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Nutrition and Health (including climate and ecological aspects)

Sample size calculations for continuous outcomes in clinical nutrition

European Journal of Clinical Nutrition volume 76, pages 1682–1689 (2022)Cite this article

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Abstract

In nutrition research, sample size calculations for continuous outcomes are important for the planning phase of many randomized trials and could also be relevant for some observational studies such as cohort and cross-sectional studies. However, only little literature dedicated to this topic exists within nutritional science. This article reviews the most common methods for sample size calculations in nutrition research. Approximate formulas are used for explaining concepts and requirements and for working through examples from the literature. Sample size calculations for the various study designs, which are covered, may all be seen as extensions of the sample size calculation for the basic two-group comparison through the application of suitable scaling factors and, possibly, modification of the significance level. The latter is needed for sample size calculations for multi-group designs and designs involving multiple primary outcomes. Like cluster-randomized designs, these types of study designs may be more challenging than standard sample size calculations. In such non-standard scenarios, there may be a need for consulting a biostatistician. Finally, it should be stressed that there may be many ways to plan a study. The final sample size calculation provided for a grant applicant, study protocol, or publication will often not only depend on considerations and input information as described in this article but will also involve restrictions in terms of logistics and/or resources.

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References

  1. Bacchetti P, Wolf LE, Segal MR, McCulloch CE. Ethics and Sample Size. Am J Epidemiol. 2005;161:105–10.

    Article  PubMed  Google Scholar 

  2. Nelson M, Margetts BM. Design, planning, and evaluation of nutritional epidemiological studies. 2nd ed. In: Margetts BM, Nelson M, editors. Design Concepts in Nutritional Epidemiology. Oxford:Oxford University Press;1997.

  3. Cole TJ. Sampling, study, and power. 2nd ed. In: Margetts BM, Nelson M, editors. Design Concepts in Nutritional Epidemiology. Oxford: Oxford University Press; 1997.

  4. Zhang W, Liu A, Zhang Z, Nansel T, Halabi S. Best (but oft-forgotten) practices: sample size and power calculation for a dietary intervention trial with episodically consumed foods. Am J Clin Nutr. 2020;112:920–5.

    Article  PubMed  PubMed Central  Google Scholar 

  5. Saracino G, Jennings LW, Hasse JM. Basic statistical concepts in nutrition research. Nutr Clin Pract. 2013;28:182–93.

    Article  PubMed  Google Scholar 

  6. Harris JE, Raynor HA. Crossover Designs in Nutrition and Dietetics Research. J Acad Nutr Dietetics. 2017;117:1023–30.

    Article  Google Scholar 

  7. Chow S-C, Shao J, Wang H, Lokhnygina Y. Sample Size Calculations in Clinical Research. 3rd ed. Boca Raton:CRC Press; 2018.

  8. Tukey JW. Tightening the clinical trial. Controlled Clin Trials. 1993;14:266–85.

    Article  PubMed  CAS  Google Scholar 

  9. Hoenig JM, Heisey DM. The Abuse of Power: The Pervasive Fallacy of Power Calculations for Data Analysis. Am Statistician. 2001;55:19–24.

    Article  Google Scholar 

  10. Fabiansen C, Yamééogo CW, Iuel-Brockdorf A-S, Cichon B, Rytter MJH, Kurpad A, et al. Effectiveness of food supplements in increasing fat-free tissue accretion in children with moderate acute malnutrition: a randomised 2 × 2 × 3 factorial trial in Burkina Faso. PLoS Med. 2017;14:e1002387.

    Article  PubMed  PubMed Central  Google Scholar 

  11. Kehlet U, Kofod J, Holst JJ, Ritz C, Aaslyng MD, Raben A. Addition of Rye Bran and Pea Fiber to Pork Meatballs Enhances Subjective Satiety in Healthy Men, but Does Not Change Glycemic or Hormonal Responses: a Randomized Crossover Meal Test Study. J Nutr. 2017;147:1700–8.

    PubMed  CAS  Google Scholar 

  12. Brown T, Ross L, Jones L, Hughes B, Banks M. Nutrition outcomes following implementation of validated swallowing and nutrition guidelines for patients with head and neck cancer. Supportive Care Cancer. 2014;22:2381–91.

    Article  Google Scholar 

  13. Kiefer E, Hoover DR, Shi Q, Dusingize JC, Cohen M, Mutimura E, et al. Association of pre-treatment nutritional status with change in CD4 count after antiretroviral therapy at 6, 12, and 24 months in Rwandan women. PloS ONE. 2011;6:e29625.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  14. Laursen R, Larnkjær A, Ritz C, Hauger H, Michaelsen KF, Mølgaard C. Probiotics and Child Care Absence Due to Infections: A Randomized Controlled Trial. Pediatrics. 2017;140:e20170735.

    Article  PubMed  Google Scholar 

  15. Raben A, Vestentoft PS, Brand-Miller J, Jalo E, Drummen M, Simpson L, et al. PREVIEW - Results from a 3-year randomised 2 x 2 factorial multinational trial investigating the role of protein, glycemic index and physical activity for prevention of type-2 diabetes. Diabetes Obes Metab. 2021;23:324–37.

    Article  PubMed  CAS  Google Scholar 

  16. Julious SA. Sample sizes for clinical trials with Normal data. Stat Med. 2004;23:1921–86.

    Article  PubMed  Google Scholar 

  17. Hsieh FY, Lavori PW, Cohen HJ, Feussner JR. An overview of variance inflation factors for sample-size calculation. Eval Health Prof. 2003;26:239–57.

    Article  PubMed  CAS  Google Scholar 

  18. R Core Team (2021). (2020). R: A language and environment for statistical computing. Vienna:R Foundation for Statistical Computing. https://www.R-project.org/.

  19. Rutterford C, Copas A, Eldridge S. Methods for sample size determination in cluster randomized trials. Int J Epidemiol. 2015;44:1051–67.

    Article  PubMed  PubMed Central  Google Scholar 

  20. Raziani F, Tholstrup T, Kristensen MD, Svanegaard ML, Ritz C, Astrup A, et al. High intake of regular-fat cheese compared with reduced-fat cheese does not affect LDL cholesterol or risk markers of the metabolic syndrome: a randomized controlled trial. Am J Clin Nutr. 2016;104:973–81.

    Article  PubMed  CAS  Google Scholar 

  21. Hothorn T, Bretz F, Westfall P. Simultaneous inference in general parametric models. Biometrical J. 2008;50:346–63.

    Article  Google Scholar 

  22. Große Ruse M, Ritz C, Hothorn LA. Simultaneous inference of a binary composite endpoint and its components. J Biopharmaceutical Stat. 2017;27:56–69.

    Article  Google Scholar 

  23. Friis H, Mwaniki D, Omondi B, Muniu E, Thiong’o F, Ouma J, et al. Effects on haemoglobin of multi-micronutrient supplementation and multi-helminth chemotherapy: a randomized, controlled trial in Kenyan school children. Eur J Clin Nutr. 2003;57:573–9.

    Article  PubMed  CAS  Google Scholar 

  24. Leon AC, Heo M. Sample sizes required to detect interactions between two binary fixed-effects in a mixed-effects linear regression model. Comput Stat Data Anal. 2009;53:603–8.

    Article  PubMed  PubMed Central  Google Scholar 

  25. Hongisto SM, Paajanen L, Saxelin M, Korpela R. A combination of fibre-rich rye bread and yoghurt containing Lactobacillus GG improves bowel function in women with self-reported constipation. Eur J Clin Nutr. 2006;60:319–24.

    Article  PubMed  CAS  Google Scholar 

  26. Jones B, Kenward MG. Design and Analysis of Cross-Over Trials. 3rd ed. Boca Raton:CRC Press; 2015.

  27. Donner A, Klar N. Design and Analysis of Cluster Randomization Trials in Health Research. Chichester:John Wiley & Sons; 2000.

  28. Hemming K, Eldridge S, Forbes G, Weijer C, Taljaard M. How to design efficient cluster randomised trials. BMJ. 2017;358:j3064.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  29. Thompson DM, Fernald DH, Mold JW. Intraclass correlation coefficients typical of cluster-randomized studies: estimates from the Robert Wood Johnson Prescription for Health projects. Ann Fam Med. 2012;10:235–40.

    Article  PubMed  PubMed Central  Google Scholar 

  30. van Breukelen GJ, Candel MJJM. Calculating sample sizes for cluster randomized trials: we can keep it simple and efficient! J Clin Epidemiol. 2012;65:1212–8.

    Article  PubMed  Google Scholar 

  31. Kerry SM, Bland JM. Statistics notes: Sample size in cluster randomisation. BMJ. 1998;316:549.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  32. Arnup SJ, McKenzie JE, Hemming K, Pilcher D, Forbes AB. Understanding the cluster randomised crossover design: a graphical illustration of the components of variation and a sample size tutorial. Trials. 2017;18:381.

    Article  PubMed  PubMed Central  Google Scholar 

  33. Gupta A, Kant S, Ramakrishnan L, Pandey RM, Khandelwal R, Kapil U, et al. Impact of daily-supervised administration of a package of iron and folic acid and vitamin B12 on hemoglobin levels among adolescent girls (12−19 years): a cluster randomized control trial. Eur J Clin Nutr. 2021;75:1588–97.

    Article  PubMed  CAS  Google Scholar 

  34. Kramer MS, Chalmers B, Hodnett ED, Sevkovskaya Z, Dzikovich I, Shapiro S, et al. PROBIT Study Group (Promotion of Breastfeeding Intervention Trial). Promotion of Breastfeeding Intervention Trial (PROBIT): a randomized trial in the Republic of Belarus. JAMA 2001;285:413–20.

    Article  PubMed  CAS  Google Scholar 

  35. Senn S, Bretz F. Power and sample size when multiple endpoints are considered. Pharm Stat. 2007;6:161–70.

    Article  PubMed  Google Scholar 

  36. Sugimoto T, Sozu T, Hamasaki T. A convenient formula for sample size calculations in clinical trials with multiple co-primary continuous endpoints. Pharm Stat. 2012;11:118–28.

    Article  PubMed  Google Scholar 

  37. Yang J, Li J, Wang S, Luo L, Liu P. Comparison of three sample size calculation methods for non-inferiority vaccine trials with multiple continuous co-primary endpoints. Hum Vaccines Immunother. 2019;15:256–63.

    Article  Google Scholar 

  38. Damsgaard CT, Lauritzen L, Hauger H, Vuholm S, Teisen MN, Ritz C, et al. Effects of oily fish intake on cardiovascular risk markers, cognitive function, and behavior in school-aged children: study protocol for a randomized controlled trial. Trials. 2016;17:510.

    Article  PubMed  PubMed Central  Google Scholar 

  39. Geiker NR, Ritz C, Pedersen SD, Larsen TM, Hill JO, Astrup A. A weight-loss program adapted to the menstrual cycle increases weight loss in healthy, overweight, premenopausal women: a 6-mo randomized controlled trial. Am J Clin Nutr. 2016;104:15–20.

    Article  PubMed  CAS  Google Scholar 

  40. Sahu SK, Smith TMF. A Bayesian method of sample size determination with practical applications. J R Stat Soc: Ser A. 2006;169:235–53.

    Article  Google Scholar 

  41. Noordzij M, Tripepi G, Dekker FW, Zoccali C, Tanck MW, Jager KJ. Sample size calculations: basic principles and common pitfalls. Nephrol Dialysis Transplant. 2010;25:1388–93.

    Article  Google Scholar 

  42. Hemming K, Girling AJ, Sitch AJ, Marsh J, Lilford RJ. Sample size calculations for cluster randomised controlled trials with a fixed number of clusters. BMC Med Res Methodol. 2011;11:102.

    Article  PubMed  PubMed Central  Google Scholar 

  43. Kangas S, Salpéteur C, Nikièma V, Talley L, Ritz C, Friis, et al. Impact of reduced dose of ready-to-use therapeutic foods in children with uncomplicated severe acute malnutrition: a randomised non-inferiority trial in Burkina Faso. PLOS Med. 2019;16:e1002887.

    Article  PubMed  PubMed Central  Google Scholar 

  44. Julious SA, Campbell MJ. Tutorial in biostatistics: sample sizes for parallel group clinical trials with binary data. Stat Med. 2012;31:2904–36.

    Article  PubMed  Google Scholar 

  45. Ritz C. Statistical analysis of continuous outcomes from parallel-arm randomized controlled trials in nutrition – a tutorial. Eur J Clin Nutr. 2021;75:161–70.

    Google Scholar 

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Author information

Authors and Affiliations

  1. National Institute of Public Health, University of Southern Denmark, Studiestræde 6, DK-1455, Copenhagen K, Denmark

    Christian Ritz

  2. Department of Nutrition, Exercise and Sports, University of Copenhagen, Rolighedsvej 26, DK-1958, Frederiksberg C, Denmark

    Mette Frahm Olsen, Benedikte Grenov & Henrik Friis

Authors
  1. Christian Ritz
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  2. Mette Frahm Olsen
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  3. Benedikte Grenov
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  4. Henrik Friis
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Contributions

CR wrote the initial draft of the paper. MFO, BG, and HF commented on and revised the paper.

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Correspondence to Christian Ritz.

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CR, MFO, BG, and HF declare no competing interests.

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Ritz, C., Olsen, M.F., Grenov, B. et al. Sample size calculations for continuous outcomes in clinical nutrition. Eur J Clin Nutr 76, 1682–1689 (2022). https://doi.org/10.1038/s41430-022-01169-4

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  • DOI: https://doi.org/10.1038/s41430-022-01169-4

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