TY - JOUR

T1 - An approximate unconditional test of non-inferiority between two proportions

AU - Kang, Seung Ho

AU - Chen, James J.

PY - 2000/8/30

Y1 - 2000/8/30

N2 - This paper investigates an approximate unconditional test for non-inferiority between two independent binomial proportions. The P-value of the approximate unconditional test is evaluated using the maximum likelihood estimate of the nuisance parameter. In this paper, we clarify some differences in defining the rejection regions between the approximate unconditional and conventional conditional or unconditional exact test. We compare the approximate unconditional test with the asymptotic test and unconditional exact test by Chan (Statistics in Medicine, 17, 1403-1413, 1998) with respect to the type I error and power. In general, the type I errors and powers are in the decreasing order of the asymptotic, approximate unconditional and unconditional exact tests. In many cases, the type I errors are above the nominal level from the asymptotic test, and are below the nominal level from the unconditional exact test. In summary, when the non-inferiority test is formulated in terms of the difference between two proportions, the approximate unconditional test is the most desirable, because it is easier to implement and generally more powerful than the unconditional exact test and its size rarely exceeds the nominal size. However, when a test between two proportions is formulated in terms of the ratio of two proportions, such as a test of efficacy, more caution should be made in selecting a test procedure. The performance of the tests depends on the sample size and the range of plausible values of the nuisance parameter.

AB - This paper investigates an approximate unconditional test for non-inferiority between two independent binomial proportions. The P-value of the approximate unconditional test is evaluated using the maximum likelihood estimate of the nuisance parameter. In this paper, we clarify some differences in defining the rejection regions between the approximate unconditional and conventional conditional or unconditional exact test. We compare the approximate unconditional test with the asymptotic test and unconditional exact test by Chan (Statistics in Medicine, 17, 1403-1413, 1998) with respect to the type I error and power. In general, the type I errors and powers are in the decreasing order of the asymptotic, approximate unconditional and unconditional exact tests. In many cases, the type I errors are above the nominal level from the asymptotic test, and are below the nominal level from the unconditional exact test. In summary, when the non-inferiority test is formulated in terms of the difference between two proportions, the approximate unconditional test is the most desirable, because it is easier to implement and generally more powerful than the unconditional exact test and its size rarely exceeds the nominal size. However, when a test between two proportions is formulated in terms of the ratio of two proportions, such as a test of efficacy, more caution should be made in selecting a test procedure. The performance of the tests depends on the sample size and the range of plausible values of the nuisance parameter.

UR - http://www.scopus.com/inward/record.url?scp=0034734436&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034734436&partnerID=8YFLogxK

U2 - 10.1002/1097-0258(20000830)19:16<2089::AID-SIM537>3.0.CO;2-B

DO - 10.1002/1097-0258(20000830)19:16<2089::AID-SIM537>3.0.CO;2-B

M3 - Article

C2 - 10931513

AN - SCOPUS:0034734436

SN - 0277-6715

VL - 19

SP - 2089

EP - 2100

JO - Statistics in Medicine

JF - Statistics in Medicine

IS - 16

ER -