TY - JOUR

T1 - Efficient calculation of test sizes for non-inferiority

AU - Almendra-Arao, Félix

N1 - Funding Information:
The author would like to express his gratitude to the unknown referees for their many constructive comments. This research was partially supported by SNI-CONACYT, COFAA-IPN, EDI-IPN and Project SIP-IPN 20090039.

PY - 2012/12

Y1 - 2012/12

N2 - The nuisance parameter presents a serious computational obstacle to the calculation of test sizes in non-inferiority tests. This obstacle is the principal reason why studies performing unconditional non-inferiority tests calculate test sizes for only a few cases, only by simulation or with gross approximations. Typically, when fine approximations are made to calculate test sizes for non-inferiority tests, the calculation is made with the exhaustive method, which demands considerable computational effort. Although Newton's method is generally more efficient than the exhaustive method, implementing the former requires that the first two derivatives of the power function have manageable closed forms. Unfortunately, for general critical regions, these derivatives have unmanageable representations. In this paper, we prove that when the critical regions are Barnard convex sets, the first two derivatives of the power function can take manageable closed forms, so Newton's method can be applied to calculate the test sizes. Because of the rapid convergence of Newton's method and the control that we have over the obtained precision, this method saves calculation time.

AB - The nuisance parameter presents a serious computational obstacle to the calculation of test sizes in non-inferiority tests. This obstacle is the principal reason why studies performing unconditional non-inferiority tests calculate test sizes for only a few cases, only by simulation or with gross approximations. Typically, when fine approximations are made to calculate test sizes for non-inferiority tests, the calculation is made with the exhaustive method, which demands considerable computational effort. Although Newton's method is generally more efficient than the exhaustive method, implementing the former requires that the first two derivatives of the power function have manageable closed forms. Unfortunately, for general critical regions, these derivatives have unmanageable representations. In this paper, we prove that when the critical regions are Barnard convex sets, the first two derivatives of the power function can take manageable closed forms, so Newton's method can be applied to calculate the test sizes. Because of the rapid convergence of Newton's method and the control that we have over the obtained precision, this method saves calculation time.

KW - Newton's method

KW - Non-inferiority tests

KW - Proportions

KW - Test sizes

KW - Unconditional tests

UR - http://www.scopus.com/inward/record.url?scp=84864118123&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2011.11.008

DO - 10.1016/j.csda.2011.11.008

M3 - Artículo

VL - 56

SP - 4138

EP - 4145

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 12

ER -