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Nutrition and Health (including climate and ecological aspects)

Statistical analysis of continuous outcomes from parallel-arm randomized controlled trials in nutrition—a tutorial

A Correction to this article was published on 14 October 2020

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Abstract

Randomized controlled trials (RCTs) play a fundamental role in establishing evidence on benefits of diet changes in nutrition. There is, however, little literature on how to analyze data obtained from such trials. This tutorial provides a detailed introduction to the statistical analysis of parallel-arm RCTs in nutrition by means of modern statistical methodology, i.e., analysis of covariance and linear mixed models are informed using specific information about the trial design. Focus will be on understanding how the trial design and possibly other aspects of the trial influence the subsequent statistical analysis. All steps of the statistical analysis will be covered and a practical example is also provided.

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Fig. 1: Two scatter plots showing covariate effects on an outcome.
Fig. 2: Revisiting Fig. 1, now showing covariates effects on an outcome separately for each dietary intervention group.
Fig. 3: Two plots showing changes in systolic blood pressure for 16 participants from baseline to end of study.
Fig. 4: Revisiting Fig. 3, now showing the different effects that the outcome is decomposed into.

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Code availability

In practice the specification of the above-mentioned statistical models depends on the statistical software used. A detailed example using the statistical environment R [42] is provided as online supplementary material (https://doi.org/10.5281/zenodo.3978040).

Change history

  • 14 October 2020

    In the original version of this article, the legends to Figs. 2, 3 and 4 were inadvertently swapped. This has now been corrected in the PDF and HTML versions of the article.

References

  1. Boushey CJ, Harris J, Bruemmer B, Archer SL. Publishing nutrition research: a review of sampling, sample size, statistical analysis, and other key elements of manuscript preparation, Part 2. J Am Diet Assoc. 2008;108:679–88. https://doi.org/10.1016/j.jada.2008.01.002.

    Article  PubMed  Google Scholar 

  2. Harris JE, Sheean PM, Gleason PM, Bruemmer B, Boushey C. Publishing nutrition research: a review of multivariate techniques—Part 2: analysis of variance. J Acad Nutr Diet. 2012;112:90–98. https://doi.org/10.1016/j.jada.2011.09.037.

    Article  PubMed  Google Scholar 

  3. Vickers AJ. The use of percentage change from baseline as an outcome in a controlled trial is statistically inefficient: a simulation study. BMC Med Res Methodol. 2001;1:6. https://doi.org/10.1186/1471-2288-1-6.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. Van Breukelen GJP. ANCOVA versus change from baseline had more power in randomized studies and more bias in nonrandomized studies. J Clin Epidemiol. 2006;59:920–5. https://doi.org/10.1016/j.jclinepi.2006.02.007.

    Article  PubMed  Google Scholar 

  5. Egbewale BE, Lewis M, Sim J. Bias, precision and statistical power of analysis of covariance in the analysis of randomized trials with baseline imbalance: a simulation study. BMC Med Res Methodol. 2014;14:49. https://doi.org/10.1186/1471-2288-14-49.

    Article  PubMed  PubMed Central  Google Scholar 

  6. Bland JM, Altman DG. Best (but oft forgotten) practices: testing for treatment effects in randomized trials by separate analyses of changes from baseline in each group is a misleading approach. Am J Clin Nutr. 2015;102:991–4. https://doi.org/10.3945/ajcn.115.119768.

    Article  CAS  PubMed  Google Scholar 

  7. Allison DB, Antoine LH, George BJ. Incorrect statistical method in parallel-groups RCT led to unsubstantiated conclusions. Lipids Health Dis. 2016;15:77. https://doi.org/10.1186/s12944-016-0242-3.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Ten Have T, Normand S, Marcus S, Brown C, Lavori P, Duan N. Intent-to-treat vs. non-intent-to-treat analyses under treatment non-adherence in mental health randomized trials. Psychiatr Ann. 2008;38:772–83. https://doi.org/10.3928/00485713-20081201-10.

    Article  PubMed  PubMed Central  Google Scholar 

  9. Mostazir M, Taylor RS, Henley W, Watkins E. An overview of statistical methods for handling nonadherence to intervention protocol in randomized control trials: a methodological review. J Clin Epidemiol. 2019;108:121–31. https://doi.org/10.1016/j.jclinepi.2018.12.002.

    Article  PubMed  Google Scholar 

  10. Rochon J. Supplementing the intent-to-treat analysis: accounting for covariates observed postrandomization in clinical trials. J Am Stat Assoc. 1995;90:292–300. https://doi.org/10.1080/01621459.1995.10476512.

    Article  Google Scholar 

  11. Lee PH. Covariate adjustments in randomized controlled trials increased study power and reduced biasedness of effect size estimation. J Clin Epidemiol. 2016;76:137–46. https://doi.org/10.1016/j.jclinepi.2016.02.004.

    Article  PubMed  Google Scholar 

  12. Kahan BC, Jairath V, Doré CJ, Morris TP. The risks and rewards of covariate adjustment in randomized trials: an assessment of 12 outcomes from 8 studies. Trials. 2014;15:139. https://doi.org/10.1186/1745-6215-15-139.

    Article  PubMed  PubMed Central  Google Scholar 

  13. Raab GM, Day S, Jill Sales J. How to select covariates to include in the analysis of a clinical trial. Control Clin Trials. 2000;21:330–42. https://doi.org/10.1016/S0197-2456(00)00061-1.

    Article  CAS  PubMed  Google Scholar 

  14. Laursen RP, 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. https://doi.org/10.1542/peds.2017-0735.

    Article  PubMed  Google Scholar 

  15. Lachin JM. Properties of simple randomization in clinical trials. Control Clin Trials. 1988;9:312–26. https://doi.org/10.1016/0197-2456(88)90046-3.

    Article  CAS  PubMed  Google Scholar 

  16. Matts JP, Lachin JM. Properties of permuted-block randomization in clinical trials. Control Clin Trials. 1988;9:327–44. https://doi.org/10.1016/0197-2456(88)90047-5.

    Article  CAS  PubMed  Google Scholar 

  17. Bell ML, Rabe BA. The mixed model for repeated measures for cluster randomized trials: a simulation study investigating bias and type I error with missing continuous data. Trials. 2020;21:148. https://doi.org/10.1186/s13063-020-4114-9.

    Article  PubMed  PubMed Central  Google Scholar 

  18. Pals SL, Murray DM, Alfano CM, Shadish WR, Hannan PJ, Baker WL. Individually randomized group treatment trials: a critical appraisal of frequently used design and analytic approaches. Am J Public Health. 2008;98:1418–24. https://doi.org/10.2105/AJPH.2007.127027.

    Article  PubMed  PubMed Central  Google Scholar 

  19. Kernan WN, Viscoli CM, Makuch RW, Brass LM, Horwitz RI. Stratified randomization for clinical trials. J Clin Epidemiol. 1999;52:19–26. https://doi.org/10.1016/S0895-4356(98)00138-3.

    Article  CAS  PubMed  Google Scholar 

  20. Kahan BC, Morris TP. Reporting and analysis of trials using stratified randomisation in leading medical journals: review and reanalysis. BMJ. 2012;345:e5840. https://doi.org/10.1136/bmj.e5840.

    Article  PubMed  PubMed Central  Google Scholar 

  21. Kangas ST, Salpéteur C, Nikièma V, Talley L, Ritz C, Friis H, 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. https://doi.org/10.1371/journal.pmed.1002887.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Geiker NRW, 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. https://doi.org/10.3945/ajcn.115.126565.

    Article  CAS  PubMed  Google Scholar 

  23. Sedgwick P. Standard deviation versus standard error. BMJ. 2011;343:d8010. https://doi.org/10.1136/bmj.d8010.

    Article  Google Scholar 

  24. Moher D, Sally Hopewell S, Schulz KF, Montori V, Götzsche PC, Devereaux PJ, et al. ConSoRT 2010 explanation and elaboration: updated guidelines for reporting parallel group randomised trials. BMJ. 2010;340:c869. https://doi.org/10.1136/bmj.c869.

    Article  PubMed  PubMed Central  Google Scholar 

  25. Senn S. Testing for baseline balance in clinical trials. Stat Med. 1994;13:1715–26. https://doi.org/10.1002/sim.4780131703.

    Article  CAS  PubMed  Google Scholar 

  26. Roberts C, Torgerson DJ. Baseline imbalance in randomised controlled trials. BMJ. 1999;319:185. https://doi.org/10.1136/bmj.319.7203.185.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Kramer MS, Chalmers B, Hodnett ED, Sevkovskaya Z, Dzikovich I, Shapiro S, et al. Promotion of Breastfeeding Intervention Trial (PROBIT): a randomized trial in the Republic of Belarus. JAMA. 2001;285:413–20. https://doi.org/10.1001/jama.285.4.413.

    Article  CAS  PubMed  Google Scholar 

  28. Altman DG, Royston P. The cost of dichotomising continuous variables. BMJ. 2006;332:1080. https://doi.org/10.1136/bmj.332.7549.1080.

    Article  PubMed  PubMed Central  Google Scholar 

  29. Van der Vaart AW. Asymptotic statistics. Cambridge: Cambridge University Press; 1998.

  30. Weisberg S. Applied linear regression. 3rd ed. Hoboken: Wiley & Sons; 2005.

  31. Senn S. Change from baseline and analysis of covariance revisited. Stat Med. 2006;25:2334–44. https://doi.org/10.1002/sim.2682.

    Article  Google Scholar 

  32. Thompson DD, Lingsma HF, Whiteley WN, Murray GD, Steyerberg EW. Covariate adjustment had similar benefits in small and large randomized controlled trials. J Clin Epidemiol. 2015;68:1068–75. https://doi.org/10.1016/j.jclinepi.2014.11.001.

    Article  PubMed  Google Scholar 

  33. Tsiatis AA, Davidian M, Zhang M, Lu X. Covariate adjustment for two-sample treatment comparisons in randomized clinical trials: a principled yet flexible approach. Stat Med. 2008;27:4658–77. https://doi.org/10.1002/sim.3113.

    Article  PubMed  PubMed Central  Google Scholar 

  34. Wang B, Ogburn EL, Rosenblum M. Analysis of covariance in randomized trials: more precision and valid confidence intervals, without model assumptions. Biometrics. 2019;75:1391–1400. https://doi.org/10.1111/biom.13062.

    Article  PubMed  Google Scholar 

  35. Bartlett JW. Robustness of ANCOVA in randomized trials with unequal randomization. Biometrics. 2020;76:1036–8. https://doi.org/10.1111/biom.13184.

    Article  PubMed  Google Scholar 

  36. Verbeke G, Lesaffre E. The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data. Comput Stat Data Anal. 1997;23:541–56. https://doi.org/10.1016/S0167-9473(96)00047-3.

    Article  Google Scholar 

  37. Jiang J. REML estimation: asymptotic behavior and related topics. Ann Stat. 1996;24:255–86.

    Article  Google Scholar 

  38. Fitzmaurice GM, Laird NM, Ware JH. Applied longitudinal analysis. 2nd ed. Hoboken: Wiley & Sons; 2011.

  39. Liang K-Y, Zeger SL. Longitudinal data analysis of continuous and discrete responses for pre–post designs. Sankhya. 2000;62:134–48. https://doi.org/10.2307/25053123.

    Article  Google Scholar 

  40. Liu GF, Lu K, Mogg R, Mallick M, Mehrotra DV. Should baseline be a covariate or dependent variable in analyses of change from baseline in clinical trials? Stat Med. 2009;28:2509–30. https://doi.org/10.1002/sim.3639.

    Article  PubMed  Google Scholar 

  41. 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. https://doi.org/10.3945/ajcn.116.134932.

    Article  CAS  PubMed  Google Scholar 

  42. R Core Team. R: a language and environment for statistical computing. Vienna: R Foundation for Statistical Computing; 2020.

  43. Lenth RV. Least-squares means: the R package LSmeans. J Stat Softw. 2016;69:1–33. https://doi.org/10.18637/jss.v069.i01.

    Article  Google Scholar 

  44. Duan N. Smearing estimate: a nonparametric retransformation method. J Am Stat Assoc. 1983;78:605–10. https://doi.org/10.2307/2288126.

    Article  Google Scholar 

  45. Laursen R, Dalskov S, Damsgaard CT, Ritz C. Back-transformation of treatment differences—an approximate method. Eur J Clin Nutr. 2014;68:277–80. https://doi.org/10.1038/ejcn.2013.259.

    Article  CAS  PubMed  Google Scholar 

  46. Yilma D, Kæstel P, Olsen MF, Abdissa A, Tesfaye M, Girma T, et al. Change in serum 25-hydroxyvitamin D with antiretroviral treatment initiation and nutritional intervention in HIV-positive adults. Br J Nutr. 2016;116:1720–7. https://doi.org/10.1017/S0007114516003743.

    Article  CAS  Google Scholar 

  47. Saquib N, Saquib J, Ioannidis JPA. Practices and impact of primary outcome adjustment in randomized controlled trials: meta-epidemiologic study. BMJ. 2013;347:f4313. https://doi.org/10.1136/bmj.f4313.

    Article  PubMed  PubMed Central  Google Scholar 

  48. DeMets DL, Cook TD, Buhr KA. Guidelines for statistical analysis plans. JAMA. 2017;318:2301–3. https://doi.org/10.1001/jama.2017.18954.

    Article  PubMed  Google Scholar 

  49. Hothorn LA. The two-step approach—a significant ANOVA F-test before Dunnett’s comparisons against a control—is not recommended. Commun Stat—Theory Methods. 2016;45:3332–43. https://doi.org/10.1080/03610926.2014.902225.

    Article  Google Scholar 

  50. Greenland S, Robins J, Pearl J. Confounding and collapsibility in causal inference. Stat Sci. 1999;14:29–46.

    Article  Google Scholar 

  51. Twisk J, Bosman L, Hoekstra T, Rijnhart J, Welten M, Heymans M. Different ways to estimate treatment effects in randomised controlled trials. Contemp Clin Trials Commun. 2018;10:80–85. https://doi.org/10.1016/j.conctc.2018.03.008.

    Article  Google Scholar 

  52. Harris JE, Raynor HA. Crossover designs in nutrition and dietetics research. J Acad Nutr Diet. 2017;117:1023–30. https://doi.org/10.1016/j.jand.2017.03.017.

    Article  PubMed  Google Scholar 

  53. Ritz C, Rønn B. Estimands: improving inference in randomized controlled trials in clinical nutrition in the presence of missing values. Eur J Clin Nutr. 2018;72:1291–5. https://doi.org/10.1038/s41430-018-0207-x.

    Article  PubMed  Google Scholar 

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Ritz, C. Statistical analysis of continuous outcomes from parallel-arm randomized controlled trials in nutrition—a tutorial. Eur J Clin Nutr 75, 160–171 (2021). https://doi.org/10.1038/s41430-020-00750-z

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