Sample Size Determination for Establishing Equivalence/Noninferiority via Ratio of Two Proportions in Matched–Pair Design

In this article, we propose approximate sample size formulas for establishing equivalence or noninferiority of two treatments in match-pairs design. Using the ratio of two proportions as the equivalence measure, we derive sample size formulas based on a score statistic for two types of analyses: hypothesis testing and confidence interval estimation. Depending on the purpose of a study, these formulas can be used to provide a sample size estimate that guarantees a prespecified power of a hypothesis test at a certain significance level or controls the width of a confidence interval with a certain confidence level. Our empirical results confirm that these score methods are reliable in terms of true size, coverage probability, and skewness. A liver scan detection study is used to illustrate the proposed methods.

[1]  T Tango,et al.  Re: Improved confidence intervals for the difference between binomial proportions based on paired data by Robert G. Newcombe, Statistics in Medicine, 17, 2635-2650 (1998) , 1999, Statistics in medicine.

[2]  T. Tango.  EQUIVALENCE TEST AND CONFIDENCE INTERVAL FOR THE DIFFERENCE IN PROPORTIONS FOR THE PAIRED-SAMPLE DESIGN , 1998 .

[3]  C. Farrington,et al.  Test statistics and sample size formulae for comparative binomial trials with null hypothesis of non-zero risk difference or non-unity relative risk. , 1990, Statistics in medicine.

[4]  Man-Lai Tang,et al.  On tests of equivalence via non‐unity relative risk for matched‐pair design , 2003, Statistics in medicine.

[5]  C. Dunnett,et al.  Significance testing to establish equivalence between treatments, with special reference to data in the form of 2X2 tables. , 1977, Biometrics.

[6]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[7]  A L Gould,et al.  Sample sizes for event rate equivalence trials using prior information. , 1993, Statistics in medicine.

[8]  P A Lachenbruch,et al.  On the sample size for studies based upon McNemar's test. , 1992, Statistics in medicine.

[9]  K. Lui,et al.  Exact equivalence test for risk ratio and its sample size determination under inverse sampling. , 1997, Statistics in medicine.

[10]  J M Nam,et al.  Establishing equivalence of two treatments and sample size requirements in matched-pairs design. , 1997, Biometrics.

[11]  J M Nam,et al.  Sample size determination in stratified trials to establish the equivalence of two treatments. , 1995, Statistics in medicine.

[12]  W W Hauck,et al.  A proposal for interpreting and reporting negative studies. , 1986, Statistics in medicine.

[13]  R G Newcombe,et al.  Improved confidence intervals for the difference between binomial proportions based on paired data. , 1998, Statistics in medicine.

[14]  J Wood,et al.  Sample Size Calculations for Trials in Health Services Research , 1999, Journal of health services research & policy.

[15]  C H Schmid,et al.  An empirical study of the effect of the control rate as a predictor of treatment efficacy in meta-analysis of clinical trials. , 1998, Statistics in medicine.

[16]  Yi Tsong,et al.  Tests for Equivalence or Noninferiority Between Two Proportions , 2000 .

[17]  David R. Bristol.  Sample sizes for constructing confidence intervals and testing hypotheses , 1989 .

[18]  P A Lachenbruch,et al.  Assessing screening tests: extensions of McNemar's test. , 1998, Statistics in medicine.

[19]  J A Bean,et al.  On the sample size for one-sided equivalence of sensitivities based upon McNemar's test. , 1995, Statistics in medicine.

[20]  Huey-miin Hsueh,et al.  Tests for equivalence or non‐inferiority for paired binary data , 2002, Statistics in medicine.

[21]  E. Keeler,et al.  Primer on certain elements of medical decision making. , 1975, The New England journal of medicine.

[22]  Mantel-Haenszel-type tests for testing equivalence or more than equivalence in comparative clinical trials. , 1994, Biometrics.