Clinical Oral Investigations

, Volume 20, Issue 6, pp 1143–1149 | Cite as

Accounting for measurement reliability to improve the quality of inference in dental microhardness research: a worked example

Original Article



Dental microhardness experiments are influenced by unobserved factors related to the varying tooth characteristics that affect measurement reproducibility. This paper explores the appropriate analytical tools for modeling different sources of unobserved variability to reduce the biases encountered and increase the validity of microhardness studies.

Materials and methods

The enamel microhardness of human third molars was measured by Vickers diamond. The effects of five bleaching agents—10, 16, and 30 % carbamide peroxide, and 25 and 38 % hydrogen peroxide—were examined, as well as the effect of artificial saliva and amorphous calcium phosphate. To account for both between- and within-tooth heterogeneity in evaluating treatment effects, the statistical analysis was performed in the mixed-effects framework, which also included the appropriate weighting procedure to adjust for confounding. The results were compared to those of the standard ANOVA model usually applied.


The weighted mixed-effects model produced the parameter estimates of different magnitude and significance than the standard ANOVA model. The results of the former model were more intuitive, with more precise estimates and better fit.


Confounding could seriously bias the study outcomes, highlighting the need for more robust statistical procedures in dental research that account for the measurement reliability. The presented framework is more flexible and informative than existing analytical techniques and may improve the quality of inference in dental research.

Clinical relevance

Reported results could be misleading if underlying heterogeneity of microhardness measurements is not taken into account. The confidence in treatment outcomes could be increased by applying the framework presented.


Tooth bleaching Reproducibility of results Statistical models Weights and measures Treatment outcome Bias 



This study was supported by Croatian Science Foundation (Project 08/31 Evaluation of new bioactive materials and procedures in restorative dental medicine).

Conflict of interest

The authors declare that they have no conflict of interest.

Compliance with Ethical Standard

This article does not contain any studies with human participants or animals performed by any of the authors. The use of extracted human teeth, for enamel microhardness measurements, was approved by the Research Ethics Committee of the School of Dental Medicine, University of Zagreb, Croatia.


  1. 1.
    Hannigan A, Lynch CD (2013) Statistical methodology in oral and dental research: pitfalls and recommendations. J Dent 41:385–392CrossRefPubMedGoogle Scholar
  2. 2.
    Fleming PS, Koletsi D, Polychronopoulou A, Eliades T, Pandis N (2013) Are clustering effects accounted for in statistical analysis in leading dental specialty journals? J Dent 41:265–270CrossRefPubMedGoogle Scholar
  3. 3.
    Masood M, Masood Y, Newton JT (2015) The clustering effects of surfaces within the tooth and teeth within individuals. J Dent Res 94(2):281–288CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Kunin AA, Evdokimova AY, Moiseeva NS (2015) Age-related differences of tooth enamel morphochemistry in health and dental caries. The EPMA Journal 6(3)Google Scholar
  5. 5.
    Somani R, Jaidka S, Singh DJ, Arora V (2014) Remineralizing potential of various agents on dental erosion. J Oral Biol Craniofac Res 4:104–108CrossRefPubMedPubMedCentralGoogle Scholar
  6. 6.
    Lia Mondelli RF, Garrido Gabriel TR, Piola Rizzante FA, Magalhaes AC, Soares Bombonatti JF, Ishikiriama SK (2015) Do different bleaching protocols affect the enamel microhardness? Eur J Dent 9:25–30CrossRefPubMedPubMedCentralGoogle Scholar
  7. 7.
    China ALP, Souza NM, Gomes Y, Alexandrino LD, Silva CM (2014) Effect of fluoride gels on microhardness and surface roughness of bleached enamel. Open Dent J 8:188–193CrossRefPubMedPubMedCentralGoogle Scholar
  8. 8.
    Joiner A, Thakker G, Cooper Y (2004) Evaluation of a 6% hydrogen peroxide tooth whitening gel on enamel and dentine microhardness in vitro. J Dent 32:27–34CrossRefPubMedGoogle Scholar
  9. 9.
    Rodrigues JA, Marchi GM, Ambrosano GMB, Heymann HO, Pimenta LA (2005) Microhardness evaluation of in situ vital bleaching on human dental enamel using a novel study design. Dent Mater 21:1059–1067CrossRefPubMedGoogle Scholar
  10. 10.
    Mujdeci A, Gokay O (2006) Effect of bleaching agents on the microhardness of tooth-colored restorative materials. J Prosthet Dent 95:286–289CrossRefPubMedGoogle Scholar
  11. 11.
    Azer SS, Machado C, Sanchez E, Rashid R (2009) Effect of home bleaching systems on enamel nanohardness and elastic modulus. J Dent 37:185–190CrossRefPubMedGoogle Scholar
  12. 12.
    Zantner C, Schwarzbach NB (2007) Surface microhardness of enamel after different home bleaching procedures. Dent Mater 23:243–250CrossRefPubMedGoogle Scholar
  13. 13.
    Xie Y, Brand JE, Jann B (2012) Estimating heterogeneous treatment effects with observational data. Sociol Methodol 42(1):314–347CrossRefPubMedPubMedCentralGoogle Scholar
  14. 14.
    Elhorst JP (2003) Specification and estimation of spatial panel data models. Int Reg Sci Rev 26(3):244–268CrossRefGoogle Scholar
  15. 15.
    Green WH (2003) Econometric analysis. Prentice Hall, New JerseyGoogle Scholar
  16. 16.
    Klaric E, Rakic M, Sever I, Milat O, Par M, Tarle Z (2015) Enamel and Dentin Microhardness and Chemical Composition After Experimental Light-activated Bleaching. Operative Dentistry 40(3)Google Scholar
  17. 17.
    Porta M (2014) A Dictionary of Epidemiology. Oxford University Press, New YorkGoogle Scholar
  18. 18.
    Bresciani E, Wagner WC, Navarro MFL, Dickens SH, Peters MC (2010) In vivo dentin microhardness beneath a calcium-phosphate cement. J Dent Res 89(8):836–841CrossRefPubMedPubMedCentralGoogle Scholar
  19. 19.
    Fleiss JL, Park MH, Chilton NW (1987) Within-mouth correlations and reliabilities for probing depth and attachment level. J Periodontol 58(7):460–463CrossRefPubMedGoogle Scholar
  20. 20.
    Alves Rde V, Machion L, Andia DC, Casati MZ, Sallum AW, Sallum EA (2005) Reproducibility of clinical attachment level and probing depth of a manual probe and a computerized electronic probe. J Int Acad Periodontol 7(1):27–30PubMedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute for TourismZagrebCroatia
  2. 2.Department of Endodontics and Restorative Dentistry, School of Dental MedicineUniversity of ZagrebZagrebCroatia

Personalised recommendations