2×2 Tables emerging out of different grange mechanisms

Alio, Kudô; Tarumi, Tomoyuki

doi:10.1080/03610927808827686

Cited by 22 publications

(4 citation statements)

References 4 publications

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“…Note that this approximation formula is similar to formula (9) on page 443 of reference 3 or formula (9) on page 351 of reference 23, in which they used variance-stabilizing transformation 2 sin-' , / x rather than 2 sinh-I (Jx) for binomial sampling. To evaluate the performance of the above approximation formula for inverse sampling, in Table IV we summarize the resulting number r of index subjects together with their corresponding powers in (5) in the situations where p1 ranges from 020 to 0.90 and p 2 ranges from 0.10 to (pl -0.1) for the desired power of 090 at 0.05-level (one-sided). We can see that on the basis of the exact conditional test, the actual powers that correspond to the minimum number of index subjects calculated by use of the approximation formula are all less than the desired power of 0.90 in the situations considered in Table IV.…”

Section: Discussionmentioning

confidence: 99%

Sample Size for the Exact Conditional Test Under Inverse Sampling

Lui

1996

Statist. Med.

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Inverse sampling is a sampling design in which one continues sampling subjects until one obtains a predetermined number of index subjects. This paper derives a procedure for calculation of the minimum required number of index subjects on the basis of the exact conditional test under inverse sampling. This paper studies quantitatively the effect on power calculations of the number of index subjects. To facilitate use of inverse sampling in study designs, this paper further provides a table that summarizes, in a variety of situations, the minimum required number of index subjects for powers equal to 0.90 and 0.80 at 0.05-level. It also includes a discussion on use of the approximation sample size formula derived on the basis of a variance-stabilizing transformation and large sample theory.

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Section: Discussionmentioning

confidence: 99%

Sample Size for the Exact Conditional Test Under Inverse Sampling

Lui

1996

Statist. Med.

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“…However, for the binomial model, Y. is not an appropriate ancillary statistic forR (46), and thus conditional inference on R is not possible. Buhrman (47) showed that when inverse sampling is used (sampling until Niyi non-cases and N2 -Y2 non-cases are found in the respective populations), exact conditional confidence limits for R can be derived (48,49). These do not appear to be useful in the usual epidemological problem.…”

Section: Prospective Studies Binomial Analysesmentioning

confidence: 99%

Statistical Analyses of the Relative Risk

Gart¹

1979

Environmental Health Perspectives

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“…It is widely considered to be a more appropriate sampling scheme than the usual binomial sampling when the subjects arrive sequentially, when the underlying response of interest is acute, and when maximum likelihood estimators of some epidemiologic measures are undefined (Kudo and Tarumi, 1978;Lui, 2000). Applications of inverse sampling now appear in various areas of medical research.…”

Section: Introductionmentioning

confidence: 99%

“…Inverse sampling (which is also known as negative binomial sampling) suggests that one should continue to sample subjects until a pre-specified number of rare events of interest is observed (Haldane, 1945). It is widely considered to be a more appropriate sampling scheme than the usual binomial sampling when the subjects arrive sequentially, when the underlying response of interest is acute, and when maximum likelihood estimators of some epidemiologic measures are undefined (Kudo and Tarumi, 1978;Lui, 2000). Applications of inverse sampling now appear in various areas of medical research.…”

Section: Introductionmentioning

confidence: 99%

Testing the Non‐Unity of Rate Ratio under Inverse Sampling

Tang

Liao

et al. 2007

Biometrical J

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Inverse sampling is considered to be a more appropriate sampling scheme than the usual binomial sampling scheme when subjects arrive sequentially, when the underlying response of interest is acute, and when maximum likelihood estimators of some epidemiologic indices are undefined. In this article, we study various statistics for testing non-unity rate ratios in case-control studies under inverse sampling. These include the Wald, unconditional score, likelihood ratio and conditional score statistics. Three methods (the asymptotic, conditional exact, and Mid-P methods) are adopted for P-value calculation. We evaluate the performance of different combinations of test statistics and P-value calculation methods in terms of their empirical sizes and powers via Monte Carlo simulation. In general, asymptotic score and conditional score tests are preferable for their actual type I error rates are well controlled around the pre-chosen nominal level, and their powers are comparatively the largest. The exact version of Wald test is recommended if one wants to control the actual type I error rate at or below the pre-chosen nominal level. If larger power is expected and fluctuation of sizes around the pre-chosen nominal level are allowed, then the Mid-P version of Wald test is a desirable alternative. We illustrate the methodologies with a real example from a heart disease study.

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2×2 Tables emerging out of different grange mechanisms

Cited by 22 publications

References 4 publications

Sample Size for the Exact Conditional Test Under Inverse Sampling

Sample Size for the Exact Conditional Test Under Inverse Sampling

Statistical Analyses of the Relative Risk

Testing the Non‐Unity of Rate Ratio under Inverse Sampling

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