use a temporal scan statistic. For a cohort of vaccinees with a subsequent event of interest, record the number of days from vaccination to the event. Ignore events that occur on the same day as the vaccination, as they may have a different background rate, as well as those that occur beyond an upper limit, such as 70 days after vaccination. If there is no relationship between the vaccine and the adverse event, we expect the adverse events to be uniformly distributed during the [1, 70]-day period. The temporal scan statistic scans the time period for any cluster of events, without any assumptions about their location or length. The method determines the statistical significance of such clusters, adjusting for the multiple testing inherent in the hundreds of overlapping time periods evaluated. As an example, temporal scan statistics were used to determine that the excess risk of seizures after vaccination with MMRV is confined to the 7- to 10-day postvaccination period (Klein et al., 2010).

The second step is to evaluate the relationship between age at vaccination and excess risk of the adverse event. The simplest and most common way to do this is to divide age into different groups, such as 6 to 12 months and 12 to 24 months, and compare the risk. It is unrealistic to assume that the risk suddenly jumps at a particular age, and for greater precision, it is better to model risk as a continuous function of age. This can be done by the use of either regression with first-, second-, and higher-degree polynomials or regression splines (Rothman et al., 2006).

In these analyses, it is important to take the underlying natural age-related risk into account. For example, the incidence of intussusceptions is very low immediately after birth, after which it gradually increases until about 5 months of age, after which it gradually decreases (Eng et al., 2012). There are a number of possible ways to adjust for this, depending on the exact study design. In a cohort study of vaccinated individuals, one can use historical data to estimate the age curve, using a polynomial function, and then use that as an offset term in the regression model. An alternative approach is to use both a risk and control interval for each individual, in a self-controlled analysis, evaluating whether the relative risk in these intervals varies by age of vaccination. Note, though, that if the natural incidence rate for the adverse event varies greatly by age in weeks rather than years, it is still necessary to incorporate an offset term based on the natural age curve even when a self-controlled analysis is conducted. In a case-control study, matching by age ensures that the age-based incidence curve is adjusted for.

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