Testing for Superiority or Inferiority after Concluding Equivalence?
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0092-8615/200 1 Copyright 0 2001 Drug Information Association Inc.
TESTING FOR SUPERIORITY OR INFERIORITY AFTER CONCLUDING EQUIVALENCE? CHRISTY CHUANG-STEIN Clinical Biostatistics I, Pharmacia Corporation, Kalamazoo, Michigan
In this paper. we examine the issue of testing for superiority or inferiority following the equivalence conclusion. We contrast this situation with that of testing for superiority after a noninferiority conclusion. We point out the fact that further testing is irrelevant in situations where the equivalence definition renders the inferred true treatment effect difference nonsignificant from the clinical perspective. Consequently, superiority in the presence of an accompanying equivalence definition has a meaning that is different from its traditional interpretation. Key Words: Confidence interval; Equivalence; Noninferiority; Superiority
BACKGROUND
era1 recent papers (2,3,4, Wiens, unpublished data; 2000, etc.) The Committee for ProprieTHERE HAS BEEN A lot of discussion on tary Medicinal Products (CPMP) of the Eurotesting for superiority following the noninfepean Agency for the Evaluation of Medicinal riority conclusion. Let p, and pc denote the Products endorsed the strategy of inferentrue (but unknown) success rates of a new tially testing for superiority following a nontreatment (t) and its comparator (c) in a raninferiority conclusion in a “Point to Condomized trial, respectively. Let A (>O) be a sider” document issued by one of its expert quantity such that if p, - pc > -A, treatment t working groups (5). It is generally agreed is said to be noninferior to its comparator c. that this sequential testing strategy should be Sample size required to draw inference on prespecified in the protocol if it is to be the noninferiority can be found in Makuch and basis for inferential decision in the study. Simon (1). While acknowledging the appropriateness Testing superiority after concluding nonof the above sequential testing, Wiens (uninferiority implies that if the hypothesis of published data; 2000) pointed out an inherent H,: p, - pc -A at a prespecified significance drug development trials. The difficulty lies level 01, then one can test Ho: pI I pc versus with the fact that for the noninferiority claim, Ha: pl > pc at the same level 01 without inflatthe primary analysis group is typically the ing the overall type I error rate. Using data evaluable (per protocol) population. On the from the same trial to examine both noninfeother hand, the primary analysis group for the riority and superiority was the subject of sevsuperiority evaluation is the intent-to-treat ( I n ) population. Because these two populations often differ, the overall type I error Reprint address: Christy Chuang-Stein, Clinical Biostatistics I, Pharmacia Corporation, 7000 Portage Road, rate associated with this sequential testing Kalamazoo. MI 49001. procedure may be inflated. Even though this 141
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is an issue worthy of further investigation, we will not address this problem in this paper. Instead, we will assume that
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