{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T06:21:49Z","timestamp":1790749309518,"version":"4.1.0"},"reference-count":61,"publisher":"Wiley","issue":"10","license":[{"start":{"date-parts":[[2011,1,17]],"date-time":"2011-01-17T00:00:00Z","timestamp":1295222400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2011,1,17]],"date-time":"2011-01-17T00:00:00Z","timestamp":1295222400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"},{"start":{"date-parts":[[2011,1,17]],"date-time":"2011-01-17T00:00:00Z","timestamp":1295222400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2011,5,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Infectious disease counts from surveillance systems are typically observed in several administrative geographical areas. In this paper, a non\u2010linear model for the analysis of such multiple time series of counts is discussed. To account for heterogeneous incidence levels or varying transmission of a pathogen across regions, region\u2010specific and possibly spatially correlated random effects are introduced. Inference is based on penalized likelihood methodology for mixed models. Since the use of classical model choice criteria such as AIC or BIC can be problematic in the presence of random effects, models are compared by means of one\u2010step\u2010ahead predictions and proper scoring rules. In a case study, the model is applied to monthly counts of meningococcal disease cases in 94 departments of France (excluding Corsica) and weekly counts of influenza cases in 140 administrative districts of Southern Germany. The predictive performance improves if existing heterogeneity is accounted for by random effects. Copyright \u00a9 2011 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.4177","type":"journal-article","created":{"date-parts":[[2011,1,18]],"date-time":"2011-01-18T03:38:32Z","timestamp":1295321912000},"page":"1118-1136","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":81,"title":["Predictive assessment of a non\u2010linear random effects model for multivariate time series of infectious disease counts"],"prefix":"10.1002","volume":"30","author":[{"given":"M.","family":"Paul","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L.","family":"Held","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2011,1,17]]},"reference":[{"key":"e_1_2_8_2_2","volume-title":"Modern Infectious Disease Epidemiology","author":"Giesecke J","year":"2002"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2531732"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1198\/016214503388619238"},{"key":"e_1_2_8_5_2","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.tm08270"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1191\/1471082X05st098oa"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00177"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3440"},{"key":"e_1_2_8_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(02)00232-X"},{"key":"e_1_2_8_10_2","doi-asserted-by":"publisher","DOI":"10.1080\/10543400600719467"},{"key":"e_1_2_8_11_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1991.10475006"},{"key":"e_1_2_8_12_2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00183"},{"key":"e_1_2_8_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9076-1_1"},{"key":"e_1_2_8_14_2","doi-asserted-by":"publisher","DOI":"10.1348\/000711005X79857"},{"key":"e_1_2_8_15_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9469.2006.00524.x"},{"key":"e_1_2_8_16_2","doi-asserted-by":"publisher","DOI":"10.2307\/2290687"},{"key":"e_1_2_8_17_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxj016"},{"key":"e_1_2_8_18_2","unstructured":"HofmannM. Statistical models for infectious disease surveillance counts. Ph.D. Thesis Ludwig\u2010Maximilians\u2010Universit\u00e4t Munich 2007. Available from:http:\/\/edoc.ub.uni\u2010muenchen.de\/6601\/."},{"key":"e_1_2_8_19_2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9876.00396"},{"key":"e_1_2_8_20_2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00353"},{"key":"e_1_2_8_21_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxm049"},{"key":"e_1_2_8_22_2","volume-title":"Model Selection and Multimodel Inference. A Practical Information\u2014Theoretic Approach","author":"Burnham KP","year":"2002"},{"key":"e_1_2_8_23_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/92.2.351"},{"key":"e_1_2_8_24_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asq042"},{"key":"e_1_2_8_25_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asn023"},{"key":"e_1_2_8_26_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/85.1.13"},{"key":"e_1_2_8_27_2","doi-asserted-by":"publisher","DOI":"10.1214\/07-AOS517"},{"key":"e_1_2_8_28_2","doi-asserted-by":"publisher","DOI":"10.2307\/2981683"},{"key":"e_1_2_8_29_2","doi-asserted-by":"publisher","DOI":"10.1002\/for.3980040305"},{"key":"e_1_2_8_30_2","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000001437"},{"key":"e_1_2_8_31_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3437-9"},{"key":"e_1_2_8_32_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00180-007-0074-8"},{"key":"e_1_2_8_33_2","volume-title":"Branching Processes: Variation, Growth, and Extinction of Populations","author":"Haccou P","year":"2007"},{"key":"e_1_2_8_34_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/4.2.279"},{"key":"e_1_2_8_35_2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522065.001.0001","volume-title":"Time Series.A Biostatistical Introduction","author":"Diggle PJ","year":"1990"},{"key":"e_1_2_8_36_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00140873"},{"key":"e_1_2_8_37_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00116466"},{"key":"e_1_2_8_38_2","doi-asserted-by":"publisher","DOI":"10.1201\/9780203492024"},{"key":"e_1_2_8_39_2","doi-asserted-by":"publisher","DOI":"10.2307\/2983331"},{"key":"e_1_2_8_40_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/78.4.719"},{"key":"e_1_2_8_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/0378-3758(95)00067-4"},{"key":"e_1_2_8_42_2","doi-asserted-by":"publisher","DOI":"10.1198\/106186002862"},{"key":"e_1_2_8_43_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1986.10478240"},{"issue":"3","key":"e_1_2_8_44_2","first-page":"624","article-title":"A note on Gauss\u2013Hermite quadrature","volume":"81","author":"Liu Q","year":"1994","journal-title":"Biometrika"},{"key":"e_1_2_8_45_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/82.1.81"},{"key":"e_1_2_8_46_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10476971"},{"key":"e_1_2_8_47_2","unstructured":"KneibT. Mixed model based inference in structured additive regression. Ph.D. Thesis LMU M\u00fcnchen: Fakult\u00e4t f\u00fcr Mathematik Informatik und Statistik 2006. Available from:http:\/\/edoc.ub.uni\u2010muenchen.de\/5011\/."},{"key":"e_1_2_8_48_2","doi-asserted-by":"publisher","DOI":"10.1007\/b98818"},{"key":"e_1_2_8_49_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2009.01191.x"},{"issue":"1","key":"e_1_2_8_50_2","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1111\/j.2517-6161.1952.tb00104.x","article-title":"Rational decisions","volume":"14","author":"Good IJ","year":"1952","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"e_1_2_8_51_2","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0450(1969)008<0985:ASSFPF>2.0.CO;2"},{"key":"e_1_2_8_52_2","doi-asserted-by":"publisher","DOI":"10.2307\/1392185"},{"key":"e_1_2_8_53_2","doi-asserted-by":"publisher","DOI":"10.1175\/WAF989.1"},{"key":"e_1_2_8_54_2","doi-asserted-by":"publisher","DOI":"10.2307\/2685470"},{"key":"e_1_2_8_55_2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00315"},{"key":"e_1_2_8_56_2","unstructured":"Robert Koch Institute. SurvStat. Available from:http:\/\/www3.rki.de\/SurvStat(March2009)."},{"key":"e_1_2_8_57_2","series-title":"Wiley Series in Probability and Statistics","volume-title":"Bayesian Methods for Nonlinear Classification and Regression","author":"Denison DGT","year":"2002"},{"issue":"3","key":"e_1_2_8_58_2","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1111\/j.2517-6161.1983.tb01258.x","article-title":"Regression, prediction and shrinkage","volume":"45","author":"Copas JB","year":"1983","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"e_1_2_8_59_2","doi-asserted-by":"publisher","DOI":"10.1177\/096228029700600206"},{"key":"e_1_2_8_60_2","doi-asserted-by":"publisher","DOI":"10.1093\/imaman\/dpl010"},{"key":"e_1_2_8_61_2","volume-title":"Elements of Statistical Computing. Numerical Computation","author":"Thisted RA","year":"1988"},{"key":"e_1_2_8_62_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971200"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.4177","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.4177","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.4177","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T21:54:19Z","timestamp":1740866059000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.4177"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,17]]},"references-count":61,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2011,5,10]]}},"alternative-id":["10.1002\/sim.4177"],"URL":"https:\/\/doi.org\/10.1002\/sim.4177","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1,17]]}}}