{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T20:11:47Z","timestamp":1791922307519,"version":"4.3.4"},"reference-count":19,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2013,8,23]],"date-time":"2013-08-23T00:00:00Z","timestamp":1377216000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2015,9,1]],"date-time":"2015-09-01T00:00:00Z","timestamp":1441065600000},"content-version":"tdm","delay-in-days":739,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2014,2,20]]},"abstract":"<jats:p>The self\u2010controlled case series method, commonly used to investigate potential associations between vaccines and adverse events, requires information on cases only and automatically controls all age\u2010independent multiplicative confounders while allowing for an age\u2010dependent baseline incidence.<\/jats:p><jats:p>In the parametric version of the method, we modelled the age\u2010specific relative incidence by using a piecewise constant function, whereas in the semiparametric version, we left it unspecified. However, mis\u2010specification of age groups in the parametric version can lead to biassed estimates of exposure effect, and the semiparametric approach runs into computational problems when the number of cases in the study is moderately large. We, thus, propose to use a penalized likelihood approach where the age effect is modelled using splines.<\/jats:p><jats:p>We use a linear combination of cubic M\u2010splines to approximate the age\u2010specific relative incidence and integrated splines for the cumulative relative incidence. We conducted a simulation study to evaluate the performance of the new approach and its efficiency relative to the parametric and semiparametric approaches. Results show that the new approach performs equivalently to the existing methods when the sample size is small and works well for large data sets. We applied the new spline\u2010based approach to data on febrile convulsions and paediatric vaccines. 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