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Originally published as JCO Early Release 10.1200/JCO.2005.09.905 on December 7 2004 © 2005 American Society of Clinical Oncology.
A Point, a Line, or an Area? Which Is the Most Important in the Pharmacological Analysis of Cancer Chemotherapy?National Cancer Center Hospital East, Kashiwa, Japan After administration, drugs are distributed within the body via the blood, and must then access receptors or otherwise gain entry to tissues to yield responses. Variations in drug responses are partly determined by variations in drug concentrations at receptors. Therefore, measurement of drug concentrations at receptors is pharmacologically important, but usually difficult. Drug concentrations in plasma are generally taken as surrogates for concentration at receptors, and knowledge of changes of drug concentrations in plasma (ie, pharmacokinetics) is necessary to optimize drug therapy. However, not only pharmacokinetic information, but also information on relationships between changes in drug concentrations in the plasma and changes in drug response (ie, pharmacodynamics) is important. Treatment of cancers with cytotoxic agents causes significant toxicities, and pharmacodynamic investigation of both efficacy and toxicity is important in cancer chemotherapy. Pharmacodynamic relationships for antitumor efficacy in solid cancers are rarely elucidated, probably because of the heterogeneity of sensitivity of tumors to chemotherapy, rather than pharmacokinetic issues. Pharmacodynamic investigation in cancer chemotherapy has mainly been performed using toxicity as an end point (especially neutropenia), and the relationship between area under the concentration-time curve (AUC) and neutrophil counts at the nadir or their ratio to pretreatment counts is usually analyzed.1 In this analysis, AUC and neutrophil counts at the nadir are summarized variables of pharmacokinetics and pharmacodynamics, respectively, but this analysis ignores the time course of drug concentrations and neutrophil counts. The time course of drug concentration changes causes the time course of neutrophil count changes, though there is a large time interval between the two variables. Pharmacodynamic relationships in cancer chemotherapy should preferably be investigated physiologically by coupling the time course of drug concentrations and the time course of neutrophil counts. However, this is seldom performed because a standard method for dealing with the large time interval between these changes has not been established. In their article in this issue of the Journal of Clinical Oncology,2 Sandström et al successfully coupled the time courses of drug concentrations and the time course of leukopenia in docetaxel and epirubicin combination chemotherapy by using a semiphysiological model for single-agent cancer chemotherapy, originally developed by Friberg et al3 The success of the model that couples the two changes seems to be attributed to using three compartments corresponding to maturation processes of leukocytes in bone marrow. These compartments connect a compartment where precursors of leukocytes proliferate and a compartment where leukocyte counts in peripheral blood are measured. This model has been applied to various anticancer agents with different administration schedules, including weekly administration.3 In addition to this model, other pharmacodynamic models have been proposed to investigate the time course of leukopenia induced by chemotherapy. Mathematical models suggested by Karlsson et al used a spline function, but the clinical relevance of parameters of these models was unclear.4,5 Minami et al proposed a semiphysiological model that incorporated a hypothetical period during which stem cells in the bone marrow were insensitive to cytotoxic agents, and a lag time which corresponded to the maturation time of leukocytes in the bone marrow.6 This model also successfully described the time course of leukopenia after chemotherapy with several different agents. Zamboni et al coupled the pharmacokinetics of topotecan and the time course of neutropenia by using an effect compartment.7 The original model by Friberg et al is similar to that of Zamboni et al, in that both of them used additional pharmacodynamic compartments between proliferating stem cells in bone marrow and measurable blood cells in peripheral blood. However, until the report by Sandström et al, there have been no reports of successful applications of semiphysiological models to the time course of bone marrow suppression induced by combination chemotherapy, which is the principal manner in which anticancer agents are used. As the authors correctly state, their model is semiphysiological, not truly physiological. Because rate constants between multiple transit compartments for maturation of leukocytes are not known, they hypothesized that they were all the same, which might not be true. Relationships between drug concentrations and the degree of inhibition of leukocyte production are linear in the model, which is theoretically unlikely. In the report by Friberg et al, a nonlinear function, the Emax model, was explored in a prototype of the semiphysiological pharmacodynamic model.3 Incorporation of the nonlinear function improved the model for some drugs but estimated parameters were accompanied by high relative SEs. Although the model does possess these limitations, it is important that it successfully coupled the kinetics of leukopenia and the concentrations of both drugs in combination chemotherapy. Why is modeling the time course of bone marrow suppression important? Complications of neutropenia depend not only on its extent but also on its duration. That is, the longer the neutropenia, the greater the risk of infection. In this sense, analyzing the entire time course of neutropenia is more important than analyzing only the extent of suppression at the nadir; that is to say, a line is more important than a point. Furthermore, in a study of a small number of patients with breast cancer treated by a 3-hour infusion of paclitaxel, chemotherapy-induced fever was associated with the area between time course of leukopenia and the line of a leukocyte count of 2,000/µL, but not with the duration of a leukocyte count less than 2,000/µL.8 This may imply that the area is more important than a line. By analyzing the entire time course of neutropenia, it is possible to estimate the area between the curve and the line of a certain leukocyte count. By using models describing the time course of neutropenia, further studies will answer the question: which is the most important, a point, a line, or an area? Controlling drug concentrations by therapeutic drug monitoring (TDM) may improve anticancer chemotherapy. However, TDM has rarely been successful in the context of chemotherapy against solid cancers. Successful control of drug concentrations within a target range might still not necessarily result in control of neutropenia.9,10 This may be related to the fact that there have been no good pharmacodynamic models that associate pharmacokinetics and pharmacodynamics. By developing good pharmacodynamic models for analyzing the entire time course of neutropenia, we may derive a new platform for TDM in cytotoxic chemotherapy, as Sandström et al discuss.2 However, even with Bayesian estimation of neutrophil counts in the pharmacodynamic model in this issue, the correlation between observed neutrophil counts and model-predicted counts was only modest, and poorer than the correlation of pharmacokinetics.2 Further improvements of the pharmacodynamic model will be necessary before it can be used for TDM. One such approach may be to incorporate characteristics of patients as covariates into the model to reduce residuals. Furthermore, a TDM strategy based on pharmacodynamic models will need to be validated in clinical trials. Author’s Disclosures of Potential Conflicts of Interest The author indicated no potential conflicts of interest. REFERENCES 1. Ratain MJ, Schilsky RL, Conley BA, et al: Pharmacodynamics in cancer therapy. J Clin Oncol 8:1739-1753, 1990[Abstract]
2. Sandström M, Lindman H, Nygren P, et al: A model describing the relationship between pharmacokinetics and hematological toxicity of the epirubicin-docetaxel regimen in breast cancer patients. J Clin Oncol 23:413-421, 2005
3. Friberg LE, Henningsson A, Maas H, et al: Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. J Clin Oncol 20:4713-4721, 2002 4. Karlsson MO, Port RE, Ratain MJ, et al: A population model for the leukopenic effect of etoposide. Clin Pharmacol Ther 57:325-334, 1995[CrossRef][Medline] 5. Karlsson MO, Molnar V, Bergh J, et al: A general model for time-dissociated pharmacokinetic-pharmacodynamic relationships exemplified by paclitaxel myelosuppression. Clin Pharmacol Ther 63:11-25, 1998[CrossRef][Medline] 6. Minami H, Sasaki Y, Saijo N, et al: Indirect-response model for the time course of leukopenia with anticancer drugs. Clin Pharmacol Ther 64:511-521, 1998[CrossRef][Medline]
7. Zamboni W, D’Argenio DZ, Stewart CF, et al: Pharmacodynamic model of topotecan-induced time course of neutropenia. Clin Cancer Res 7:2301-2308, 2001 8. Minami H, Sasaki Y, Watanabe T, et al: Pharmacodynamic modeling of the entire time course of leukopenia after a 3-hour infusion of paclitaxel. Jpn J Cancer Res 92:231-238, 2001[CrossRef][Medline] 9. Ando Y, Minami H, Saka H, et al: Therapeutic drug monitoring of etoposide in a 14-day infusion for non-small-cell lung cancer. Jpn J Cancer Res 87:200-205, 1996[CrossRef][Medline] 10. Ando Y, Minami H, Saka H, et al: Therapeutic drug monitoring in 21-day oral etoposide treatment for lung cancer. Jpn J Cancer Res 87:856-861, 1996[CrossRef][Medline]
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Copyright © 2005 by the American Society of Clinical Oncology, Online ISSN: 1527-7755. Print ISSN: 0732-183X
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