title: Accounting for measurement reliability to improve the quality of inference in dental microhardness research: a worked example.
abstract: OBJECTIVE
  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.
  
  
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Institute for Tourism, Vrhovec 5, 10000, Zagreb, Croatia.
authors.forename: Ivan
authors.initials: I
authors.lastname: Sever
authors.affiliation: Department of Endodontics and Restorative Dentistry, School of Dental Medicine, University of Zagreb, Gunduliceva 5, 10000, Zagreb, Croatia. eklaric@sfzg.hr.
authors.forename: Eva
authors.initials: E
authors.lastname: Klaric
authors.affiliation: Department of Endodontics and Restorative Dentistry, School of Dental Medicine, University of Zagreb, Gunduliceva 5, 10000, Zagreb, Croatia.
authors.forename: Zrinka
authors.initials: Z
authors.lastname: Tarle
mesh_terms: D002130:Calcium Phosphates / Q000737:chemistry; D000077463:Carbamide Peroxide; D003743:Dental Enamel / Q000187:drug effects*; D006244:Hardness; D006801:Humans; D006861:Hydrogen Peroxide / Q000737:chemistry*; D066298:In Vitro Techniques; D008964:Molar, Third; D010545:Peroxides / Q000737:chemistry*; D015203:Reproducibility of Results; D012464:Saliva, Artificial / Q000737:chemistry; D013499:Surface Properties; D058205:Tooth Bleaching Agents / Q000737:chemistry*; D014508:Urea / Q000031:analogs & derivatives* / Q000737:chemistry
chemical_list: D002130:Calcium Phosphates; D010545:Peroxides; D012464:Saliva, Artificial; D058205:Tooth Bleaching Agents; C519480:amorphous calcium phosphate; D000077463:Carbamide Peroxide; D014508:Urea; D006861:Hydrogen Peroxide
keywords: Bias; Reproducibility of results; Statistical models; Tooth bleaching; Treatment outcome; Weights and measures