� r 0 = 0 , r n = max 0 , r n − 1 + log . f ∞ ( x n ) M. H¨ ohle 8/ 28

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References Results: Monitoring Meningococci Finetype C Use first 3 years to estimate β in a Poisson GLM with S = 1. Monitor with A = 4 . 5 and κ = 2. µ t κµ t 10 No. infected 8 6 4 2 0 2005 2006 2007 2008 1 1 1 1 time (months) A Markov chain approximation (H., 2010) yields median ∞ ( T A ) = 226 and P ∞ ( T A ≤ 48) = 0 . 11. M. H¨ ohle 9/ 28

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References Spatio-temporal monitoring (1) – Setup Let X be a Poisson process in the three-dimensional region W × [0 , T ] where W ⊆ R 2 and having space-time intensity function λ ( s , t ). Let N ( A ) denote the random number of events of X in region A ⊆ W × [0 , T ] and define � µ ( A ) = E ( N ( A )) = λ ( s , t ) d s dt . A In other words we assume N ( A ) ∼ Po( µ ( A )). Furthermore, we will assume a separable intensity λ ( s , t ) = µ λ S ( s ) λ T ( t ) , with µ > 0, and λ S ( s ) and λ T ( t ) denoting spatial and temporal marginal densities. M. H¨ ohle 10/ 28

Motivation Case Study Temporal Monitoring Spatio-temporal Monitoring Discussion References Spatio-temporal monitoring (2) – Hypothesis Null Intensity λ ( s , t ) = µ λ S ( s ) λ T ( t ). Alternative For a time τ > 0 and a cylinder C τ we have λ ( s , t ) = µ λ S ( s ) λ T ( t ) (1 + ε I C τ ( s , t )) where I C τ ( s , t ) is an indicator function for ( s , t ) ∈ C τ and ε > 0 is the predetermined relative intensity change . M. H¨ ohle 11/ 28