A pharmacodynamic analysis method to determine the relative importance of drug concentration and treatment time on effect

Abstract

Purpose: The pharmacodynamics of most drugs follow the empirical relationship, Cⁿ × T=h, where C is drug concentration, T is exposure time and h is drug exposure constant. The value of n indicates the relative importance of C and T in determining the effect. An n value greater than 1.0 indicates that for two infusions that produce the same C × T, a short infusion that delivers high concentrations over a short duration will produce a greater Cⁿ × T and therefore a greater effect, compared to a long infusion that delivers lower concentrations. The reverse is true for an n value less than 1.0 and would support the use of a slow infusion. Hence, it is important to determine the n values and whether the n value significantly differs from 1.0. This report describes a three-step method for this purpose. Methods: First, we obtained experimental data on the relationship between drug concentration, treatment time and effect, and analyzed the data with a three-dimensional surface response method to obtain the pharmacodynamic model parameters and the magnitude of data variability. The experiments used mitomycin C and two human cancer cell lines, i.e. bladder RT4 and pharynx FaDu cells. The n values obtained from four experiments ranged from 1.04 to 1.16 for FaDu cells and from 1.14 to 1.46 for RT4 cells. The variability in the effect data decreased from 11.9% at 0% effect to 6.14% at 100% effect. Second, these results were used with Monte Carlo simulations to generate 100 concentration-time-effect data sets, which contained randomly and normally distributed data variability comparable to the experimentally observed variability, for each experimentally determined n value. This is analogous to performing 100 experiments under the same experimental conditions. Third, we analyzed the simulated data sets to obtain 100 estimated n values. The frequency with which these estimated n values fell above or below 1.0 indicated the probability that the experimentally determined n value used in the Monte Carlo simulations was truly different from 1.0. We defined this frequency for individual experiments as F_one, and calculated the overall probability for multiple experiments (F_multiple). A probability of greater than 97.5% (i.e. P < 0.05 for a two-tailed test) was considered statistically significant. Results: Analysis of the mitomycin C pharmacodynamic data yielded F_one and F_multiple of 99% to 100% for FaDu and RT4 cells, indicating that the n values for these cells were significantly higher than 1.0. A comparison of the statistical significance of the n value analyzed by the three-step pharmacodynamic analysis method, a conventional statistical method such as the Student's t-test and nonlinear regression analysis, indicated two advantages for the pharmacodynamic method: fewer experiments were required (theoretically only one experiment with three replicates would be sufficient) and a higher statistical significance of the n value was obtained. Conclusions: In summary, the three-step pharmacodynamic study design and analysis method can be used to define the relative importance of drug concentration and treatment time on drug effect.