Multiple-Stage Procedures for Drug Screening

Schultz, John R.; Nichol, F. R.; Elfring, Gary L.; Weed, Sheldon D.

doi:10.2307/2529393

Cited by 87 publications

(47 citation statements)

References 5 publications

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“…Schultz et al [8] developed recursive formulae for calculating the operating characteristics of general k-stage designs with the possibility of acceptance and rejection at each stage. Early acceptance is appropriate for situations where patients are very limited or the drug is very expensive.…”

Section: Discussionmentioning

confidence: 99%

Optimal two-stage designs for phase II clinical trials

Simon

1989

Controlled Clinical Trials

3,349

2,224

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The primary objective of a phase II clinical trial of a new drug or regimen is to determine whether it has sufficient biological activity against the disease under study to warrant more extensive development. Such trials are often conducted in a multiinstitution setting where designs of more than two stages are difficult to manage. This paper presents two-stage designs that are optimal in the sense that the expected sample size is minimized if the regimen has low activity subject to constraints upon the size of the type 1 and type 2 errors. Two-stage designs which minimize the maximum sample size are also determined. Optimum and "minimax" designs for a range of design parameters are tabulated. These designs can also be used for pilot studies of new regimens where toxicity is the endpoint of interest.

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Section: Discussionmentioning

confidence: 99%

Optimal two-stage designs for phase II clinical trials

Simon

1989

Controlled Clinical Trials

3,349

2,224

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“…It should be noted that, in the case that X is a Bernoulli variable, the recursive relationship had been used in [63] for designing hypothesis tests for drug screening. In the special case of fully sequential sampling (i.e., the increment of sample sizes is unity), (26) reduces to the recursive formula given at the bottom of page 49 of [35] for computing ν(s).…”

Section: Recursive Computationmentioning

confidence: 99%

“…Throughout this subsection, we assume that the multistage sampling schemes follow stopping rules derived from Chernoff bounds as described in Section 4.3.1. Moreover, we assume that the sample sizes n 1 , · · · , n s are chosen as the ascending arrangement of all distinct elements of the set defined by (63). With regard to the tightness of the double-decision-variable method, we have Theorem 36 Let R be a subset of real numbers.…”

Section: Asymptotic Analysis Of Sampling Schemesmentioning

confidence: 99%

Coalescence of low-viscosity fluids in air

Case

2009

Phys. Rev. E

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In this paper, we have established a unified framework of multistage parameter estimation. We demonstrate that a wide variety of statistical problems such as fixed-sample-size interval estimation, point estimation with error control, bounded-width confidence intervals, interval estimation following hypothesis testing, construction of confidence sequences, can be cast into the general framework of constructing sequential random intervals with prescribed coverage probabilities. We have developed exact methods for the construction of such sequential random intervals in the context of multistage sampling. In particular, we have established inclusion principle and coverage tuning techniques to control and adjust the coverage probabilities of sequential random intervals. We have obtained concrete sampling schemes which are unprecedentedly efficient in terms of sampling effort as compared to existing procedures.

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“…Similar algorithms for calculating probabilities were done by Schultz, et al (1973) (see Jennison and Turnbull, 2000, pp. 236-237).…”

Section: Finite Stopping Boundariesmentioning

confidence: 99%

On Using Truncated Sequential Probability Ratio Test Boundaries for Monte Carlo Implementation of Hypothesis Tests

Kim¹,

Hachey²

2007

Journal of Computational and Graphical Statistics

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When designing programs or software for the implementation of Monte Carlo (MC) hypothesis tests, we can save computation time by using sequential stopping boundaries. Such boundaries imply stopping resampling after relatively few replications if the early replications indicate a very large or very small p-value. We study a truncated sequential probability ratio test (SPRT) boundary and provide a tractable algorithm to implement it. We review two properties desired of any MC p-value, the validity of the p-value and a small resampling risk, where resampling risk is the probability that the accept/reject decision will be different than the decision from complete enumeration. We show how the algorithm can be used to calculate a valid p-value and confidence intervals for any truncated SPRT boundary. We show that a class of SPRT boundaries is minimax with respect to resampling risk and recommend a truncated version of boundaries in that class by comparing their resampling risk (RR) to the RR of fixed boundaries with the same maximum resample size. We study the lack of validity of some simple estimators of p-values and offer a new simple valid p-value for the recommended truncated SPRT boundary. We explore the use of these methods in a practical example and provide the MChtest R package to perform the methods.

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Multiple-Stage Procedures for Drug Screening

Cited by 87 publications

References 5 publications

Optimal two-stage designs for phase II clinical trials

Optimal two-stage designs for phase II clinical trials

Coalescence of low-viscosity fluids in air

On Using Truncated Sequential Probability Ratio Test Boundaries for Monte Carlo Implementation of Hypothesis Tests

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