Sample Size Calculations for Studies with Correlated Observations

Liu, Guanghan; Liang, Kung-Yee

doi:10.2307/2533554

Cited by 306Statistical Methods in Clinical TrialsStatistical Methods and Bayesian InferenceStatistical Methods in Epidemiology

Sample Size Calculations for Studies with Correlated Observations

Liu, Guanghan, Liang, Kung-Yee·1997·Biometrics

DOI 10.2307/2533554

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Abstract

Correlated data occur frequently in biomedical research. Examples include longitudinal studies, family studies, and ophthalmologic studies. In this paper, we present a method to compute sample sizes and statistical powers for studies involving correlated observations. This is a multivariate extension of the work by Self and Mauritsen (1988, Biometrics 44, 79-86), who derived a sample size and power formula for generalized linear models based on the score statistic. For correlated data, we appeal to a statistic based on the generalized estimating equation method (Liang and Zeger, 1986, Biometrika 73, 13-22). We highlight the additional assumptions needed to deal with correlated data. Some special cases that are commonly seen in practice are discussed, followed by simulation studies.

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With an alpha of 0.05, an estimated correlation of 0.5 between measurements and a power of 0.85, the sample size needed to detect a small to medium effect (f = 0.35) is 160.
“This analysis revealed that with an alpha of 0.05, an estimated correlation of 0.5 between measurements and a power of 0.85 the sample size needed to detect a small to medium effect (f = 0.35) is 160.”
From Personalized exposure and experience sampling method feedback versus exposure as usual for obsessive–compulsive disorder: a study protocol for a randomized controlled trial (2024) · cites this paper as [42]

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Authors: Liu, G., & Liang, K.-Y.
Affiliations: Merck & Co., Inc., Rahway, NJ, USA (United States) (US)
Johns Hopkins University (US)
Venue: Biometrics
Publisher: JSTOR
Published: 1997-09
Volume: 53
Issue: 3
Pages: 937
ISSN: 0006-341X (ISSN-L)
DOI: 10.2307/2533554
OpenAlex: W1970913176
Cited by: 306
References: 19
Citations by year: 2026: 13 · 2025: 11 · 2024: 8 · 2023: 10 · 2022: 16 · 2021: 12 · 2020: 21 · 2019: 30 · 2018: 16 · 2017: 17 · 2016: 13 · 2015: 14 · 2014: 13 · 2013: 13 · 2012: 9
FWCI: 2.94
Type: journal article
Language: en
Open access: closed
Locations: Biometrics (publishedVersion)
PubMed (publishedVersion)
Funders: National Institute of General Medical Sciences (GM49909, R01GM049909)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
Keywords: sample size determination, statistical power, correlated observations, generalized estimating equations, longitudinal data, family studies, generalized linear models, score statistic
MeSH terms: Biometry, Family, Humans, Longitudinal Studies, Monte Carlo Method, Ophthalmology, Regression Analysis, Research Design, Models, Statistical

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Sample Size Calculations for Studies with Correlated Observations

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