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QUANTITATIVE CLINICAL PHARMACOLOGY

Modeling of In Vitro Drug Activity and Prediction of Clinical Outcome in Acute Myeloid Leukemia

Angelica Quartino, MSc, Mats O. Karlsson, PhD, Agneta Freijs, PhD, Niclas Jonsson, PhD, Peter Nygren, MD, PhD, Jörgen Kristensen, MD, PhD, Elin Lindhagen, PhD and Rolf Larsson, MD, PhD

From the Division of Pharmacokinetics and Drug Therapy, Department of Pharmaceutical Biosciences, Uppsala University, Sweden (Ms Quartino, Dr Karlsson, Dr Freijs, Dr Jonsson); Division of Clinical Pharmacology, Department of Medical Science, Uppsala University, Sweden (Dr Kristensen, Dr Lindhagen, Dr Larsson); and Section of Oncology, Department of Oncology, Radiology and Clinical Immunology, University Hospital, Uppsala, Sweden (Dr Nygren).

Address for correspondence: Angelica Quartino, MSc, Division of Pharmacokinetics and Drug Therapy, Uppsala University, Box 591, S-751 24 Uppsala, Sweden.


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 ACKNOWLEDGEMENTS
 REFERENCES
 
The objectives of this study were to develop a population pharmacodynamic model describing the in vitro drug sensitivity of tumor cells and to relate in vitro parameters to clinical outcome. Cell samples from 179 patients with acute myelocytic leukemia were exposed to cytosine arabinoside and daunorubicin, and cytotoxicity was analyzed using the fluorometric microculture cytotoxicity assay. A sigmoid Emax-model for daunorubicin and an Emax-model for cytosine arabinoside described the data. The model predicted drug potency (EC50) adequately from 1 concentration measurement. A logistic regression on individual in vitro parameters of 46 patients treated with the daunorubicin plus cytosine arabinoside regimen showed that the probability of complete response was significantly (P < .05) related to the product of the Emax/EC50 ratio of the two drugs. The findings demonstrate the value of population pharmacodynamic modeling of in vitro drug sensitivity data and a significant relationship between the in vitro parameters and clinical outcome.

Key Words: Acute myelocytic leukemia • cytosine arabinoside • daunorubicin • fluorometric microculture cytotoxicity assay • NONMEM

During the past decades, different in vitro drug sensitivity assays have been used to predict clinical outcome in individual patients with various malignancies.1,2 Although most of the results were obtained from clonogenic assays, several nonclonogenic short-term assay systems with both cytotoxic and proliferative endpoints have shown comparable results.1-3 Overall, these in vitro assays have shown predictive capabilities for clinical outcome with an overall specificity of 92% and a sensitivity of 72% for drug resistance.2 For some assays, good correlation with patient survival has been reported.2-5

Acute myelocytic leukemia (AML) is commonly treated with the antimetabolite cytosine arabinoside (AraC) for 7 days and an anthracycline (eg, daunorubicin [Dnr]) during the first 3 days. With this chemotherapy, 75% to 80% of younger adults with de novo AML achieve complete remission. Nevertheless, a majority of these patients will relapse within 2 years, with only a small chance of a second remission. The prognosis is even worse for older patients, and disease-free survival is rare.6 A major problem with the treatment of AML is drug resistance; hence, predictive methods and individualized therapy could be of value to optimize treatment outcome.

One important issue concerning in vitro drug sensitivity assays is the selection of the drug exposure strategy. Ideally, full concentration-response curves should be obtained, and then the concentration causing 50% cell death, EC50, could be used to describe drug potency.7-10 Because of limited availability of tumor cells, this is not always possible, and the drug effect may have to be measured at only 1 or a few fixed concentrations. In the case of only 1 concentration, this may be chosen either to mimic clinically achievable concentrations11 or merely to produce as large a scatter in test results as possible to differentiate sensitive from resistant samples.12-14

In the field of clinical pharmacokinetics and pharmacodynamics, development of powerful computer software for population analysis using mixed-effect modeling, often denoted "population-based methods," in combination with Bayesian parameter estimation methodology has allowed investigators to estimate individual pharmacodynamic parameters using only a limited number of data points.15 The essential requirements are accurate estimates of population parameters of a specified mathematical model and the effect of 1 or more measured concentrations in the individual patient concerned.

The aims of the study were to develop a population-based pharmacodynamic model for the in vitro drug sensitivity of leukemic cell samples from patients with AML to predict individual pharmacodynamic parameters for Dnr and AraC and to predict the probability of clinical outcome based on the model.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 ACKNOWLEDGEMENTS
 REFERENCES
 
Tumor Samples
Assay results from 179 successfully analyzed samples from adult patients with AML were used. Leukemic cells were obtained from bone marrow or peripheral blood by 1.077 g/mL Ficoll-Paque (Pharmacia, Uppsala, Sweden) density gradient centrifugation.12 Viability was determined by trypan blue exclusion test, and the proportion of tumor cells was judged by inspection of May-Grünwald-Giemsa-stained cytocentrifugate preparations by a cytopathologist. Culture medium RPMI 1640 supplemented with 10% heat-inactivated fetal calf serum (FCS, Hyclone, Cramlington, UK), 2 mM glutamine, 50 µg/mL streptomycin, and 60 µg/mL penicillin was used throughout. In some cases, the cells were cryopreserved in medium containing 10% dimethylsulfoxide (DMSO; Sigma Chemical Co, St Louis, Mo) and 90% heat-activated FCS and were assayed at a later time point. Tumor sampling and the collection of clinical data were approved by the local ethical committee at the Uppsala University Hospital.

Regents and Drugs
Fluorescein diacetate (Sigma Chemical) was dissolved in DMSO and kept frozen (-20°C) as a stock solution (10 mg/mL) protected from light. AraC and Dnr were obtained from Sigma Chemical. Experimental plates were prepared with 20 {rho}L/well drug solution at 10 times the desired final concentration (ranging from 0.02 to 12.5 µg/mL and from 0.004 to 12.5 µg/mL for AraC and Dnr, respectively) with aid of a programmed pipetting robot (Propette, Perkin Elmer, Norwalk, Conn). The plates were stored frozen at -70°C until further use. The experiments were performed with continuous drug exposure.

Measurement of Cytotoxicity
The principal steps of the fluorometric microculture cytotoxicity assay (FMCA) have been described previously.12,16 On day 1, 180 µL of the tumor cell preparation (0.5 x 105 cells) was seeded per well in V-shaped 96-well experimental microtiter plates prepared as described above. Six blank wells received only culture medium, and 6 wells with cells but without drugs served as control. The culture plates were then incubated at 37°C in a humidified atmosphere containing 95% air and 5% CO2. At the end of the 72-hour incubation period, the plates were centrifuged (200g, 5 minutes), and the medium was removed by aspiration in the microtiter plate washer. After 1 wash with phosphate buffered saline (PBS), 100 µL of PBS containing fluorescein diacetate (10 µg/mL) was added column-wise to control, experimental, and blank wells with the aid of an automated 96-well dispenser (Multidrop, Labsystems, Helsinki, Finland).

Subsequently, the plates were incubated for 1 hour before we read the fluorescence in a fluorometer (Fluoroscan 2, Labsystems, Helsinki, Finland). The fluorometer was blanked against wells containing PBS including the fluorescent dye but without cells. Quality criteria for a successful assay included a fluorescence signal in control cultures of at least 5 times the blank value, a control coefficient of variation (CV) of <30%, and >70% tumor cells in control wells before incubation. The overall success rate using these criteria is approximately 80% for AML samples. Only successfully analyzed samples are reported here. The results obtained are expressed as survival index (SI) defined as fluorescence in percentage of control cultures, with blank values subtracted.

In Vitro Data
A total of 154 samples were divided into a learning data set of 124 samples, on which Dnr was tested on all samples and AraC on all except 2 samples, and an evaluation data set of 30 samples on which both Dnr and AraC were tested. In the learning data set, 1 (43% of total number of Dnr measurements/21% of total number of AraC measurements), 2 (20%/38%), 4 (0%/1%), or 5 (37%/40%) concentrations of each drug were tested. For the samples included in the evaluation data set, SI values from 5 concentrations of each drug were obtained. A total of 700 SI measurements were included in the learning data set and 300 in the evaluation data set.

In addition, in vitro response measurements were performed on another 25 tumor samples after data analysis was completed for the first 154 individuals. For those samples, 1 or 2 concentrations of each drug were available. These data were only used in the modeling of clinical outcome.

Clinical Data
The clinical data were retrospectively collected. Information on clinical outcome was available for 46 of the 179 patients. The 46 patients were treated with the 3+7 Dnr+AraC regimen consisting of Dnr 45 mg/m2 as a daily bolus during the first 3 days and AraC 100 mg/m2 daily given as continuous infusion over 7 days. For the 46 patients, the in vitro response measurements were correlated to clinical outcome. Complete response (CR) was defined as <5% blast cells in bone marrow aspirates for AML M1 and M5a, ≤10% blast cells for other groups of the French-American-British classification,17 and >50% marrow cellularity after a maximum of 3 courses of chemotherapy. Partial response (PR) was defined as >50% reduction of leukemic cells in bone marrow and failure to meet the criteria of CR. If the patient did not meet the criteria for CR or PR, his or her disease was defined as nonresponsive (NR). Of the 46 patients, 26 were classified as CR, 6 as PR, and 14 as NR.

Model Development
The data analysis was performed with the first-order conditional estimation method in the software program NONMEM (version VI, Globomax, Hanover, Md).18 Model adequacy was evaluated using goodness-of-fit plots using the program Xpose 3.10419 (Jonsson and Karlsson, Uppsala, Sweden, http://xpose.source-forge.net), implemented into S-plus 6.1 (Insightful Corp, Seattle, Wash), precision in parameter estimates, and the objective function value (OFV) from the NONMEM output. To differentiate between 2 nested models with a difference of 1 df at P < .01, a decrease in OFV of 6.63 was required.

Pharmacodynamic Modeling
SI values from the learning data set for Dnr and AraC were analyzed simultaneously using a nonlinear mixed-effects (fixed and random) regression model to derive typical population values and corresponding variances that described the interpatient variability. A stepwise procedure was used to find the model that best fit the data. An Emax model and a sigmoid Emax model with a baseline were fitted to the data according to the following equation:

Formula(1)

where E0, Emax, and EC50 are the baseline, the maximal inhibitory effect, and the concentration at half the maximal inhibitory effect, respectively. The slope of the effect concentration relationship was fixed to a value of 1 in the Emax model, whereas it was estimated in the sigmoid Emax model. The slope was assumed to be equal in all individual samples.

An exponential interpatient model was used to describe the variability ({eta}) in the EC50, where {eta} is distributed with a mean zero and variance {omega}2EC50, and for Emax, a logit transformation was used to bind individual estimates to be between 0 and 1. The covariance matrix for random effects was used to test correlation between the pharmacodynamic parameters of the two drugs.

The residual variability ({epsilon}), which incorporates assay variability, model misspecification, and any other unexplained variability, was described with an additive error model.

Using the population pharmacodynamic in vitro model derived from the 124 samples of the learning data set, we performed Bayesian parameter (Emax, EC50) estimation on the evaluation data set. The Bayesian method allows estimation of individual sample parameters by using a few concentration-effect measurements from 1 sample in conjunction with preexisting information on the population characteristics (means and variances) of the pharmacodynamic parameters. The predictive performance of the population pharmacodynamic model was evaluated by comparing the Bayesian estimation of individual sample EC50 based on the full evaluation data set, that is, 5 concentration-effect measurements per sample, with an estimated EC50 parameter value based on only 1 measurement per sample. The EC50 estimate based on 5 concentrations was taken as reference, and the single concentration with lowest mean absolute error (MAE)20 compared with the reference was selected as the most appropriate of the 5 available concentrations.


Figure 1
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  		Figure 1. The observed (circles) and median (lines) survival index (SI, %) at different concentrations of daunorubicin (Dnr) (A) and cytosine arabinoside (AraC) (B). The solid line is the corresponding population model prediction based on the typical population pharmacodynamic parameter estimates.

 
The final population pharmacodynamic model was evaluated by reestimating the parameters using the evaluation data set and comparing them with the parameter estimates from the learning data set.

Probability of Clinical Outcome Modeling
For the 46 patients treated with the 3+7 Dnr+AraC regimen, the individual Bayesian estimates of the pharmacodynamic parameters (Emax and EC50) from the in vitro model were correlated to the categorical clinical outcome (CR, PR, and NR). The probability of the 3 clinical outcomes was modeled with a proportional odds model.21 As explanatory variables for CR, PR, and NR in the proportional odds model, 3 variables for each drug were investigated: Emax, EC50, and Emax/EC50. If the clinically achieved concentrations are high compared with EC50, then interpatient variability in Emax would be anticipated to be the most important parameter (ie, the one correlating best with clinical outcome). At concentrations lower than EC50, the Emax-relationship can be approximated with a linear relationship where the slope is the Emax/EC50 ratio. Therefore, if the clinically achieved concentrations are lower than EC50, the Emax/EC50 ratio is expected to correlate best with clinical outcome. If the concentrations achieved are similar to the population average of EC50, the individual variability in this parameter can be expected to be the most important one for predicting clinical outcome.

Thus, it may be possible to elucidate, from the type of correlation between in vitro parameters and clinical outcome, whether the tumor is exposed to low, intermediate, or high concentrations compared with EC50. These variables (Emax, EC50, and Emax/EC50) were tried in the proportional odds model: (1) alone for each drug, (2) in an additive, or (3) in a multiplicative way. In the first case, only one drug is needed to have a good response, whereas an additive model implies that too low exposure to one drug could be compensated by an increased exposure to the other drug. The multiplicative model predicts that exposure of both drugs is required to get a good response.

In addition, a joint pharmacodynamic and proportional odds model was developed to describe both the continuous in vitro drug sensitivity data and the categorical clinical outcome data simultaneously for all 179 patients (full data set), and hence more certain estimates of the population parameters and variances were acquired.


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 ACKNOWLEDGEMENTS
 REFERENCES
 
The Dnr data were best described by a sigmoid Emax model, whereas an Emax model fit the AraC data best. The observed SI concentration measurements and the corresponding population model prediction are plotted for Dnr and AraC in Figure 1.

The typical population parameter values, the interpatient coefficient of variations (CV%), and the relative standard error of the estimates (RSE %) are summarized in Table I. On average, Dnr was about 3 times more potent than AraC, inferred from the estimated EC50 values of the drugs. The EC50 values of Dnr and AraC varied considerably between patients with a CV of 125% and 105%, respectively. The corresponding variabilities for Emax were 15% and 32%. The correlation coefficient between EC50 for the two drugs was low (0.08), whereas for Emax it was high (0.89), implying that individuals with high Emax values of Dnr also had high Emax values of AraC and vice versa.


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  		Table I Estimated Parameters for the Pharmacodynamic Model of Daunorubicin (Dnr) and Cytosine Arabinoside (AraC) and the Proportional Odds Model for Clinical Outcome

 


Figure 2
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  		Figure 2. Bayesian predictions of concentration at half the maximal inhibitory effect (EC50) based on 1 versus 5 concentration-effect measurements of daunorubicin (Dnr) (A) and cytosine arabinoside (AraC) (B). The solid line represents the line of identity. The single concentration used was 0.1 µg/mL for both drugs.

 
When we evaluated the pharmacodynamic model using the evaluation data set, the estimated parameters were similar to the estimates obtained by the learning data set (Table I). The main differences were seen in the estimated residual variability that decreased because the fit was improved and the slope factor that was estimated close to 1 for Dnr using the evaluation data set. This implies that a sigmoid Emax model may not be necessary to describe the evaluation data set, although it significantly improved the description of the learning data set.

The Bayesian estimation of EC50 was predicted with good accuracy for both drugs from only 1 concentration-effect measurement, as shown in Figure 2. The single concentration that provided the best estimates (lowest calculated MAE) of EC50 was 0.1 µg/mL for both drugs, a value close to the typical value of EC50 in the population. In the case of AraC, the concentration of 0.5 µg/mL had a mean absolute error only slightly higher than the corresponding value for 0.1 µg/mL.

The clinical outcome data were best described by a proportional odds model where the probability of response was predicted by the product of the Emax/EC50 ratio of the two drugs (P < .05). This predictor varied substantially between the patients with a CV of 72%; thus, it may be used to discriminate between patients. A probability of CR of 0.3 was estimated when the product was low and close to 1.0 when it was higher than 15, as depicted in Figure 3. A parallel decrease in the probability for NR and PR was apparent. No observed NR patients had a ratio >8, whereas this was apparent for approximately 50% responding with CR. In the PR group, 1 patient had a ratio exceeding 8 among the observed patients. The simulated 90% prediction interval around the estimated probabilities for each clinical outcome includes the observed proportion of each response, as shown in Figure 3.


Figure 3
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  		Figure 3. Correlation between individual pharmacodynamic in vitro parameters for daunorubicin (Dnr) and cytosine arabinoside (AraC) and the presence or absence of therapeutic response. The estimated probability of complete response (CR), partial response (PR), or no response (NR) versus the product of the respective ratios of maximal inhibitory effect (Emax)/concentration at half the maximal inhibitory effect (EC50) of Dnr and AraC is shown. The vertical lines represent the 90% prediction interval around the predicted probability for each clinical outcome in that quartile. The symbols represent the observed proportion of CR, PR, and NR per quartile.

 
A simultaneous fit of the in vitro data and the clinical outcome resulted in similar pharmacodynamic parameter estimates and estimated probabilities of clinical outcome as a separate fit of the two types of data, as shown in Table I.


   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 ACKNOWLEDGEMENTS
 REFERENCES
 
In the present study, we (1) developed a nonlinear mixed effects model that could adequately describe the in vitro response data, (2) demonstrated that adequate precision in individual pharmacodynamic parameters could be obtained from sparse sampling, and (3) showed that clinical outcome in this population was significantly related to in vitro parameters.

By using a sigmoid Emax model or an Emax model to describe the inhibitory concentration-effect relationship for two model drugs, Dnr and AraC, we could characterize both with respect to typical population model parameters and the associated interpatient variability. Dnr showed a higher Emax and steeper slope compared with AraC, which could be anticipated from the mode of drug action, Dnr being a largely AUC-dependent drug22 and AraC being a time-dependent drug.23 However, Emax was quite large also for AraC despite the fact that AraC is postulated to be S-phase specific and proliferation during the present assay conditions is probably minimal.24 This suggests that leukemic cells also in other stages of the cell cycle are sensitive to the cytotoxic actions of AraC.

For the purpose of individualization, it was possible to predict EC50 from only 1 concentration-effect measurement with a rather high degree of accuracy for both drugs, which could be of practical importance when a limited amount of sample material prohibits testing of many drug concentrations. The FMCA is currently under development for the 384-well microtiter plate format, to enable testing of more drugs or drug concentrations with the same amount of sample material, and the current results could be used to optimize new experimental designs. Development of similar pharmacodynamic models for other drugs and cell types may aid in the comparison of in vitro drug effect data and clinical plasma concentrations.

The population in vitro pharmacodynamic model also provides a tool for selection of an optimal concentration for an in vitro assay by using the estimated typical population value of EC50, where between-sample variability is maximal. Thus, the conditions for differentiation between sensitive and resistant samples would be optimal at this concentration. Interestingly, the EC50 concentrations observed here were close to the empirically derived concentrations reported previously.12 Interlaboratory comparisons of results from different assays using different drug concentrations might also be facilitated.

When estimated pharmacodynamic parameters of the drugs and combinations thereof were related to clinical outcome using a proportional odds model, the parameter best correlated with clinical outcome was the product of the ratio of Emax to EC50 of the two drugs. Pharmacologically, the Emax/EC50 expression reflects the sensitivity of the leukemic cells at low drug concentrations at the beginning of the effect-concentration curve. Interestingly, these concentrations are very close to those clinically achievable in patient plasma using the 3+7 Dnr+AraC regimen.25

Furthermore, the product of the two drugs indicates that both drugs are needed for a good response; hence, specific drug interactions may be important.

The variability in Emax and EC50 and the ratios thereof between patients was extensive for both drugs, indicating the potential importance of individualization of therapy with respect to selection of both drug and dose. The choice of drug depends on the individual Emax/EC50 value, where a high value is preferable over a low value, the latter indicating that the drug is ineffective against the cancer cells or only active at relatively high concentrations.

The results indicate a better predictive ability for drug sensitivity compared with drug resistance. This observation is in contrast to findings previously published with this assay, as well as similar assays, with better predictability of resistance.26 This may be attributable to the fact that the present correlations were based on the combined measure of Dnr and AraC derived from information about the whole concentration-response curve, but it could also to some extent be attributable to the more homogenous drug treatment and patient material in the present study, with all patients treated with Dnr+AraC and a majority of samples coming from de novo AML patients.


   CONCLUSIONS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
ACKNOWLEDGEMENTS
 REFERENCES
 
A joint pharmacodynamic model for Dnr and AraC including covariances across drugs could adequately describe the in vitro drug sensitivity data. Even with sparse sensitivity measurements, adequate information on drug potency can be obtained. The model for clinical outcome is mechanistically reasonable and supports the dual therapy.


   ACKNOWLEDGEMENTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 ACKNOWLEDGEMENTS
REFERENCES
 
Financial disclosure: This work was supported by the Swedish Cancer Society, Stockholm, Sweden.

DOI: 10.1177/0091270007302563


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 ACKNOWLEDGEMENTS
 REFERENCES
 

1. Fruehauf JP. In vitro assay-assisted treatment selection for women with breast or ovarian cancer. Endocr Relat Cancer. 2002;9: 171-182.[Abstract]

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6. Stone RM, O'Donnell MR, Sekeres MA. Acute myeloid leukemia. Hematology Am Soc Hematol Educ Program. 2004: 98-117.

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9. Bosanquet AG, Burlton AR, Bell PB. Parameters affecting the ex vivo cytotoxic drug sensitivity of human hematopoietic cells. J Exp Ther Oncol. 2002;2: 53-63.[CrossRef][Medline] [Order article via Infotrieve]

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12. Larsson R, Kristensen J, Sandberg C, Nygren P. Laboratory determination of chemotherapeutic drug resistance in tumor cells from patients with leukemia, using a fluorometric microculture cytotoxicity assay (FMCA). Int J Cancer. 1992;50: 177-185.[Web of Science][Medline] [Order article via Infotrieve]

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17. Bennett JM, Catovsky D, Daniel MT, et al. Proposals for the classification of the acute leukaemias. French-American-British (FAB) co-operative group. Br J Haematol. 1976;33: 451-458.[Web of Science][Medline] [Order article via Infotrieve]

18. NONMEM: Nonlinear-Mixed Effects Modeling. Hanover, Md: Globomax.

19. Jonsson EN, Karlsson MO. Xpose—an S-PLUS based population pharmacokinetic/pharmacodynamic model building aid for NONMEM. Comput Methods Programs Biomed. 1999;58: 51-64.[CrossRef][Web of Science][Medline] [Order article via Infotrieve]

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22. Danesi R, Fogli S, Gennari A, Conte P, Del Tacca M. Pharmacokinetic-pharmacodynamic relationships of the anthracycline anticancer drugs. Clin Pharmacokinet. 2002;41: 431-44.[CrossRef][Web of Science][Medline] [Order article via Infotrieve]

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