Sample size determination for 2-step studies with dichotomous response

Man Lai Tang; Nian Sheng Tang; Vincent J. Carey

doi:10.1016/j.jspi.2004.07.016

Sample size determination for 2-step studies with dichotomous response

Man Lai Tang^*
, Nian Sheng Tang
, Vincent J. Carey

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

10 Citations (Scopus)

Abstract

In this article, we consider problems with correlated data that can be summarized in a 2 × 2 table with structural zero in one of the off-diagonal cells. Data of this kind sometimes appear in infectious disease studies and two-step procedure studies. We propose two kinds of approximate sample size formulas, based on rate ratio, for comparison of the marginal and conditional probabilities in a correlated 2 × 2 table with structural zero. The first type of formula is derived to guarantee a pre-specified power of a hypothesis test at certain significance level while the second type of formula is developed to bound the width of a confidence interval with specified confidence level. Our empirical studies confirm that sample size formulas based on the log-transformation and score tests outperform that based on the Wald's test. We illustrate our methodologies with a real example from a two-phase treatment study.

Original language	English
Pages (from-to)	1166-1180
Number of pages	15
Journal	Journal of Statistical Planning and Inference
Volume	136
Issue number	3
DOIs	https://doi.org/10.1016/j.jspi.2004.07.016
Publication status	Published - 1 Mar 2006

User-Defined Keywords

Asymptotic inference
Correlated binary data
Rate ratio
Score test
Structural zero

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10.1016/j.jspi.2004.07.016

Cite this

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title = "Sample size determination for 2-step studies with dichotomous response",

abstract = "In this article, we consider problems with correlated data that can be summarized in a 2 × 2 table with structural zero in one of the off-diagonal cells. Data of this kind sometimes appear in infectious disease studies and two-step procedure studies. We propose two kinds of approximate sample size formulas, based on rate ratio, for comparison of the marginal and conditional probabilities in a correlated 2 × 2 table with structural zero. The first type of formula is derived to guarantee a pre-specified power of a hypothesis test at certain significance level while the second type of formula is developed to bound the width of a confidence interval with specified confidence level. Our empirical studies confirm that sample size formulas based on the log-transformation and score tests outperform that based on the Wald's test. We illustrate our methodologies with a real example from a two-phase treatment study.",

keywords = "Asymptotic inference, Correlated binary data, Rate ratio, Score test, Structural zero",

author = "Tang, \{Man Lai\} and Tang, \{Nian Sheng\} and Carey, \{Vincent J.\}",

note = "Funding Information: The author would like to thank the Editor, Professor Andrew Gelman, and the referee for many valuable comments and suggestions. The first author would like to thank Hoi-Sze Chow for her encouragement during the preparation of the revision. The work of the first author was supported by a grant from the Research Grant Council of the Hong Kong Special Administration Region (project CUHK 4371/04M). The work of the second author was supported by The Mathematical Tianyuan Younger Fund of the National Natural Science Foundation from China (10226005) and The Natural Science Foundation of Yunnan Province. ",

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doi = "10.1016/j.jspi.2004.07.016",

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T1 - Sample size determination for 2-step studies with dichotomous response

AU - Tang, Man Lai

AU - Tang, Nian Sheng

AU - Carey, Vincent J.

N1 - Funding Information: The author would like to thank the Editor, Professor Andrew Gelman, and the referee for many valuable comments and suggestions. The first author would like to thank Hoi-Sze Chow for her encouragement during the preparation of the revision. The work of the first author was supported by a grant from the Research Grant Council of the Hong Kong Special Administration Region (project CUHK 4371/04M). The work of the second author was supported by The Mathematical Tianyuan Younger Fund of the National Natural Science Foundation from China (10226005) and The Natural Science Foundation of Yunnan Province.

PY - 2006/3/1

Y1 - 2006/3/1

N2 - In this article, we consider problems with correlated data that can be summarized in a 2 × 2 table with structural zero in one of the off-diagonal cells. Data of this kind sometimes appear in infectious disease studies and two-step procedure studies. We propose two kinds of approximate sample size formulas, based on rate ratio, for comparison of the marginal and conditional probabilities in a correlated 2 × 2 table with structural zero. The first type of formula is derived to guarantee a pre-specified power of a hypothesis test at certain significance level while the second type of formula is developed to bound the width of a confidence interval with specified confidence level. Our empirical studies confirm that sample size formulas based on the log-transformation and score tests outperform that based on the Wald's test. We illustrate our methodologies with a real example from a two-phase treatment study.

AB - In this article, we consider problems with correlated data that can be summarized in a 2 × 2 table with structural zero in one of the off-diagonal cells. Data of this kind sometimes appear in infectious disease studies and two-step procedure studies. We propose two kinds of approximate sample size formulas, based on rate ratio, for comparison of the marginal and conditional probabilities in a correlated 2 × 2 table with structural zero. The first type of formula is derived to guarantee a pre-specified power of a hypothesis test at certain significance level while the second type of formula is developed to bound the width of a confidence interval with specified confidence level. Our empirical studies confirm that sample size formulas based on the log-transformation and score tests outperform that based on the Wald's test. We illustrate our methodologies with a real example from a two-phase treatment study.

KW - Asymptotic inference

KW - Correlated binary data

KW - Rate ratio

KW - Score test

KW - Structural zero

UR - https://www.scopus.com/pages/publications/28044462647

U2 - 10.1016/j.jspi.2004.07.016

DO - 10.1016/j.jspi.2004.07.016

M3 - Journal article

AN - SCOPUS:28044462647

SN - 0378-3758

VL - 136

SP - 1166

EP - 1180

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 3

ER -

Sample size determination for 2-step studies with dichotomous response

Abstract

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