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Missing data create challenges in clinical research because they lead to loss of statistical power and potentially to biased results. Missing covariate data must be handled with suitable approaches to prepare datasets for pharmacometric analyses, such as population pharmacokinetic and pharmacodynamic analyses. To this end, various statistical methods have been widely adopted. Here, we introduce two machine-learning (ML) methods capable of imputing missing covariate data in a pharmacometric setting. Based on a previously published pharmacometric analysis, we simulated multiple missing data scenarios. We compared the performance of four established statistical methods, listwise deletion, mean imputation, standard multiple imputation (hereafter "Norm"), and predictive mean matching (PMM) and two ML based methods, random forest (RF) and artificial neural networks (ANNs), to handle missing covariate data in a statistically plausible manner. The investigated ML-based methods can be used to impute missing covariate data in a pharmacometric setting. Both traditional imputation approaches and ML-based methods perform well in the scenarios studied, with some restrictions for individual methods. The three methods exhibiting the best performance in terms of least bias for the investigated scenarios are the statistical method PMM and the two ML-based methods RF and ANN. ML-based approaches had comparable good results to the best performing established method PMM. Furthermore, ML methods provide added flexibility when encountering more complex nonlinear relationships, especially when associated parameters are suitably tuned to enhance predictive performance.

Modeling of retrospectively collected multi-center data of a rare disease in pediatrics is challenging because laboratory data can stem from several decades measured with different assays. Here we present a retrospective pharmacometrics (PMX) based data analysis of the rare disease congenital hypothyroidism (CH) in newborns and infants. Our overall aim is to develop a model that can be applied to optimize dosing in this pediatric patient population since suboptimal treatment of CH during the first 2 years of life is associated with a reduced intelligence quotient between 10 and 14 years. The first goal is to describe a retrospectively collected dataset consisting of 61 newborns and infants with CH up to 2 years of age. Overall, 505 measurements of free thyroxine (FT4) and 510 measurements of thyrotropin or thyroid-stimulating hormone were available from patients receiving substitution treatment with levothyroxine (LT4). The second goal is to introduce a scale/location-scale normalization method to merge available FT4 measurements since 34 different postnatal age- and assay-specific laboratory reference ranges were applied. This method takes into account the change of the distribution of FT4 values over time, i.e. a transformation from right-skewed towards normality during LT4 treatment. The third goal is to develop a practical and useful PMX model for LT4 treatment to characterize FT4 measurements, which is applicable within a clinical setting. In summary, a time-dependent normalization method and a practical PMX model are presented. Since there is no on-going or planned development of new pharmacological approaches for CH, PMX based modeling and simulation can be leveraged to personalize dosing with the goal to enhance longer-term neurological outcome in children with the rare disease CH. Supplementary Information The online version contains supplementary material available at 10.1007/s10928-021-09765-w.

The objectives are to characterize oscillations of physiological functions such as heart rate and body temperature, as well as the sleep cycle from behavioral states in generally stable preterm neonates during the first 5 days of life. Heart rate, body temperature as well as behavioral states were collected during a daily 3-h observation interval in 65 preterm neonates within the first 5 days of life. Participants were born before 32 weeks of gestational age or had a birth weight below 1500 g; neonates with asphyxia, proven sepsis or malformation were excluded. In total 263 observation intervals were available. Heart rate and body temperature were analyzed with mathematical models in the context of non-linear mixed effects modeling, and the sleep cycles were characterized with signal processing methods. The average period length of an oscillation in this preterm neonate population was 159 min for heart rate, 290 min for body temperature, and the average sleep cycle duration was 19 min. Oscillation of physiological functions as well as sleep cycles can be characterized in very preterm neonates within the first few days of life. The observed parameters heart rate, body temperature and sleep are running in a seemingly uncorrelated pace at that stage of development. Knowledge about such oscillations may help to guide nursing and medical care in these neonates as they do not yet follow a circadian rhythm.

Clinical pharmacology is a multidisciplinary data sciences field that utilizes mathematical and statistical methods to generate maximal knowledge from data. Pharmacometrics (PMX) is a well‐recognized tool to characterize disease progression, pharmacokinetics, and risk factors. Because the amount of data produced keeps growing with increasing pace, the computational effort necessary for PMX models is also increasing. Additionally, computationally efficient methods, such as machine learning (ML) are becoming increasingly important in medicine. However, ML is currently not an integrated part of PMX, for various reasons. The goals of this article are to (i) provide an introduction to ML classification methods, (ii) provide examples for a ML classification analysis to identify covariates based on specific research questions, (iii) examine a clinically relevant example to investigate possible relationships of ML and PMX, and (iv) present a summary of ML and PMX tasks to develop clinical decision support tools., Clinical Pharmacology & Therapeutics, 107 (4), ISSN:0009-9236, ISSN:1532-6535

Context Copeptin is the C-terminal fragment of the arginine vasopressin (AVP) prohormone whose measurement is more robust than that of AVP. Similar release and clearance characteristics have been suggested promoting copeptin as a surrogate marker. Objective To characterize the physiology of osmotically regulated copeptin release and its half-life in direct comparison with plasma AVP. Design Ninety-one healthy volunteers underwent a standardized three-phase test protocol including (1) osmotic stimulation into the hypertonic range by hypertonic-saline infusion followed by osmotic suppression via (2) oral water load and (3) subsequent glucose infusion. Plasma copeptin, AVP, serum sodium, and osmolality levels were measured in regular intervals. Results In phase 1, an increase in median osmotic pressure [289 (286; 291) to 311 (309; 314) mOsm/kg H2O] caused similar release kinetics of plasma copeptin [4 (3.1; 6) to 29.3 (18.6; 48.2) pmol/L] and AVP [1 (0.7; 1.6) to 10.3 (6.8; 18.8) pg/mL]. Subsequent osmotic suppression to 298 (295; 301) mOsm/kg at the end of phase 3 revealed markedly different decay kinetics between both peptides—an estimated initial half-life of copeptin being approximately 2 times longer than that of AVP (26 vs 12 minutes). Conclusion Copeptin is released in equimolar amounts with AVP in response to osmotic stimulation, suggesting its high potential as an AVP surrogate for differentiation of osmotic disorders. Furthermore, we here describe the decay kinetics of copeptin in response to osmotic depression enabling to identify a half-life for copeptin in direct comparison with AVP.

Infliximab, an anti-tumour necrosis factor (TNF)-α monoclonal antibody, has been approved in chronic inflammatory disease, including rheumatoid arthritis, Crohn’s disease and ankylosing spondylitis. This study aimed to investigate and characterise target-mediated drug disposition of infliximab and antigen mass turnover during infliximab treatment. In this retrospective cohort of 186 patients treated with infliximab for rheumatoid arthritis, Crohn’s disease or ankylosing spondylitis, trough infliximab concentrations were determined from samples collected between weeks 0 and 22 after treatment initiation. Target-mediated pharmacokinetics of infliximab was described using target-mediated drug disposition modelling. Target-mediated elimination parameters were determined for rheumatoid arthritis and Crohn’s disease, assuming ankylosing spondylitis with no target-mediated elimination. The quasi-equilibrium approximation of a target-mediated drug disposition model allowed a satisfactory description of infliximab concentration–time data. Estimated baseline TNF-α amounts were similar in Crohn’s disease and rheumatoid arthritis (R0 = 0.39 vs 0.46 nM, respectively), but infliximab-TNF complex elimination was slower in Crohn’s disease than in rheumatoid arthritis (kint = 0.024 vs 0.061 day−1, respectively). Terminal elimination half-lives were 13.5, 21.5 and 16.5 days for rheumatoid arthritis, Crohn’s disease and ankylosing spondylitis, respectively. Estimated amounts of free target were close to baseline values before the next infusion suggesting that TNF-α inhibition may not be sustained over the entire dose interval. The present study is the first to quantify the influence of target antigen dynamics on infliximab pharmacokinetics. Target-mediated elimination of infliximab may be complex, involving a multi-scale turnover of TNF-α, especially in patients with Crohn’s disease. Additional clinical studies are warranted to further evaluate and fine-tune dosing approaches to ensure sustained TNF-α inhibition.

Context Copeptin is a surrogate marker for arginine vasopressin (AVP) release in response to hyperosmolal stimuli such as diabetic ketoacidosis (DKA). Objective The objective of this work is to characterize kinetics of copeptin and osmolality, and their dynamic relationship during rehydration and insulin therapy in children with type 1 diabetes (T1D) and DKA. Design and Setting A prospective, observational, multicenter study was conducted. Patients and Intervention Children with T1D admitted for DKA underwent serial serum copeptin and osmolality measurements from start of rehydration at 14 time points during 72 hours. Main Outcome Measures Measurements included temporal course of copeptin and osmolality (kinetics), relationship between both (dynamics), and association between-subject variability (BSV) (coefficient of variation, CV%). Results Twenty-eight children (20 newly diagnosed T1D) aged 1 to 16 years were included. Copeptin decreased from 95 pmol/L (95% CI, 55-136 pmol/L) (CV%, 158%) to 9.7 pmol/L (95% CI, 8.1-11.4 pmol/L) (CV%, 31%) with a 50% recovery time (t1/2) of 7.1 hours (range, 5.1-11.5 hours) (114%). Serum osmolality decreased from 321 mOsm/kg (range, 315-327 mOsm/kg) (4%) to 294 mOsm/kg (range, 292-296 mOsm/kg) (1%) with a t1/2 of 4.3 hours (range, 3.0-5.6 hours) (64%). Copeptin levels doubled with each osmolality increase by 15 mOsm/kg (range, 10-21 mOsm/kg) (59%), from 9.8 pmol/L (range, 7.3-12.3 pmol/L) (48%) to 280 mOsm/kg. Copeptin kinetics differed between newly diagnosed and known T1D patients (P = .001), and less between mild vs moderate-severe DKA (P = .04). Conclusions First, this study characterized for the first time copeptin kinetics and dynamics in the high hyperosmolar range in children with DKA. Second, it revealed significant differences in copeptin kinetics between newly diagnosed and known T1D patients that may be explained by changes at the osmoreceptor and renal AVP receptor level due to longstanding osmotic diuresis and DKA.

Caffeine is widely used in preterm neonates suffering from apnea of prematurity (AOP), and it has become one of the most frequently prescribed medications in neonatal intensive care units. Goal of this study is to investigate how caffeine citrate treatment affects sleep‐wake behavior in preterm neonates. The observational study consists of 64 preterm neonates during their first 5 days of life with gestational age (GA)

Ceftazidime is a parenteral cephalosporin frequently used in pregnant women for treatment of urinary tract or intrauterine infections. Despite its regular use in pregnant women, ceftazidime disposition in both mother and fetus is not well understood, and a pharmacokinetic (PK) model that allows characterization and simulation of both maternal and preterm neonatal ceftazidime disposition is not available. In this study, 10 pregnant women with suspected or proven intrauterine infections in the late second and early third trimester were treated with 1 g of ceftazidime intravenously every 6 hours. During ceftazidime treatment, one maternal and umbilical cord blood sample was taken at delivery to quantify ceftazidime concentrations in the mother and preterm neonate. Data showed that ceftazidime concentrations in the mother were comparable to those observed in the neonate. Based on these data, a PK model was developed to describe maternal disposition, ceftazidime distribution over the placenta, and elimination in the neonate. The maternal substructure of the model was parameterized according to a previously reported ceftazidime model with minor adjustments to account for pregnancy-related effects on renal elimination of ceftazidime. The expanded population PK model with an additional neonatal compartment was fitted to measured drug concentrations in the neonate. The neonatal elimination rate constant at delivery was close to that estimated for the mother. The presented results show that ceftazidime readily crosses the placenta and indicate that perinatal PK behavior of ceftazidime in preterm neonates can be expected to be similar to those observed in their mothers.

Fentanyl and its derivatives sufentanil, alfentanil, and remifentanil are potent opioids. A comprehensive review of the use of fentanyl and its derivatives in the pediatric population was performed using the National Library of Medicine PubMed. Studies were included if they contained original pharmacokinetic parameters or models using established routes of administration in patients younger than 18 years of age. Of 372 retrieved articles, 44 eligible pharmacokinetic studies contained data of 821 patients younger than 18 years of age, including more than 46 preterm infants, 64 full-term neonates, 115 infants/toddlers, 188 children, and 28 adolescents. Underlying diagnoses included congenital heart and pulmonary disease and abdominal disorders. Routes of drug administration were intravenous, epidural, oral-transmucosal, intranasal, and transdermal. Despite extensive use in daily clinical practice, few studies have been performed. Preterm and term infants have lower clearance and protein binding. Pharmacokinetics was not altered by chronic renal or hepatic disease. Analyses of the pooled individual patients’ data revealed that clearance maturation relating to body weight could be best described by the Hill function for sufentanil (R 2 = 0.71, B max 876 mL/min, K 50 16.3 kg) and alfentanil (R 2 = 0.70, B max (fixed) 420 mL/min, K 50 28 kg). The allometric exponent for estimation of clearance of sufentanil was 0.99 and 0.75 for alfentanil clearance. Maturation of remifentanil clearance was described by linear regression to bodyweight (R 2 = 0.69). The allometric exponent for estimation of remifentanil clearance was 0.76. For fentanyl, linear regression showed only a weak correlation between clearance and bodyweight in preterm and term neonates (R 2 = 0.22) owing to a lack of data in older age groups. A large heterogeneity regarding study design, clinical setting, drug administration, laboratory assays, and pharmacokinetic estimation was observed between studies introducing bias into the analyses performed in this review. A limitation of this review is that pharmacokinetic data, based on different modes of administration, dosing schemes, and parameter estimation methods, were combined.

Overdosing occurs frequently because of prescription errors in neonates, infants, children, adolescents, and adults. Currently there is no quantitative approach that can be used by clinicians to adjust dosing so that toxic drug concentrations can be brought back to levels observed with safe and efficacious therapeutic doses. We present a mathematical solution that offers the time between last overdosing and next therapeutic dose to achieve therapeutic drug concentrations as soon as possible. To facilitate applications of this solution in clinical practice, a minimal amount of information has to be provided, and no simulations are necessary to compute the optimal waiting time. For educational purposes, we provide access to an online decision support tool for overdosing situations (Time to next Dose Calculator) that (1) computes the waiting time after accidental overdosing in patients with normal elimination and (2) computes the waiting time and adjusted reference dosing for patients with abnormal elimination. This user-friendly online tool will help clinicians to quickly adjust a dosing schedule in overdosing situations to mitigate risk for negative clinical consequences.

Pregnant women, fetuses, and newborns are particularly vulnerable patient populations. During pregnancy, the body is subject to physiological changes that influence the pharmacokinetics and pharmacodynamics of drugs. Inappropriate dosing in pregnant women can result in sub-therapeutic or toxic effects, putting not only the pregnant woman but also her fetus at risk. During neonatal life, maturation processes also affect pharmacokinetics and pharmacodynamics of drugs. Inappropriate dosing in newborns leads not only to short-term complications but can also have a negative impact on the long-term development of infants and children. For these reasons, it is crucial to characterize physiological changes in pregnant women, describe placental transfer kinetics of drugs, and describe physiological changes related to the transition from intrauterine to extrauterine life and maturation processes in preterm and term neonates. Quantitative pharmacological approaches such as pharmacometric and physiologically-based modeling and model-based simulations can be useful to better understand and predict such physiological changes and their effects on drug exposure and response. This review article (1) gives an overview of physiological changes in pregnant women, their fetuses, and (pre)term neonates, (2) presents case studies to illustrate applications of new modeling and simulation approaches, and (3) discusses challenges and opportunities in optimizing and personalizing treatments during pregnancy and neonatal life.

Aims A dramatic increase in newborn infants with neonatal abstinence syndrome has been observed and these neonates are frequently treated with complex methadone dosing schemes to control their withdrawal symptoms. Despite its abundant use, hardly any data on the pharmacokinetics (PK) of methadone is available in preterm neonates. Therefore we investigated developmental PK of methadone and evaluated current dosing strategies and possible simplification in this vulnerable population. Methods A single-centre open-label prospective study was performed to collect PK data after a single oral dose of methadone in preterm neonates. A population PK model was built to characterize developmental PK of (R)- and (S)-methadone. Model-based simulations were performed to identify a simplified dosing strategy to reach and maintain target methadone exposure. Results A total of 121 methadone concentrations were collected from 31 preterm neonates. A one-compartment model with first order absorption and elimination kinetics best described PK data for (R)- and (S)-methadone. Clearance increases with advancing gestational age and differs between R- and S-enantiomer, being slightly higher for the former (0.244 vs 0.167 L/h). Preterm neonates reached target exposure after 48 hours with currently used dosing schedules. Output from simulations revealed that target exposures can be achieved with a simplified dosing strategy during the first 4 days of treatment. Conclusion Methadone clearance in preterm neonates increases with advancing gestational age and its disposition is influenced by its chirality. Simulations that account for developmental PK changes indicate a shorter methadone dosing strategy can maintain target exposure to control withdrawal symptoms.

Bispecific antibodies (BsAbs) bind to two different targets, and create two binary and one ternary complex (TC). These molecules have shown promise as immuno‐oncology drugs, and the TC is considered the pharmacologically active species that drives their pharmacodynamic effect. Here, we have presented a general target‐mediated drug disposition (TMDD) model for these BsAbs, which bind to two different targets on different cell membranes. The model includes four different binding events for BsAbs, turnover of the targets, and internalization of the complexes. In addition, a quasi‐equilibrium (QE) approximation with decreased number of binding parameters and, if necessary, reduced internalization parameters is presented. The model is further used to investigate the kinetics of BsAb and TC concentrations. Our analysis shows that larger doses of BsAbs may delay the build‐up of the TC. Consequently, a method to compute the optimal dosing strategy of BsAbs, which will immediately create and maintain maximal possible TC concentration, is presented.

Machine learning models may enhance the early detection of clinically relevant hyperbilirubinemia based on patient information available in every hospital. We conducted a longitudinal study on preterm and term born neonates with serial measurements of total serum bilirubin in the first two weeks of life. An ensemble, that combines a logistic regression with a random forest classifier, was trained to discriminate between the two classes phototherapy treatment vs. no treatment. Of 362 neonates included in this study, 98 had a phototherapy treatment, which our model was able to predict up to 48 h in advance with an area under the ROC-curve of 95.20%. From a set of 44 variables, including potential laboratory and clinical confounders, a subset of just four (bilirubin, weight, gestational age, hours since birth) suffices for a strong predictive performance. The resulting early phototherapy prediction tool (EPPT) is provided as an open web application. Early detection of clinically relevant hyperbilirubinemia can be enhanced by the application of machine learning. Existing guidelines can be further improved to optimize timing of bilirubin measurements to avoid toxic hyperbilirubinemia in high-risk patients while minimizing unneeded measurements in neonates who are at low risk.

In pharmacokinetics/pharmacodynamics (PKPD) the measured response is often delayed relative to drug administration, individuals in a population have a certain lifespan until they maturate or the change of biomarkers does not immediately affects the primary endpoint. The classical approach in PKPD is to apply transit compartment models (TCM) based on ordinary differential equations to handle such delays. However, an alternative approach to deal with delays are delay differential equations (DDE). DDEs feature additional flexibility and properties, realize more complex dynamics and can complementary be used together with TCMs. We introduce several delay based PKPD models and investigate mathematical properties of general DDE based models, which serve as subunits in order to build larger PKPD models. Finally, we review current PKPD software with respect to the implementation of DDEs for PKPD analysis.

We present competitive and uncompetitive drug-drug interaction (DDI) with target mediated drug disposition (TMDD) equations and investigate their pharmacokinetic DDI properties. For application of TMDD models, quasi-equilibrium (QE) or quasi-steady state (QSS) approximations are necessary to reduce the number of parameters. To realize those approximations of DDI TMDD models, we derive an ordinary differential equation (ODE) representation formulated in free concentration and free receptor variables. This ODE formulation can be straightforward implemented in typical PKPD software without solving any non-linear equation system arising from the QE or QSS approximation of the rapid binding assumptions. This manuscript is the second in a series to introduce and investigate DDI TMDD models and to apply the QE or QSS approximation. published

Target-mediated drug disposition (TMDD) describes drug binding with high affinity to a target such as a receptor. In application TMDD models are often over-parameterized and quasi-equilibrium (QE) or quasi-steady state (QSS) approximations are essential to reduce the number of parameters. However, implementation of such approximations becomes difficult for TMDD models with drug–drug interaction (DDI) mechanisms. Hence, alternative but equivalent formulations are necessary for QE or QSS approximations. To introduce and develop such formulations, the single drug case is reanalyzed. This work opens the route for straightforward implementation of QE or QSS approximations of DDI TMDD models. The manuscript is the first part to introduce DDI TMDD models with QE or QSS approximations.

Transit compartment models (TCM) are important tools in pharmacokinetic/pharmacodynamic (PKPD) modeling. In this work we investigate the relationship between TCMs with arbitrary initial values and lifespan models (LSM) with non-constant past and constant lifespan. We show that the total population in all transit compartments converges to a LSM, if the number of compartments n tends to infinity. The key to obtain this result is to establish a relationship between the initial values of the TCM and the non-constant past of the LSM. We apply the result to two already published PKPD models.

Drugs interact with their targets in different ways. A diversity of modeling approaches exists to describe the combination effects of two drugs. We investigate several combination effect terms (CET) regarding their underlying mechanism based on drug-receptor binding kinetics, empirical and statistical summation principles and indirect response models. A list with properties is provided and the interrelationship of the CETs is analyzed. A method is presented to calculate the optimal drug concentration pair to produce the half-maximal combination effect. This work provides a comprehensive overview of typically applied CETs and should shed light into the question as to which CET is appropriate for application in pharmacokinetic/pharmacodynamic models to describe a specific drug-drug interaction mechanism. published

This study investigates the combined effects of gemcitabine and trabectedin (ecteinascidin 743) in two pancreatic cancer cell lines and proposes a pharmacodynamic (PD) model to quantify their pharmacological interactions. Effects of gemcitabine and trabectedin upon the pancreatic cancer cell lines MiaPaCa-2 and BxPC-3 were investigated using cell proliferation assays. Cells were exposed to a range of concentrations of the two drugs, alone and in combination. Viable cell numbers were obtained daily over 5 days. A model incorporating nonlinear cytotoxicity, transit compartments, and an interaction parameter ψ was used to quantify the effects of the individual drugs and combinations. Simultaneous fitting of temporal cell growth profiles for all drug concentrations provided reasonable cytotoxicity parameter estimates (the cell killing rate constant K max and the sensitivity constant KC 50) for each drug. The interaction parameter ψ was estimated as 0.806 for MiaPaCa-2 and 0.843 for BxPC-3 cells, suggesting that the two drugs exert modestly synergistic effects. The proposed PD model enables quantification of the temporal profiles of drug combinations over a range of concentrations with drug-specific parameters. Based upon these in vitro studies, trabectedin may have augmented benefit in combination with gemcitabine. The PD model may have general relevance for the study of other cytotoxic drug combinations.

Objective To identify dosing strategies that will assure stable caffeine concentrations in preterm neonates despite changing caffeine clearance during the first 8 weeks of life. Methods A 3-step simulation approach was used to compute caffeine doses that would achieve stable caffeine concentrations in the first 8 weeks after birth: (1) a mathematical weight change model was developed based on published weight distribution data; (2) a pharmacokinetic model was developed based on published models that accounts for individual body weight, postnatal, and gestational age on caffeine clearance and volume of distribution; and (3) caffeine concentrations were simulated for different dosing regimens. Results A standard dosing regimen of caffeine citrate (using a 20 mg/kg loading dose and 5 mg/kg/day maintenance dose) is associated with a maximal trough caffeine concentration of 15 mg/L after 1 week of treatment. However, trough concentrations subsequently exhibit a clinically relevant decrease because of increasing clearance. Model-based simulations indicate that an adjusted maintenance dose of 6 mg/kg/day in the second week, 7 mg/kg/day in the third to fourth week and 8 mg/kg/day in the fifth to eighth week assures stable caffeine concentrations with a target trough concentration of 15 mg/L. Conclusions To assure stable caffeine concentrations during the first 8 weeks of life, the caffeine citrate maintenance dose needs to be increased by 1 mg/kg every 1-2 weeks. These simple adjustments are expected to maintain exposure to stable caffeine concentrations throughout this important developmental period and might enhance both the short- and long-term beneficial effects of caffeine treatment.

We consider a population where every individual has a unique lifespan. After expiring of its lifespan the individual has to leave the population. A realistic approach to describe these lifespans is by a continuous distribution. Such distributed lifespan models (DLSMs) were introduced earlier in the indirect response context and consist of the mathematical convolution operator to describe the rate of change. Therefore, DLSMs could not directly be implemented in standard PKPD software. In this work we present the solution representation of DLSMs with and without a precursor population and an implementation strategy for DLSMs in ADAPT , NONMEM and MATLAB . We fit hemoglobin measurements from literature and investigate computational properties.

Combination therapies are widely used in the treatment of patients with cancer. Selecting synergistic combination strategies is a great challenge during early drug development. Here, we present a pharmacokinetic/pharmacodynamic (PK/PD) model with a smooth nonlinear growth function to characterize and quantify anticancer effect of combination therapies using time-dependent data. To describe the pharmacological effect of combination therapy, an interaction term was introduced into a semi-mechanistic anticancer PK/PD model. This approach enables testing of a pharmacological hypothesis with respect to an anticipated pharmacological synergy of drug combinations, such as an assumed pharmacological synergy of complementary inhibition of a particular signaling pathway. The model was applied to three real data sets derived from preclinical screening experiments using xenograft mice. The suggested model fitted well the observed data from mono- to combination-therapy and allowed physiologically meaningful interpretation of the experiments. The tested drug combinations were assessed for their ability to act as synergistic modulators of tumor growth inhibition by the interaction parameter psi. The presented approach has practical implications because it can be applied to standard xenograft experiments and may assist in the selection of both optimal drug combinations and administration schedules. The unique feature of the presented approach is the ability to characterize the nature of combined drug interaction as well as to quantify the intensity of such interactions by assessing the time course of combined drug effect.