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## Lesson 6: Sample Size and Power - Part B

Scott A. Can they help to do a better job? Help employees overcome obstacles and develop scientific thinking to solve problems. Understanding the changes. Solving a Lean vs. Hint: The problem statement is never the problem. Control Charts and Capability Analysis. The supplementary material available at Biostatistics online also compares the performances of the 3 proposed statistics T 1 , T 2 , and T 3 using the 3 different estimation methods M 1 , M 2 , and M 3.

The results can be summarized as follows:. In general, T 2 and T 3 , using M 3 , give consistently good performance. In particular, T 3 demonstrates robust behavior for almost all settings, while T 2 gives conservative performance when sample size is small and moderate. We therefore recommend T 3 using M 3. All sample size formulae for controlling a prespecified power are asymptotically valid in the sense that the exact power for the estimated sample size is close to the prespecified power level.

Similarly, all sample size formulae for controlling the confidence interval width are asymptotically valid in the sense that both the prespecified coverage and half-width are well controlled. Required sample sizes are generally smaller for T 3 , than for T 1 or T 2. In this section, we illustrate our proposed methodology using as an example the clinical laboratory study described in Section 1. Briefly, 30 positive control sera serum samples from penicillin-allergic subjects with a positive clinical history and a positive penicillin skin test and 30 negative control sera sera from subjects with no history of penicillin allergy and a negative skin test were tested for BPO determinant—specific IgE antibodies by RAST using different conjugates coupled to the solid phase.

The standard procedure is benzylpenicillin conjugated to HSA and the new procedure is benzylpenicillin conjugated to SP. The results are summarized in Table 2. Suppose that we focus now on the CML method. Clearly, the sample sizes that are obtained from different statistics do not differ substantially in this example. Suppose now that another investigator wants to rerun the experiment using similar settings, but with the aim of estimating the rate ratios of the sensitivities and specificities i. In all the cases, we observe that the sample sizes based on the logarithmic transformation statistic are slightly smaller than those based on Wald-type or Fieller-type statistic.

Our findings in this article are consistent with those of comparative binomial trials see Farrington and Manning, and noninferiority trials see Tang, That is, the sample-based and constrained least squares methods can produce incorrect sample sizes and inflated type I error rates, whereas the CML method usually produces accurate sample sizes with fairly well-controlled type I error rates. In general, we find that both logarithmic transformation and Fieller-type statistics are desirable choices in equivalence trial sample size calculations.

## Non-inferiority trials: determining whether alternative treatments are good enough

We consider sensitivity and specificity separately, although there are summary indices that combine both sensitivity and specificity. Two common choices for this purpose include Youden's index and the likelihood ratio of a positive or negative test see, Biggerstaff, Extension of the present work to these indices is under consideration. The authors are grateful to the editor and referees for their valuable suggestions that greatly enhanced the manuscript and to Professor N. Balakrishnan for reading the article for us.

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The second author would like to thank Ms Chow Hoi-Sze Daisy for her kind encouragement during the preparation of the manuscript. Conflict of Interest: None declared. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Sign In or Create an Account.

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Article Navigation. Close mobile search navigation Article Navigation. Volume 8. Article Contents. Sample size determination for matched-pair equivalence trials using rate ratio Nian-Sheng Tang. Oxford Academic. Google Scholar. Man-Lai Tang. Shun-Fang Wang. Article history. Revision Received:. Cite Citation. Permissions Icon Permissions.

Abstract In this article, we compare Wald-type, logarithmic transformation, and Fieller-type statistics for the classical 2-sided equivalence testing of the rate ratio under matched-pair designs with a binary end point. We assume that the disease status i. A reference diagnostic test and a new diagnostic test are then administered to each of these n g sampled subjects in random order.

The equivalence between the new and reference diagnosis procedures can be described by the following interval hypotheses:. Table 1. View Large. To test the interval hypothesis H 0 g in 2. This consists of testing the following 1-sided hypotheses see, Dunnett and Gent, ; Schuirmann, :. Often, the estimation of treatment difference is of more interest than the testing of specific hypotheses.

It is well known that an equivalence hypothesis can be tested via the confidence interval approach Tang and others ; Liu and others It then follows from 2. Table 2. Table 3. The null hypothesis of interest is. Bioequivalence trials, intersection union tests and equivalence confidence sets with discussion.