2.1

CFOA wear quantification in RCT studies

Gypsum replicas of 16 Tetric-C, 17 Tetric-EC, 16 Gradia-DP, 18 Filtek Supreme, 19 Z100 were taken from two previously published randomized clinical trial studies that evaluated the occlusal contact area/OCA wear resistance of the five composites, but did not report on the CFOA wear. The data presented in this paper focuses on CFOA. A 3D laser scanning technique determined the in vivo CFOA wear by quantifying the vertical loss of substance along the CFOA of gypsum replicas. Match 3D (Willytec, GmbH), a specially developed image analysis software was used to superimpose follow-up images recorded after 6, 12, 24, 36, 48 and 60 months on baseline images, by aligning the three user-defined references. If the standard deviation is less than 20 μm, the match was accepted , following which a digital subtraction of the follow-up image from the baseline was performed to arrive at a differential image to quantify the vertical wear along the CFOA in μm (see for details on matching procedure).

2.2

Statistical analyses of clinical CFOA wear magnitude

The CFOA wear data of five materials were compared with each other at six time points (at month 6 up to month 60) by means of pair wise contrasts ( F -test) to which Bonferroni correction for multiple testing was applied. The repeated measurements were summarized by a wear-rate, ρ , for each material, considering a non-linear relationship of wear, W , with time, t ( Fig. 2 ) where

ρ is the wear rate (μm/month), W is wear (μm), t is time (month), i is 1 for month 6, 2 for month 36, and 3 for month 60, j is i − 1.

Non-linear wear model. Wear rate ( ρ ) prediction in a non-linear wear model with three time slopes. Time is expressed in months during period1/ running-in-wear from BL-baseline (1 month following P -placement of restorations) to t ₁ -6 months through period2/ early-stage wear from t ₁ to t ₂ -36 months and period3/ steady-state wear from t ₂ to t ₃ -60 months and their corresponding wear ( W ) is quantified in μm. Wear rate is estimated by the slope of the line fitting the wear data in period1, period2 and period3.

For example, ρ 1 is estimated from the slope of the line fitting the wear data recorded in period1/ running-in wear (from baseline to month 6), from ρ ₂ being the slope in period2/ early-stage wear (between months 6 and 36), and ρ ₃ the slope in period3/ steady-state wear (between months 36 and 60)

2.3

Statistical modelling of the clinical CFOA wear rate and patient data

The patient data available for each of the 31 subjects (8 males, 23 females) include age, gender, cavity type, surface area, type of restorative, and CFOA wear measurements done at six time points. In order to describe the relationship between the response variable (CFOA wear rate) and some of the covariates (material, time, patient) a mixed effect model was fitted to the data set. The goal was to summarize the in vivo performance of the different materials as an in vivo index by ranking the estimated material-related coefficients in the linear mixed model.

2.4

Estimation of material-related coefficients

The data set comprising the categorical covariates such as material, time, patient, and CFOA wear magnitude were inserted in a data frame of PROC MXED as a table with columns corresponding to variables and rows to observations. The following formula was applied to the data set to obtain the results to which various extractor functions are applied to obtain values for the estimated covariates:

where Y _ijk is an in vivo index and is the sum of the material effect, M _i with operator as a covariate, and time effect, T _j , as fixed effects plus a patient effect, P _k , as a random effect with covariates – cavity type, surface area, tooth (upper/lower), and ε _ijk which is an error term measured by R -squared (close to 1) for the observation of the procedural and material effects M _i and T _j in a patient group P _k assuming to be independent and normally distributed.

The four major sections of the results are: a descriptive part, statistics characterizing the model, summary of parameter estimates of the random effects and that of the fixed-effects. Based on the model-fit statistics such as Akaike’s Information Criteria (AIC), the best fitting model (lowest AIC) is selected for each material, among the different models fit to the same data. A statistical significance was accepted at p < 0.05. Generally, the parameter/covariate estimates in a statistical model represent the “best guess” at the unknown values of the model parameters. Such estimates are provided by the third part of the results as a table of estimates and standard errors of random and fixed-effects parameters. Since the material-related effect is of primary interest in this study, estimates of material-related effects M _i adjusted for patient covariates were then used as a summarizing in vivo ranking to be correlated later with other in vitro variables. This estimate, M _i is basically a numerical value mentioned in the results table labeled as intercept.

2.5

Ranking of the material-related coefficients

With the predicted estimate M _i for each material referred to as ‘ x ’, a relative rank was defined as 1 + ( n − 1) ( x − m )/( M − m ) in order to take into account the relative differences between materials, where m is the minimum (mean) of the estimates, M the maximum (mean) of the estimates, and n ( n = 5) the number of materials.

2.6

In vitro scratch tests

Two specimens per composite measuring 2 mm × 5 mm were fabricated by inserting the material into a silicone mold in one increment, covering the surfaces with acetate strips and light cured with the Elipar Freelight SN-939800005306 (3 M ESPE) at ≥400 mW/cm ² for 40 s. The specimens were removed from their molds, embedded in a self-curing acrylic resin, treated in a grinding machine rotating at 200 rpm on SiC grinding papers of decreasing abrasiveness from 320 down to 1200-grit under continuous water cooling, polished using felt cloths with 3, 1 and 0.25 μm embedded diamond, Al ₂ O ₃ and SiO ₂ grains and put in an ultrasonic water bath for 5 min to remove any remaining debris.

The polished specimens with the wide face mounted in epoxy were subjected to scratching tests performed in a MUST micro-tribometer (Falex Tribology N.V., Belgium) with a stainless steel cantilever (stiffness – 1.137 N/m) and diamond tip (radius – 5 μm) in the edge-forward direction. During the tests, the specimens moved under the loaded indenter of normal loads, F _n , of 15, 25, and 35 mN at a constant speed of 0.05 mm/s for a total length of 1 mm. On each test sample ( n = 2/composite), five scratches were made. The data collected included applied normal force and tangential force with respect to the position along the scratch.

2.7

3D interferometry and SEM imaging of scratches

Scratches were imaged with a non-contact white light interferometric profilometer (WYKO NT 2000) equipped with a WYKO Vision-32 analysis software. The hardness, H _s , of the scratched material was calculated from the scratch width, w , at a given normal load, F _n from the formula :

After the analysis by 3D interferometry, the specimens were gold sputtered and investigated in SEM.

2.8

Statistical modeling of the scratch performance data

All analyses were performed using SAS software (version 9.2 Windows). Scratch width, w , depth, d and hardness, H _s calculated by imaging the scratch tracks were used as data set. Average values obtained from 10 measurements done on 2 samples per composite ( n = 5) for these three variables were investigated. The presence of regression relationships between the dependent variable – scratch hardness and other predictors – scratch width and depth were tested at a statistical significance of 0.05. In order to indicate the existence of a linear relationship between the variables, the coefficient of determination, R ² , was calculated, and eventually a relative rank was assigned to the tested material.

2.9

Correlative ranking

Concerning the ranking order, rank 1 in the case of in vivo wear measurements corresponds to the least wear/better wear resistance, while rank 1 for hardness measurements refers to the lowest hardness. Pearson’s correlation coefficient between clinical/in vivo and in vitro ranking order was calculated.

2.1

CFOA wear quantification in RCT studies

Gypsum replicas of 16 Tetric-C, 17 Tetric-EC, 16 Gradia-DP, 18 Filtek Supreme, 19 Z100 were taken from two previously published randomized clinical trial studies that evaluated the occlusal contact area/OCA wear resistance of the five composites, but did not report on the CFOA wear. The data presented in this paper focuses on CFOA. A 3D laser scanning technique determined the in vivo CFOA wear by quantifying the vertical loss of substance along the CFOA of gypsum replicas. Match 3D (Willytec, GmbH), a specially developed image analysis software was used to superimpose follow-up images recorded after 6, 12, 24, 36, 48 and 60 months on baseline images, by aligning the three user-defined references. If the standard deviation is less than 20 μm, the match was accepted , following which a digital subtraction of the follow-up image from the baseline was performed to arrive at a differential image to quantify the vertical wear along the CFOA in μm (see for details on matching procedure).

2.2

Statistical analyses of clinical CFOA wear magnitude

The CFOA wear data of five materials were compared with each other at six time points (at month 6 up to month 60) by means of pair wise contrasts ( F -test) to which Bonferroni correction for multiple testing was applied. The repeated measurements were summarized by a wear-rate, ρ , for each material, considering a non-linear relationship of wear, W , with time, t ( Fig. 2 ) where

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