Statistical approaches to establishing vaccine safety

Abstract

In a vaccine safety trial, the primary interest is to demonstrate that the vaccine is sufficiently safe, rejecting the null hypothesis that the relative risk of an adverse event attributable to the new vaccine is above a prespecified value, greater than one. We evaluate the exact probability of type I error of the likelihood score test, with sample size determined by normal approximation, by enumeration of the binomial outcomes in the rejection region and show that it exceeds the nominal level. In the case of rare adverse events, we recommend the Poisson approximation as an alternative and develop the corresponding conditional and unconditional tests. We give sample size and power calculations for these tests. We also propose optimal randomization strategies which either (i) minimize the total number of adverse cases or (ii) minimize the expected number of subjects when the vaccine is unsafe. We illustrate the proposed methods using a hypothetical vaccine safety study.

Subject allocation and study curtailment for fixed event comparative poisson trials

“…For example, using the arcsine transformation, a similar result to (6) now gives k = 1=(1 + √ q) person years to treatment minimizes T (E) for adverse event studies, which places a smaller portion in treatment. Others have also observed that T (E) and E[N u+t ] for comparative Poisson studies of adverse events tend to be minimized with more subjects in the untreated group [7].…”

“…The author thanks Bill Blackwelder for helpful discussion on this paper and two anonymous referees for very thorough review and insightful comments, including derivation of formula (7).…”

“…For the related problem of comparing binomial proportions between two samples, allocating more subjects to groups with lower rates under H a often maximizes power [3,4], particularly for superiority hypotheses [5,6]. Dragalin et al [7] evaluated subject randomization ratios for comparative Poisson designs similar to those considered here; their null hypothesis was H 0 : r * = r 0 (for r 0 ¿1) rather than H 0 : r * = 1, and found that unequal subject allocation often decreased required T and expected N u+t below that for equal subject allocation [7]. It should be noted, however, that the logistic ability of studies to maintain a planned allocation k varies due to random drop-out or discovery of ineligibility if subjects are followed for short lengths of time, and also due to di erential subject follow up for studies of persons followed indeÿnitely until the date of analysis.…”

“…But as many have noted [7][8][9][10], if treatment group of cases is known as they occur, studies can be stopped once (i) C + 1 cases occur in the treatment group and H 0 accepted or (ii) T − C cases occur in the untreated subjects and H 0 rejected. Consider a study with k = 0:5 allocation and a onesided type 1 error of = 0:025 that will be stopped at T = 72 events in both groups.…”

“…For any given size and power, a study stopped at T = 20 Alzheimer's diseases cases might be less expensive and ethically preferable to one stopped at T = 30, while a study with N u+t = 100 000 person years should be cheaper than one with N u+t = 150 000. Two strategies that may reduce N u+t and T are: (1) optimizing k, the portion of person years under treatment [2][3][4][5][6][7] and (2) early (or curtailed) stopping once the number of cases in the treated or untreated group indicates that the null hypothesis already has been rejected or accepted [8][9][10].…”