Advanced Analysis of Variance, Random Effects and Mixed Effects Models

  • Ton J. Cleophas
  • Aeilko H. Zwinderman


In clinical trials it is common to assume a fixed effects research model. This means that the patients selected for a specific treatment are assumed to be homogeneous and have the same true quantitative effect and that the differences observed are residual, meaning that they are caused by inherent variability in biological processes, rather than some hidden subgroup property. If, however, we have reasons to believe that certain patients due to co-morbidity, co-medication, age or other factors will respond differently from others, then the spread in the data is caused not only by the residual effect but also by between patient differences due to some subgroup property. It may even be safe to routinely treat any patient effect as a random effect, unless there are good arguments no to do so. Random effects research models require a statistical approach different from that of fixed effects models (Anonymous 2006; Campbell 2006; Gao 2003).


Health Center Treatment Efficacy Random Effect Model Fixed Effect Model Residual Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Anonymous (2006) Distinguishing between random and fixed variables, effects and coefficients. Newson, USP 656 Winter 2006, pp 1–3Google Scholar
  2. Anonymous (2011a) Random effects models. Wikipedia, the free encyclopedia. Accessed 15 Dec 2011
  3. Anonymous (2011b) Variance components and mixed models. Accessed 15 Dec 2011
  4. Boeckman AJ, Sheiner LB, Beal SL (1992) NONMEM user’s guide. NONMEM Project Group, University of California, San FranciscoGoogle Scholar
  5. Brier ME, Aronoff GR (1996) Application of artificial neural networks to clinical pharmacology. Int J Clin Pharmacol Ther 34:510–514PubMedGoogle Scholar
  6. Campbell MJ (2006) Random effects models. In: Campbell MJ (ed) Statistics at square two, 2nd edn. Blackwell Publishing/BMJ Books, Oxford/Malden, pp 67–83CrossRefGoogle Scholar
  7. Dalla Costa T, Nolting A, Rand K, Derendorf H (1997) Pharmacokinetic-pharmacodynamic modelling of the in vitro antiinfective effect of piperacillin-tazobactam combinations. Int J Clin Pharmacol Ther 35:426–433PubMedGoogle Scholar
  8. Gao S (2003) Special models for sampling survey. In: Lu Y, Fang J (eds) Advanced medical statistics, 1st edn. World Scientific, River Edge, pp 685–709CrossRefGoogle Scholar
  9. Hays WL (1988) Random effects and mixed models. In: Statistics, 4th edn. Holt, Rhinehart and Winnston Inc, Chicago, pp 479–543Google Scholar
  10. Lima JJ, Beasley BN, Parker RB, Johnson JA (2005) A pharmacodynamic model of the effects of controlled-onset extended-release verapamil on 24-hour ambulatory blood pressure. Int J Clin Pharmacol Ther 43(4):187–194PubMedGoogle Scholar
  11. Lotsch J, Kobal G, Geisslinger G (2004) Programming of a flexible computer simulation to visualize pharmacokinetic-pharmacodynamic models. Int J Clin Pharmacol Ther 42:15–22PubMedGoogle Scholar
  12. Mahmood I (2003) Center specificity in the limited sampling model (LSM): can the LSM developed from healthy subjects be extended to disease states? Int J Clin Pharmacol Ther 41:517–523PubMedGoogle Scholar
  13. Meibohm B, Derendorf H (1997) Basic concepts of pharmacokinetic/pharmacodynamic (PK/PD) modelling. Int J Clin Pharmacol Ther 35:401–413. ReviewPubMedGoogle Scholar
  14. Mueck W, Becka M, Kubitza D, Voith B, Zuehlsdorf M (2007) Population model of the pharmacokinetics and pharmacodynamics of rivaroxaban–an oral, direct factor xa inhibitor–in healthy subjects. Int J Clin Pharmacol Ther 45:335–344PubMedGoogle Scholar
  15. SPSS Statistical Software. Accessed 15 Dec 2011

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Ton J. Cleophas
    • 1
    • 2
  • Aeilko H. Zwinderman
    • 1
    • 3
  1. 1.Applied to Clinical TrialsEuropean Interuniversity College of Pharmaceutical MedicineLyonFrance
  2. 2.Department of MedicineAlbert Schweitzer HospitalDordrechtNetherlands
  3. 3.Department of Biostatistics and EpidemiologyAcademic Medical CenterAmsterdamNetherlands

Personalised recommendations