dose and the time from the second to the third dose, by including both of them as two separate independent variables. The same applies for early-onset adverse events after subsequent doses.

If an excess risk is found, it is not clear from this design whether it is an excess risk due to the time length between the vaccinations or if there is an excess risk driven purely by the first dose and where the timing of the adverse event is such that it happens soon after the second dose in children that receive the second dose sooner. By estimating the temporal function of any excess risk due to dose number 1 alone, this can be adjusted for by including it either as an offset term or as an additional variable in the regression model, which then also may include children who never received dose two. An alternative, simpler approach is to limit the study to children where the doses are given at least x days apart, where x is chosen to be large enough that it is unlikely that there is any excess risk beyond that time that is purely due to the first dose.

If there is some evidence from the observational study that there is a differential risk depending on the time between vaccinations but it is not conclusive, then a randomized trial could be conducted. For example, in a study of a rotavirus vaccine, children may be randomized to receive the three doses at age 2, 4, and 6 months of age, according to the CDC-recommended vaccine schedule, plus a placebo dose at age 9 months, versus three doses at age 2, 6, and 9 months, plus a placebo dose at age 4 months. The results from the observational study, with its wide variety of schedules, can be used to inform the definition of the study arms in the randomized trial. Note, though, that if the adverse event is rare, a randomized trial is not a feasible approach, as the required sample size would be very large, and hence, the cost of the trial would be prohibitively expensive.

Late-Onset Adverse Events

Data

The use of electronic health data is suitable for late-onset adverse events that occur within a few years after the last dose and for vaccines for which all doses of interest are given within a year or two. For late-onset events and longer times between doses, health plan data may be less suitable, as only some members will have been enrolled long enough to be informative.

Methods

The same methods used for early-onset events can be used for late-onset adverse events, with some modifications. Most importantly, rather than defining adverse events in terms of a predefined risk window after the last



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