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Am J Epidemiol. 2012 Nov 15;176(10):949-57. doi: 10.1093/aje/kws158. Epub 2012 Oct 25.

Characterizing vaccine-associated risks using cubic smoothing splines.


Estimating risks associated with the use of childhood vaccines is challenging. The authors propose a new approach for studying short-term vaccine-related risks. The method uses a cubic smoothing spline to flexibly estimate the daily risk of an event after vaccination. The predicted incidence rates from the spline regression are then compared with the expected rates under a log-linear trend that excludes the days surrounding vaccination. The 2 models are then used to estimate the excess cumulative incidence attributable to the vaccination during the 42-day period after vaccination. Confidence intervals are obtained using a model-based bootstrap procedure. The method is applied to a study of known effects (positive controls) and expected noneffects (negative controls) of the measles, mumps, and rubella and measles, mumps, rubella, and varicella vaccines among children who are 1 year of age. The splines revealed well-resolved spikes in fever, rash, and adenopathy diagnoses, with the maximum incidence occurring between 9 and 11 days after vaccination. For the negative control outcomes, the spline model yielded a predicted incidence more consistent with the modeled day-specific risks, although there was evidence of increased risk of diagnoses of congenital malformations after vaccination, possibly because of a "provider visit effect." The proposed approach may be useful for vaccine safety surveillance.

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