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tected in a study of this size. The committee could only conclude that this study provided no evidence of a large effect.

A different approach was taken to calculate the power of the statistical tests used in a retrospective epidemiologic study by Shields and colleagues (1988). As described in Chapters 4 and 5 of this report, Shields and colleagues ascertained the age distribution of cases of SIDS and of a number of neurologic disorders in Denmark during two time periods with different vaccination schedules. During the 1967-1968 time period, DPT was given at ages 5, 6, 7, and 15 months; in 1972-1973, DPT was given at ages 5 and 9 weeks and 10 months. Shields and colleagues recorded the number of adverse events occurring in the following age intervals: 1 to 3, 4 to 8, 9 to 11, 12 to 14, 15 to 19, and 20 to 23 months. Although Shields and colleagues tested whether the entire distributions of cases differed between the two time periods, the committee's power calculations were based on a comparison of the proportions in two noncontinuous age groups.1 Group 1 was defined as age 4 to 8 months and age 12 or more months, so that a possible increase in the number of cases consistent with the 1967-1968 vaccination schedule could be detected. Group 2 was defined as ages 1 to 3 months and 9 to 11 months, so that a possible increase in the number of cases consistent with the 1972-1973 vaccination schedule could be detected.

The power calculations are based on the assumption that if there is an increase in the risk of the adverse event shortly following DPT vaccination, the proportion of cases in the time period in which most of the vaccinations take place should increase. More precisely, define pi as the expected number of cases in age group 1 in time period i, p0 as the expected proportion of non-vaccine-associated cases in the same group (independent of time period), and qi as the proportion of vaccinations in the same age group and time period. Furthermore, suppose that a proportion k/(1 + k) of the adverse events in an age-period group are caused by the vaccines so that the expected value of pi equals (p0 + qi k)/(1 + k). Under these assumptions, given qi and the number of vaccinations administered in each time period as reported by Shields and colleagues (1988), one can calculate the expected difference between the two time periods in the proportion of cases in age group 1, p2 - p1, its standard deviation, and thus the power of the test for a given value of k. Such calculations were performed for a range of appropri-

1 A more general version of the power calculations involving more than two groups was developed by Frederick Mosteller and Elizabeth Burdick of Harvard University (personal communication, 1991), and formed the mathematical basis of the simplified model used by the committee. The more complete model requires computer simulations for evaluation and is, thus, more complicated to implement. It was found, however, to yield results similar to those of the simplified model used here.



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