In mixture toxicity, concentration-effect data are often used to generate conclusions on combined effect. While models of combined effect are available for such assessments, proper fitting of the data is critical to obtaining accurate conclusions. In this study an asymmetry parameter (s) was evaluated for data-fitting and compared with our previous approach. Inhibition of bioluminescence was assessed with Vibrio fischeri at 15, 30 and 45-minutes of exposure with seven or eight concentrations and a control (each duplicated) for each single-chemical (A or B) and mixture (A:B). Concentration-effect data were fitted to sigmoid curves using the four-parameter logistic function (4PL) and the five-parameter logistic minus one-parameter (5PL-1P) function. For the 4PL, parameters included minimum effect, maximum effect, EC50 and slope, while for the 5PL-1P the minimum effect parameter was removed and an asymmetry parameter was added. A total of 72 mixture toxicity data sets were evaluated, representing 432 single-chemical and 216 mixture curves. Mean coefficients of determination (r2) for all 648 curves showed that the 5PL-1P gave better fitting (0.9982 ± 0.0018) than the 4PL (0.9973 ± 0.0030). For both functions, the sum-of-squares of the residuals (SS-Res) was determined for each curve. The 5-parameter rational regression best described the relationship between the decrease in sum-of-squares of the residuals (i.e., 4PL: SS-Res – 5PL-1P: SS-Res) and log s, with fitting improved the most at low values of s (s < 0.8). This held even when curves with r2 values ≤ 0.9970 were removed from the analyses. Subsequent review of the combined effects obtained via the 4PL and the 5PL-1P functions resulted in a change in the interpretation of combined effect in 39/216 (18%) cases.

The value of time-dependent toxicity (TDT) data in predicting mixture toxicity was examined. Single chemical (A and B) and mixture (A + B) toxicity tests using Microtox® were conducted with inhibition of bioluminescence (Vibrio fischeri) being quantified after 15, 30 and 45-min of exposure. Single chemical and mixture tests for 25 sham (A1:A2) and 125 true (A:B) combinations had a minimum of seven duplicated concentrations with a duplicated control treatment for each test. Concentration/response (x/y) data were fitted to sigmoid curves using the five-parameter logistic minus one parameter (5PL-1P) function, from which slope, EC25, EC50, EC75, asymmetry, maximum effect, and r2 values were obtained for each chemical and mixture at each exposure duration. Toxicity data were used to calculate percentage-based TDT values for each individual chemical and mixture of each combination. Predicted TDT values for each mixture were calculated by averaging the TDT values of the individual components and regressed against the observed TDT values obtained in testing, resulting in strong correlations for both sham (r2 = 0.989, n = 25) and true mixtures (r2 = 0.944, n = 125). Additionally, regression analyses confirmed that observed mixture TDT values calculated for the 50% effect level were somewhat better correlated with predicted mixture TDT values than at the 25 and 75% effect levels. Single chemical and mixture TDT values were classified into five levels in order to discern trends. The results suggested that the ability to predict mixture TDT by averaging the TDT of the single agents was modestly reduced when one agent of the combination had a positive TDT value and the other had a minimal or negative TDT value.