Tests for equivalence or non‐inferiority for paired binary data

Abstract

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.

Evaluation of Chimeric Japanese Encephalitis and Dengue Viruses for Use in Diagnostic Plaque Reduction Neutralization Tests

“…The kappa statistic for intraclass correlation was 1, with a P value of Ͻ0.01 and a lower 95% confidence bound of 0.89, showing a strong, positive correlation. The noninferiority test from Liu et al (34) indicated that the antibody cross-reactivity of the DENV serotypes observed with the ChimeriVax-DENV was not greater than the cross-reactivity observed with the prototype DENV (P ϭ 0.02). It should be noted that one of the specimens originally classified as a DENV3 infection showed no neutralizing titer with either the chimeric or the prototype DENV3.…”

“…Antibody cross-reactivity to the prototype DENV was compared to that of the ChimeriVax-DENV by comparing how frequently a heterologous (cross-reactive) titer indicated positivity (even if the homologous titer was fourfold greater, indicating a correct diagnosis). A noninferiority test for proportions (34) was then used to determine whether the ChimeriVax-DENV produced more cross-reactive results than the prototype DENV. A secondary question asked how similar the neutralizing antibody titers were against the prototype viruses and the ChimeriVax viruses.…”

Simultaneous Non‐inferiority Test of Sensitivity and Specificity for Two Diagnostic Procedures in the Presence of a Gold Standard

“…This paper uses the restricted maximum likelihood estimation (RMLE) approach (Nam, 1997) to estimate the standard errors s e ; s p and s WS . Since several investigations indicate that it performs well (Tango, 1998;Liu, et al, 2002). The RMLEs of unknown p 01j1 ; p 10j1 ; p 10j0 and p 01j0 under the null hypothetical constraints q e ¼ Àd e and q p ¼ Àd p are given bỹ…”

Cardioplegia and ventricular late potentials in cardiac surgical patients

“…Under the assumption that a 5.5% difference in the pre-post probabilities reflects equivalence, we would conclude the two probabilities are equivalent if the estimated confidence interval for the difference is fully contained inside the interval (-0.055, 0.055). We used an exact 90% confidence interval obtained from McNemar's procedure to account for the paired binary data for our test of equivalence [16].…”