Sample Size Calculation for Poisson Endpoint Using the Exact Distribution of Difference Between Two Poisson Random Variables

Menon, Sandeep; Massaro, Joseph M.; Lewis, Jerry W.; Pencina, Michael J.; Wang, Yongcheng; Lavin, Philip T.

doi:10.1198/sbr.2011.10015

Cited by 3 publications

(6 citation statements)

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“…Given that the methodology described in Section 2.2 relies upon asymptotic theory, the operating characteristics computed using multivariate normal distribution functions could be a poor approximation to their empirical values. Therefore, to permit strict error control we now extend the results of Menon et al (2011) to group sequential designs. To achieve this, note that the sum of the outcomes in arm j in stage k, Y jk say, has the following distribution based on the familiar result that the sum of independent Poisson random variables is itself Poisson…”

Section: Design Based On Exact Calculationsmentioning

confidence: 99%

“…where I ðÁÞ is the modified Bessel function of the first kind, and we make use of the particular representation presented in Menon et al (2011). Our test statistic at analysis k for the exact design is then T Sk ¼T 1 þ Á Á Á þT k : Now, within the context of exact group sequential designs for Bernoulli distributed outcome variables, it is well understood that the interim test statistics do not in general have a simple distribution (Jung 2012).…”

Section: Design Based On Exact Calculationsmentioning

confidence: 99%

“…In contrast, for randomized two-arm experiments with Poisson distributed outcome variables, several authors have proposed approximate procedures for study design (Thode 1997;Shiue and Bain 1982;Mathews 2010), but it was only comparatively recently that Menon et al (2011) described an alternative approach based on the exact distribution of the difference between two Poisson variables. They demonstrated that when the anticipated difference between the Poisson rates in the two arms was large, the sample size required by their approach was typically 5-10% smaller than that based on a normal approximation.…”

Section: Introductionmentioning

confidence: 99%

“…First, we describe how established group sequential design theory can be applied in this setting, allowing widely available software for design determination to be employed, and operating characteristics to be approximately controlled. Following this, we detail a novel design that allows for the exact computation of a design's operating characteristics based on the extension of the approach of Menon et al (2011) to group sequential experiments. To allow maximal efficiency gains to be attained from the group sequential tests, we then describe an effective means of choosing stopping boundaries in a near-optimal manner.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Exact group sequential designs for two-arm experiments with Poisson distributed outcome variables

Grayling

Wason

Mander

2019

Communications in Statistics - Theory and Methods

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We describe and compare two methods for the group sequential design of two-arm experiments with Poisson distributed data, which are based on a normal approximation and exact calculations respectively. A framework to determine near-optimal stopping boundaries is also presented. Using this framework, for a considered example, we demonstrate that a group sequential design could reduce the expected sample size under the null hypothesis by as much as 44% compared to a fixed sample approach. We conclude with a discussion of the advantages and disadvantages of the two presented procedures.

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Section: Design Based On Exact Calculationsmentioning

confidence: 99%

Section: Design Based On Exact Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact group sequential designs for two-arm experiments with Poisson distributed outcome variables

Grayling

Wason

Mander

2019

Communications in Statistics - Theory and Methods

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“…13 Approaches to sample size planning of studies aiming to detect differences between the parameters of two Poisson distributions were considered by Menon et al. 14 and Shan. 12…”

Section: Introductionmentioning

confidence: 99%

On powerful exact nonrandomized tests for the Poisson two-sample setting

Wellek

2020

Stat Methods Med Res

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In the case of two independent samples from Poisson distributions, the natural target parameter for hypothesis testing is the ratio of the two population means. The conditional tests which have been derived for this class of problems already in the 1940s are well known to be optimal in terms of power only when randomized decisions between hypotheses are admitted at the boundary of the respective rejection regions. The major objective of this contribution is to show how the approach used by Boschloo in 1970 for constructing a powerful nonrandomized version of Fisher’s exact test for hypotheses about the odds ratio between two binomial parameters can successfully be adapted for the Poisson case. The resulting procedure, which we propose to term Poisson-Boschloo test, depends on some cutoff for the observed total number of events, the variable upon which conditioning has to be done. We show that for any fixed specific alternative, this cutoff can be chosen in such a way that the resulting nonrandomized test falls short in power of the randomized UMPU test only by a negligible amount. Thus, sample size calculation for the Poisson-Boschloo test can be carried out nearly exactly by means of the same computational procedure as has to be used for the randomized UMPU test. Since the power of the latter is accessible to elementary computational tools, this result makes approximate methods of sample size calculation for the Poisson-Boschloo test dispensable. It is furthermore shown how the construction of a Poisson-Boschloo type test extends to the case that interest is in establishing equivalence in the strict, two-sided sense rather than noninferiority. Although proceeding to two-sided equivalence considerably complicates the construction, comparing the resulting test procedure in terms of power with the exact randomized UMPU test leads essentially to the same conclusions as in the noninferiority case.

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Proportions and Rates

Ryan

2013

Sample Size Determination and Power

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Sample Size Calculation for Poisson Endpoint Using the Exact Distribution of Difference Between Two Poisson Random Variables

Cited by 3 publications

References 5 publications

Exact group sequential designs for two-arm experiments with Poisson distributed outcome variables

Exact group sequential designs for two-arm experiments with Poisson distributed outcome variables

On powerful exact nonrandomized tests for the Poisson two-sample setting

Proportions and Rates

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