Consecutive outpatients with simultaneous serum total calcium and albumin measurements determined by Calgary Laboratory Services (CLS) over a 2 month time period were included. CLS provides laboratory testing for the Calgary Health Region (population 1.1 million) using instruments and reagents from a single vendor (Roche Diagnostics Ltd, Laval, PQ, Canada). Tests were conducted using the Arsenazo III dye binding method for calcium and the BCP reagent for albumin. Quality was satisfactory during the study period and assured by use of multi-rule quality control procedures at three levels [6], maintenance of clinical laboratory accreditation by the College of Physicians and Surgeons of Alberta with successful evaluation by proficiency testing programs provided by the College of American Pathologists (Northfield, IL, USA) and Ceqal (Vancouver, Canada). Exclusion criteria were: age < 18 years, serum creatinine > 200 μ mol/L, albumin < 20 g/L or > 50 g/L, total calcium > 3.0 mmol/L, or elevations in serum parathyroid hormone, alkaline phosphatase, or alanine transaminase above the reference range (reflecting the presence of conditions which may influence serum calcium levels). Vitamin D concentrations were not assessed. Only the first simultaneous total calcium and albumin result per patient during the study period were employed. The distribution of serum calcium concentrations was assessed graphically and found to follow a normal distribution.

The study cohort was divided randomly into a 75% derivation sample and a 25% validation sample. A simple (ordinary least squares) linear regression equation for the association between total calcium and albumin was determined from the derivation sample [4, 5, 7, 8], and the regression equation was then cross-validated in the validation sample in the following manner. First, the validity of the regression equation was examined by calculating the amount of shrinkage in the predictive power of the equation [9]. This was carried out by applying the regression equation derived from the derivation sample to the validation sample to obtain a predicted calcium value for each subject. Measured calcium was then regressed on predicted calcium to obtain an estimate of the variance accounted for in the validation sample. The adjusted r^{2} for the validation sample was subtracted from that of the derivation sample to arrive at an estimate of the amount of shrinkage, an indication of how much the predictive ability decreases when the equation is applied to other samples. If the shrinkage is small the regression is considered internally valid [9]. Moreover, in a sensitivity analysis a bootstrapping procedure was undertaken as an additional assessment of the internal validity. The Bootstrapping procedure conceptually involves copying samples of a data set on top of themselves infinitely creating a mega data file [10]. A total of 1,000 re-samples were randomly drawn with replacement from the full sample. Analyses were then conducted on each new sample with regression parameters estimated for each sample including the original sample. Bootstrapping can provide regression coefficients, standard errors, and confidence intervals [10].

To compare discrepancies in the classification of calcium status with a published equation [1], corrected calcium concentrations were determined with each formula for 343 subjects with albumin concentration below the laboratory reference range (albumin < 33 g/L). The pattern of the individual differences for the hypoalbuminemic patients as well as the mean agreement with 95% limits of agreement was assessed using a Bland-Altman plot. This technique plots the difference in calcium concentration between the two equations against the mean of the two values for each subject [11]. Agreement in classification of calcium status between formulas was also assessed as follows; as hypo-, normo-, and hyper-calcemic by the weighted Kappa statistic [12], and as within or outside the laboratory reference range using McNemar's test. All analyses were conducted with the use of SAS software (version 8.01, SAS Institute Inc., Cary, NC, USA) or STATA (version 8.0, Stata Corp., College Station, TX, USA). The institutional review board at the University of Calgary approved the study.