title: A pharmacodynamic analysis method to determine the relative importance of drug concentration and treatment time on effect.
abstract: OBJECTIVE
  The pharmacodynamics of most drugs follow the empirical relationship, 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 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 x T, a short infusion that delivers 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 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.
authors.affiliation: College of Pharmacy, The Ohio State University, Columbus 43210, USA.
authors.forename: N J
authors.initials: NJ
authors.lastname: Millenbaugh
authors.forename: M G
authors.initials: MG
authors.lastname: Wientjes
authors.forename: J L
authors.initials: JL
authors.lastname: Au
mesh_terms: D000465:Algorithms; D000903:Antibiotics, Antineoplastic / Q000493:pharmacokinetics / Q000494:pharmacology / Q000627:therapeutic use; D000970:Antineoplastic Agents / Q000493:pharmacokinetics / Q000494:pharmacology* / Q000627:therapeutic use; D006801:Humans; D016685:Mitomycin / Q000493:pharmacokinetics / Q000494:pharmacology / Q000627:therapeutic use; D008954:Models, Biological; D009010:Monte Carlo Method; D012044:Regression Analysis; D013997:Time Factors; D014407:Tumor Cells, Cultured
chemical_list: D000903:Antibiotics, Antineoplastic; D000970:Antineoplastic Agents; D016685:Mitomycin