Tests for Equivalence or Noninferiority Between Two Proportions

Self Cite

135

Assessment of therapeutic equivalence or non-inferiority between two medical diagnostic procedures often involves comparisons of the response rates between paired binary endpoints. The commonly used and accepted approach to assessing equivalence is by comparing the asymptotic confidence interval on the difference of two response rates with some clinical meaningful equivalence limits. This paper investigates two asymptotic test statistics, a Wald-type (sample-based) test statistic and a restricted maximum likelihood estimation (RMLE-based) test statistic, to assess equivalence or non-inferiority based on paired binary endpoints. The sample size and power functions of the two tests are derived. The actual type I error and power of the two tests are computed by enumerating the exact probabilities in the rejection region. The results show that the RMLE-based test controls type I error better than the sample-based test. To establish an equivalence between two treatments with a symmetric equivalence limit of 0.15, a minimal sample size of 120 is needed. The RMLE-based test without the continuity correction performs well at the boundary point 0. A numerical example illustrates the proposed procedures.

“…Denote the sample estimates of p 10 and p 01 byp 10 = x 10 =n andp 01 = x 01 =n, respectively. Under the trinomial model, the estimateÂ =p 10 (2) at the level is given by…”

Section: Asymptotic Testsmentioning

confidence: 99%

Tests for equivalence or non‐inferiority for paired binary data

Liu

Hsueh

Hsieh

et al. 2001

Self Cite

135

“…Similarly, the larger the 2 -value the greater the loss of speciÿcity we expect from the combined test. In general, it is proposed that 0:106 1; D ; 2; D 60:20 for rate di erence and 1; R ; 2; R = 1:25 for rate ratio [12]. In practice, one would expect greater gain (i.e.…”

Section: Discussionmentioning

confidence: 99%

On simultaneous assessment of sensitivity and specificity when combining two diagnostic tests

Tang

2004

Diagnostic tests are seldom adopted in isolation. Few tests have high sensitivity and specificity simultaneously. In these cases, one can increase either the sensitivity or the specificity by combining two component tests under either the 'either positive' rule or the 'both positive' rule. However, there is a tradeoff between sensitivity and specificity when these rules are applied. We propose three statistical procedures to simultaneously assess the sensitivity and specificity when combining two component tests. Measurements of interest include rate difference and rate ratio. Our empirical results demonstrate that (i) the asymptotic test procedures for both measurements and approximate test procedure for rate difference possess inflated type I error rate; (ii) the exact test procedures for both measurements possess deflated type I error rate; and (iii) the approximate (unconditional) test procedure for rate ratio becomes an reliable alternative and nicely controls the actual type I error rate in small to moderate sample sizes. Moreover, the approximate (unconditional) test procedure is computationally less intensive than the exact (unconditional) test procedure. We illustrate our methodologies with a real example from a residual nasopharyngeal carcinoma (RNP) study.

“…A rigorous proof (also for the case of the di erence of the binomial probabilities) is obtained by MartÃ n AndrÃ es and Herranz Tejedor in a recently submitted manuscript (personal communication). Kang and Chen [14] (see also reference [15]) proposed an approximate unconditional test for non-inferiority between two binomial proportions and found in a comparison study that its type I error and power are intermediate between the likelihood score and unconditional exact tests. Unfortunately, the computational e ort required for implementation of these two approaches increases drastically with the sample size.…”

Section: Normal Approximationmentioning

confidence: 99%

Statistical approaches to establishing vaccine safety

Dragalin

Fedorov

Cheuvart

2002

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.