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

Purpose: The pharmacodynamics of most drugs follow the empirical relationsh ip, C-n x 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 o f C and T in determining the effect. An n value greater than 1.0 indicates that for two infusions that produce the same C x T, a short infusion that d elivers high concentrations over a short duration will produce a greater C- n x T and therefore a greater effect, compared to a long infusion that deli vers 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 de termine the n values and whether the n value significantly differs from 1.0 . This report describes a three-step method for this purpose. Methods: Firs t, we obtained experimental data on the relationship between drug concentra tion, treatment time and effect, and analyzed the data with a three-dimensi onal surface response method to obtain the pharmacodynamic model parameters and the magnitude of data variability. The experiments used mitomycin C an d 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 da ta 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 concentrati on-time-effect data sets, which contained randomly and normally distributed data variability comparable to the experimentally observed variability, fo r each experimentally determined n value. This is analogous to performing 1 00 experiments under the same experimental conditions. Third, we analyzed t he 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 proba bility that the experimentally determined n value used in the Monte Carlo s imulations was truly different from 1.0. We defined this frequency for indi vidual experiments as F-one, and calculated the overall probability for mul tiple experiments (F-multiple). A probability of greater than 97.5% (i.e. P < 0.05 for a two-tailed test) was considered statistically significant. Re sults: 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 valu es for these cells were significantly higher than 1.0. A comparison of the statistical significance of the n value analyzed by the three-step pharmaco dynamic analysis method, a conventional statistical method such as the Stud ent's t-test and non-linear regression analysis, indicated two advantages f or the pharmacodynamic method: fewer experiments were required (theoretical ly only one experiment with three replicates would be sufficient) and a hig her statistical significance of the n value was obtained. Conclusions: In s ummary, the three-step pharmacodynamic study design and analysis method can be used to define the relative importance of drug concentration and treatm ent time on drug effect.