Sample Size Considerations for Assessing Vaccine Consistency Through Equivalence
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SAMPLE SIZE CONSIDERATIONS FOR ASSESSING VACCINE CONSISTENCY THROUGH EQUIVALENCE BRIGITTE CHEUVART, PHD Senior Statistician
ANNEBOLLAERTS, MSc Statistician SmithKline Beecham Biological s.a., Rixensart, Belgium
The aim of a consistency study is toprove equivalence between multiplepairs ofproduction batches. In this paper it is shown that an adequate overall power to conclude consistency can be achieved by using the principle of Bonferroni adjustment on the type I1 error: Simulations suggest that the nominul alpha level for pairwise comparison of batches can be increased above 0.05 in order to maintain the overall type I error of concluding false consistency below 0.05. Key Words: Multiple comparison; Equivalence; Vaccine; Consistency; Sample size
INTRODUCTION VACCINE DEVELOPMENT IS contingent to specific regulatory requirements. One of them is to ensure that the vaccine production process leads to consistent batches in terms of efficacy/safety response (1). The classical design to address consistency is to randomize subjects to different batches. The number of available batches is usually limited to 3-5 when the vaccine is in the development phase. Responses observed for each batch are then compared to each other and there is evidence of consistency if the response does not vary clinically significantly among batches. This comparison relates to the issue of equivalence and multiple comparisons since one wants to rule out that at least two batches differ significantly. Methodology to deal with equivalence has been developed in
the past decade (2) but most of the literature on multiple comparisons addresses the case where a study is successful when one rejects the null hypothesis for at least one of the multiple comparisons (3). It is recognized that, when one wants to rejects simultaneously the null hypothesis for all comparisons, no penalty (eg, Bonferroni adjustment) should be applied on the nominal alpha level used in each comparison ( 4 3 . The negative impact on the power is acknowledged but sample size considerations for maintaining an adequate type I1 error (type I1 error= 1 -power) have not been discussed to the authors’ knowledge. This paper is an attempt to clarify how the sample size could be adjusted to successfully conclude, in this case of interest, consistency.
THE PRINCIPLE FOR SAMPLE SIZE COMPUTATION Reprint address: Brigitte Cheuvan. Smithfine Beecham Biological s.a., Clinical R&D, 89 Rue de I’Institut, B1330 Rixensart, Belgium.
The objective of a consistency study is to rule out the possibility that the batches differ
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Brigitte Cheuvart and Anne Bollaerts
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from each other by more than a given clinically defined value, 6. This can be formally expressed as: Ho (no consistency): for at least two batches (i,j), Distance(i,j) > 6. versus Ha (consistency): for all pair of batches (ij), Distance(i,j) < = 6. The distance between two batches could
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