All analyses involved multilevel modeling, conducted using HLM 6.08 (Raudenbush, Bryk, Cheong, & Congdon, 2000).
Data processing and descriptive analyses were conducted using Version 9.3 of the SAS System for Windows (Cary, NC, USA), with multilevel logistic modelling conducted using adaptive quadrature via the xtmelogit command of Stata Version 12 for Windows (College Station, TX: StataCorp LP).
These variables were entered into multivariate logistic regression models conducted using the backward stepwise method: first, all the variables have been included, then, using a stepwise procedure, the variables with not statistically significant association have been removed.
Standard meta-analysis involving the fixed effects model and conventional random effects model was conducted using the standard error and effect size reported in each study [ 24, 27].
A second set of tests associated with the inefficiency model was conducted using the Cobb-Douglas function model [f].
To understand the mechanistic aspect between surface functionalities and the chromium ions, kinetic models were conducted using pseudo-second-order model and intraparticle diffusion model, respectively.
The random-effects model was performed, using the DerSimonian and Laird's method [26], while the fixed-effects model was conducted using the Mantel-Haenszel's method [25].
Tests of the validity of the Förster model were conducted using the transition density cube (TDC) method, which provides the exact Coulombic interaction within a certain model chemistry.
Modeling was conducted using Modeller 9v11.
Nonlinear time history analyses of the finite element model were conducted using the ground motion suites.
