A new Bayesian method to forecast and fine tune individual hemodialysis dose.

BACKGROUND: The most commonly used formulas for hemodialysis dose are based on single-pool urea kinetics; i.e., they consider the body as a single compartment and use an ad hoc adjustment for postdialysis urea rebound. We present a new urea kinetic modeling approach, individualized Bayesian urea kinetic modeling (IBKM), which incorporates prior knowledge. This method uses measurements made during previous treatments to forecast a patient's postdialysis urea rebound and clearance and provides a choice of possible dialysis parameters to achieve a desired clearance goal. METHODS: We used data from 18 patients (a total of 38 hemodialysis sessions) to build the model. All patients had been on thrice-weekly hemodialysis for at least 1 year before enrollment, and their dialysis prescription remained unchanged during the study period. Recorded variables included blood urea nitrogen (BUN) measurements and dialysis prescription parameters (dialyzer size, KoA, treatment time, blood and dialysis flow). The population distribution of urea kinetic parameters-derived from the 18 patients' data-and individual urea kinetic data (i.e., pre- and postdialysis BUN) are used in the IBKM method to make individual predictions. RESULTS: Estimates (mean+/-SE) of population urea kinetic parameters are generation rate 0.17+/-0.01 mmol/min, clearance between extracellular and intracellular compartments 646+/-60 mL/min, and total volume of distribution 31.5+/-1.5 L, of which the extracellular volume is 36+/-4%. The effective dialysis clearance is estimated to be 9.0+/-1.7%, less than the expected dialyzer clearance. IBKM predictions of postdialysis equilibrated BUN concentrations are accurate: a root mean squared error of 3.4% of the "postrebound" BUN concentration at 30 min, a value in the range of urea measurement error itself. CONCLUSIONS: IBKM can estimate not only the urea kinetics of an actual hemodialysis, but it can also predict a patient's target hemodialysis dose for any desired, flexible hemodialysis treatment. The method should prove useful for bedside monitoring, forecasting, and fine tuning of hemodialysis dose.

The need for mixed-effects modeling with population dichotomous data.

Over the past 25 years sophisticated data analytic techniques have been developed which can lead to improved analyses, but at additional computational cost. In particular, this applies to the approach where interindividual random effects are included in a data analytic model for population pharmacokinetic data, which can often lead to substantially improved estimates of fixed-effect parameters. However, there are also commonly occurring situations, notably with some types of pharmacodynamic data, where such improvement is not realized. This study simulates some simple population dichotomous data, and secondarily, some related continuous data. These data are analyzed using both mixed-effect (ME) models that include interindividual random effects and naive (NA) models that do not include interindividual random effects, and it is seen that use of an ME model does not inevitably lead to gains over use of an NA model. In fact, using maximum likelihood estimation with both types of models, the root mean square estimation errors for fixed effect parameters can actually be larger with an ME model than with the corresponding NA model. Using a form of restricted maximum likelihood estimation with the ME model, the two types of models yield root mean square errors which are comparable, but which still do not suggest that there is always marked advantage in using the ME model.

Selecting reliable pharmacokinetic data for explanatory analyses of clinical trials in the presence of possible noncompliance.

For single-dose concentration-time data collected in clinical trials to be useful for explanatory pharmacokinetic (PK) or pharmacokinetic-pharmacodynamic (PK-PD) analyses, the following two assumptions on the data must hold: (i) the times of the concentration (PK) observations are known, and (ii) the patient's recent past dosing history (times and amounts) is known. If either (or both) of these assumptions does not hold, and data analysis proceeds as if it did, biased estimates may result. Assumption (i) usually does hold as study personnel observe and record PK sampling times. Assumption (ii) is a problem when, as is often the case of outpatient studies, one must rely on patient recall for past dosing history. This paper presents a technique to avoid assumption (ii) by identifying for deletion those PK observation occasions likely exhibiting unreliable preceding dose histories. To so identify occasions, a Bayes objective function (posterior density) for the data is maximized in its parameters for each individual. The likelihood factor of this function is a mixture pharmacostatistical model expressing the likelihood of the observed concentration(s) under three mutually exclusive events: the prescribed dose preceding the occasion was not taken at all (NT), the prescribed dose was taken at the specified time (T), or the prescribed dose was taken at an unspecified time (U). Suspect observations are identified as those whose maximum corresponding likelihood component is other than T. The approach as defined here relies on the following assumptions in addition to (i): (ii) population PK (i.e., the distribution of PK parameters in the population being sampled) is known, at least approximately. (iii) PK samples (at least 1 or 2 per occasion) are available, (iv) doses taken are of the stated magnitude, and (v) the drug has a short half-life. Simulations reveal that especially when more than one PK sample is available per study occasion, the methodology chooses a set of PK observations that should perform better in subsequent explanatory analyses, or as a basis for estimating individual PK parameters, than do other simpler methods.

Evaluating pharmacokinetic/pharmacodynamic models using the posterior predictive check.

The posterior predictive check (PPC) is a model evaluation tool. It assigns a value (pPPC) to the probability that the value of a given statistic computed from data arising under an analysis model is as or more extreme than the value computed from the real data themselves. If this probability is too small, the analysis model is regarded as invalid for the given statistic. Properties of the PPC for pharmacokinetic (PK) and pharmacodynamic (PD) model evaluation are examined herein for a particularly simple simulation setting: extensive sampling of a single individual's data arising from simple PK/PD and error models. To test the performance characteristics of the PPC, repeatedly, "real" data are simulated and for a variety of statistics, the PPC is applied to an analysis model, which may (null hypothesis) or may not (alternative hypothesis) be identical to the simulation model. Five models are used here: (PK1) mono-exponential with proportional error, (PK2) biexponential with proportional error, (PK2 epsilon) biexponential with additive error, (PD1) Emax model with additive error under the logit transform, and (PD2) sigmoid Emax model with additive error under the logit transform. Six simulation/analysis settings are studied. The first three, (PK1/PK1), (PK2/PK2), and (PD1/PD1) evaluate whether the PPC has appropriate type-I error level, whereas the second three (PK2/PK1), (PK2 epsilon/PK2), and (PD2/PD1) evaluate whether the PPC has adequate power. For a set of 100 data sets simulated/analyzed under each model pair according to a stipulated extensive sampling design, the pPPC is computed for a number of statistics in three different ways (each way uses a different approximation to the posterior distribution on the model parameters). We find that in general; (i) The PPC is conservative under the null in the sense that for many statistics, prob(pPPC < or = alpha) < alpha for small alpha. With respect to such statistics, this means that useful models will rarely be regarded incorrectly as invalid. A high correlation of a statistic with the parameter estimates obtained from the same data used to compute the statistic (a measure of statistical "sufficiency") tends to identify the most conservative statistics. (ii) Power is not very great, at least for the alternative models we tested, and it is especially poor with "statistics" that are in part a function of parameters as well as data. Although there is a tendency for nonsufficient statistics (as we have measured this) to have greater power, this is by no means an infallible diagnostic. (iii) No clear advantage for one or another method of approximating the posterior distribution on model parameters is found.

Making the most of sparse clinical data by using a predictive-model-based analysis, illustrated with a stavudine pharmacokinetic study.

A small-scale clinical investigation was done to quantify the penetration of stavudine (D4T) into cerebrospinal fluid (CSF). A model-based analysis estimates the steady-state ratio of AUCs of CSF and plasma concentrations (R(AUC)) to be 0.270, and the mean residence time of drug in the CSF to be 7.04 h. The analysis illustrates the advantages of a causal (scientific, predictive) model-based approach to analysis over a noncausal (empirical, descriptive) approach when the data, as here, demonstrate certain problematic features commonly encountered in clinical data, namely (i) few subjects, (ii) sparse sampling, (iii) repeated measures, (iv) imbalance, and (v) individual design variation. These features generally require special attention in data analysis. The causal-model-based analysis deals with features (i) and (ii), both of which reduce efficiency, by combining data from different studies and adding subject-matter prior information. It deals with features (iii)--(v), all of which prevent 'averaging' individual data points directly, first, by adjusting in the model for interindividual data differences due to design differences, secondly, by explicitly differentiating between interpatient, interoccasion, and measurement error variation, and lastly, by defining a scientifically meaningful estimand (R(AUC)) that is independent of design.

Pharmacokinetic/pharmacodynamic modeling in drug development.

We propose a framework for considering the role of pharmacokinetic/pharmacodynamic modeling in drug development and an appraisal of its current and potential impact on that activity. After some introduction, definitions, and background information on drug development, we discuss subject-matter models that underlie pharmacokinetic/pharmacodynamic modeling and show how they determine appropriate statistical models. We discuss the broad role modeling can play in drug development, enhancing primarily the "learning" steps, i.e. acquiring the information needed for the label and for planning efficient confirmatory clinical trials. Examples of past applications of modeling to drug development are presented in tabular form, followed by a discussion of some practical issues in application. Modeling will not reach its potential utility until it is manifest as a visible and separate work unit within a drug development program. We suggest that that work unit is the "in numero" study: a protocol-driven exercise designed to extract additional information, and/or answer a specific drug-development question, through an integrated model-based (meta-) analysis of existent raw data, often pooled across separate (clinical) studies.

Quantitative characterization of therapeutic index: application of mixed-effects modeling to evaluate oxybutynin dose-efficacy and dose-side effect relationships.

BACKGROUND: Describing a therapeutic index for a drug is important for evaluating safe and effective dosage regimens. Therapeutic index can be evaluated as the relative position of the dose-efficacy and the dose-side effect curves. Oxybutynin XL (Ditropan XL), a once-daily oral controlled-release formulation for oxybutynin chloride, is being developed. Oxybutynin XL efficacy and side-effect data obtained from two parallel-group, randomized, controlled clinical trials were modeled to evaluate the therapeutic index. METHODS: A nonlinear mixed-effects model was used to characterize the oxybutynin dose-efficacy and dose-dry mouth relationship. Weekly urge urinary incontinence episodes, the primary efficacy variable, is a discrete variable (counts) with only non-negative integer values and was therefore modeled as a Poisson variable. The probability of dry mouth severity (the most frequently reported side effect), assessed on a categorical four-point scale, was modeled with a proportional odds model. In the modeling process, it was assumed that the time effect was the same for the active and placebo treatments and that the drug effect was additive. RESULTS AND CONCLUSIONS: The urge urinary incontinence episodes declined log-linearly, and no significant difference was observed between the two formulations. However, there was a trend toward higher efficacy with oxybutynin XL than with immediate-release oxybutynin at the same dose in one study. Dose-dry mouth analysis showed that the probability of dry mouth with an increasing dose was significantly lower with oxybutynin XL than with immediate-release oxybutynin in the second study, and a similar trend was observed in the first study. By combining the dose-urge urinary incontinence and dose-dry mouth relationship, a wider therapeutic index was predicted for oxybutynin XL than for immediate-release oxybutynin.

Population pharmacokinetics of nevirapine, zidovudine, and didanosine in human immunodeficiency virus-infected patients. The National Institute of Allergy and Infectious Diseases AIDS Clinical Trials Group Protocol 241 Investigators.

The population pharmacokinetics of nevirapine (NVP), zidovudine (ZDV), and didanosine (ddI) were evaluated in a total of 175 patients infected with human immunodeficiency virus randomized to receive either a double combination of ZDV plus ddI or a triple combination of NVP plus ZDV plus ddI as a substudy of the AIDS Clinical Trials Group Protocol 241. Levels (approximating 3.5 determinations/patient) of the three drugs in plasma were measured during 44 of a total 48 weeks of study treatment, and a set of potential covariates was available for nonlinear mixed-effect modeling analysis. A one-compartment model with zero-order input and first-order elimination was fitted to the NVP data. Individual oral clearance (CL) and volume of distribution (V) averaged 0.0533 liters/h/kg of body weight and 1.17 liters/kg, respectively. Gender was the only covariate which significantly correlated with the CL of NVP. ZDV and ddI data were described by a two-compartment model with zero-order input and first-order elimination. Individual mean oral CL, VSS (volume of distribution at steady state), and V of ZDV were 1.84 liters/h/kg and 6.68 and 2.67 liters/kg, respectively, with body weight and age as correlates of CL and body weight as a correlate of VSS. The average individual oral CL, VSS, and V of ddI were 1.64 liters/h/kg and 3.56 and 2.74 liters/kg, respectively, with body weight as a significant correlate of both CL and VSS. The relative bioavailability (F) of ZDV and ddI in the triple combination compared to that in the double combination was also evaluated. No significant effects of the combination regimens on the F of ddI were detected (FTRIPLE = 1.05 and FDOUBLE = 1 by definition), but the F of ZDV was markedly reduced by the triple combination, being only 67.7% of that of the double combination. Large (>50%) intraindividual variability was associated with both ZDV and ddI pharmacokinetics. Individual cumulative area under the plasma drug level-time curve of the three drugs was calculated for the entire study period as a measure of drug exposure based on the individual data and the final-model estimates of structural and statistical parameters.

A population pharmacokinetic-pharmacodynamic analysis of repeated measures time-to-event pharmacodynamic responses: the antiemetic effect of ondansetron.

This paper presents and illustrates methodology for specifying, estimating, and evaluating a predictive model for repeated measures time-to-event responses. The illustrative example specifies a model of the antiemetic effect vs. concentration relationship for the 5-HT3 antagonist ondansetron in the human ipecac model for emesis. A key part of this model is a time-dependent log hazard function for emesis that is increased by ipecac administration and decreased by ondansetron concentration. The model is fit using an approximate maximum likelihood method. The data consist of the time free of emeses and, for those individuals with emetic episodes, the time(s) of the episode(s). Model evaluation is accomplished using residual plots adapted to time-to-event data and a "posterior predictive check" wherein observed data statistics are compared to those obtained from data simulated from the fitted model. The ondansetron concentration required to obtain a 50% reduction in the hazard of emesis is estimated to be 1.4 +/- 0.2 ng/ml, and the rate constant for elimination of ipecac-induced hazard is 1.5 +/- 0.2 hr-1.

Characterizing patterns of drug-taking behavior with a multiple drug regimen in an AIDS clinical trial.

OBJECTIVE: To characterize drug-taking behavior using continuous electronic monitoring in an AIDS clinical trial. SETTING: This was a substudy of AIDS Clinical Trials Group (ACTG) protocol 175, a phase II/III study of dideoxynucleoside monotherapy versus combination therapy in asymptomatic HIV-positive subjects. Participants were required to comply with regimens containing zidovudine, zalcitabine and didanosine, or matching placebos; the total daily pill count was 16. DESIGN: For participants at two ACTG 175 sites, electronic devices were used to monitor drug-taking behavior of all study medications over a period of approximately 90 days. MEASUREMENTS: Four indices of drug-taking behavior were calculated and their distributions and relationship to the prescribed regimen were examined. RESULTS: Data from 41 subjects were analyzed. Of the prescribed doses of zidovudine, zalcitabine and didanosine, 88, 84 and 82%, respectively, were taken. Of these, 55, 66 and 79%, respectively, were taken at the prescribed dosing frequency. The median percentage of days on which participants failed to take any of the doses was 2-5%. There was a trend towards lower adherence in the combination therapy arms compared with those assigned to receive monotherapy. In this analysis, older patients demonstrated better adherence, although patient characteristics, in general, were poorly predictive of adherence. CONCLUSION: Drug-taking behavior for all three active study medications differed from that prescribed. One result of this erratic adherence was that study participants sustained little antiretroviral effect during more than 25% of the monitoring period.

A Markov mixed effect regression model for drug compliance.

Patient compliance (adherence) with prescribed medication is often erratic, while clinical outcomes are causally linked to actual, rather than nominal medication dosage. We propose here a hierarchical Markov model for patient compliance. At the first stage, conditional upon individual random effects and a set of individual-specific nominal daily dose times, we assume that (i) the subject-specific probability of taking zero, one, or more than one dose associated with a given nominal dose time depends on the value of certain covariates, and on the number of doses associated with the immediate previous time, but is independent of any other previous or future dosing events (the Markov hypothesis); and (ii) the set of 'errors' between actual dose times associated with each nominal time is multivariate normally distributed, conditional on covariates and the number of such actual dose times, as in (i). At the second stage, a multivariate normal distribution is assumed for the individual random effects. We fit this model by maximum likelihood to data collected over three months using an electronic system for recording actual dose times in HIV-positive patients assigned to a regimen of zidovudine thrice daily. Beyond its value for describing and quantifying compliance behaviour, as illustrated here, the model may prove useful for explanatory analyses of clinical trials.

Passive versus electrotransport-facilitated transdermal absorption of ketorolac.

OBJECTIVE: To investigate the bioavailability (extent and rate of absorption) of ketorolac from two cutaneous absorption sources, active electrotransport and passive transdermal, and to examine the enantiomeric selectivity of bioavailability for each source. METHODS: Based on a crossover study in 12 healthy volunteers, the extent and rate of absorption of ketorolac, delivered by a patch, were found by estimating the input rate function of the drug. For that purpose, deconvolution was used in two steps. First, intravenous data were analyzed to estimate the ketorolac disposition function, and second, postpatch data were deconvolved to estimate the unknown patch input profile given the disposition function estimated in the first step. Because the input rate function curves to be estimated for the patches may be of arbitrary shape, a spline was used to model the patch input function, whereas intravenous data were modeled with use of a sum of exponentials. Differences in the extent of absorption (F) for the four treatment-enantiomer combinations were further examined with a mixed-effect regression model, based on the sets of four individual estimates of bioavailability. RESULTS: On average, the F value for the active electrotransport treatment, which exhibited the faster absorption rate, was four times greater than the F for the passive transdermal treatment. Further, during the passive treatment, R-ketorolac yielded an average F that is 42% greater than that for S-ketorolac and also exhibited a smaller absorption lag-time. During the active treatment, there was no important enantiomeric difference in either extent or rate of absorption.

Population pharmacokinetics/pharmacodynamics of docetaxel in phase II studies in patients with cancer.

PURPOSE: The population pharmacokinetic/pharmacodynamic (PK/PD) approach was prospectively integrated in the clinical development of docetaxel to assess the PK profile in a large population of patients and investigate systemic exposure as a prognostic factor for clinical outcome. PATIENTS AND METHODS: PK analysis was performed at first course in 24 phase II studies of docetaxel monotherapy using four randomized limited-sampling schedules. Bayesian estimates of clearance (CL), area under the concentration-time curve (AUC), and peak and duration of plasma levels greater than threshold levels were used as measures of exposure. PD data included for efficacy, response rate, time to first response, and time to progression (TTP) in breast cancer and non-small-cell lung cancer (NSCLC), and for toxicity, grade 4 neutropenia, and febrile neutropenia at first course and time to onset of fluid retention. PK/PD analysis was conducted using logistic and Cox multivariate regression models. RESULTS: PK protocol implementation was successful. Most of the patients registered (721 of 936, 77%) were sampled and 68% were assessable for PK (640 patients). First-course docetaxel AUC was a significant predictor (P = .0232) of TTP in NSCLC (n = 151). Docetaxel CL was a strong independent predictor (P < .0001) of both grade 4 neutropenia and febrile neutropenia (n = 582). Cumulative dose was the strongest predictor (P < .0001) of the time to onset of fluid retention (n = 631). However, the duration of exposure over 0.20 micromol/L (0.16 microg/mL) at first course was an independent predictor (P = .0029). Few patients (n = 25, 4%) received the recommended dexamethasone premedication. CONCLUSION: First-course docetaxel PK is a predictor of first-course hematologic toxicity, but also of fluid retention, which is cumulative in nature. Patients with elevated hepatic enzymes have a 27% reduction in docetaxel CL and are at a higher risk of toxicity. A starting dose of 75 mg/m2 is currently being evaluated in this population. Prospective implementation of large-scale population PK/PD evaluation is feasible in early drug development and this approach generates clinically relevant findings.

Use of a pharmacokinetic/pharmacodynamic model to design an optimal dose input profile.

A model for the pharmacodynamic effect of a drug (designated only X), and the use of the model to explore optimal input is described. The data analyzed here are from a crossover comparison study of the effect of 4 active treatments, yielding distinct concentration vs. time curves, plus placebo in 32 subjects. The model expresses total effect as the sum of placebo effect and (pure) drug effect. The latter allows for possible tolerance (found) and time effects (not found). Random effects allow interindividual differences to be expressed. Conditioning on the fitted model, a population optimal input profile is designed that obeys certain protocol constraints. The profile minimizes the expectation of a sum of squared differences between target effect and the resulting response over a given time interval. The target is a fixed constant, chosen to be either the individuals' maximum effect level in response to a baseline input regimen used in the study or the maximum effect level for the typical individual in the population in response to this regimen, as predicted from the model. The expectation is taken over the estimated nonparametric distribution of the 32 subjects' random effects. As one goal of early clinical studies of drugs may be to provide a basis for designing an optimal delivery profile (with respect to a specified loss function), we suggest this report as an example of a reasonable way to go about finding such a profile.

Pharmacokinetics of saquinavir, zidovudine, and zalcitabine in combination therapy.

We investigated the pharmacokinetics of zidovudine, zalcitabine, and saquinavir in AIDS Clinical Trial Group protocol 229. Patients received either saquinavir, zalcitabine, or a combination of both, together with zidovudine three times a day. Approximately 100 patients were enrolled in each treatment arm, and intensive pharmacokinetic studies were performed on about 25 patients per arm at weeks 1 and 12. We estimated the pharmacokinetic parameters of all three drugs by using parametric and nonparametric methods. The mean values of the pharmacokinetic parameters of zidovudine (clearance [CL]/bioavailability [F], 168 liters/h; volume of distribution [V]/F, 185 liters; half-life, 0.76 h) and zalcitabine (CL/F, 25 liters/h; V/F, 92.2 liters; half-life, 2.7 h) were similar to those reported previously. For saquinavir, the mean pharmacokinetic parameter estimates using parametric methods were as follows: maximum concentration of drug in serum [Cmax], 70.8 ng/ml; time to Cmax, 3.11 h; area under the curve, 809 ng x h/ml; CL/F, 989 liters/h; V/F, 1,503 liters; half-life, 1.38 h. For all three drugs, clearance decreased with age. Weight did not influence the clearance of zidovudine, but the clearance of zalcitabine and saquinavir increased with weight. There were no differences in pharmacokinetic parameters between study weeks and arms, suggesting that there is no change in kinetics with chronic administration and that there are no significant pharmacokinetic interactions among these three drugs.

Exposure-response relationships for saquinavir, zidovudine, and zalcitabine in combination therapy.

The relationship of CD4+ cell response, level of RNA in plasma, and quantitative peripheral blood mononuclear cell (PBMC) titer to apparent drug exposure was investigated by using data from AIDS Clinical Trial Group protocol 229, a multicenter randomized study. Patients received either saquinavir, zalcitabine, or a combination of both, along with open-label zidovudine. Approximately 100 patients were enrolled in each arm, and the primary study duration was 24 weeks. Individual drug exposure, the area under the concentration-time curve, was estimated by using population-based pharmacokinetic methods. Response was defined as the maximum increase in CD4+ cell count or the maximum decrease in RNA in plasma or PBMC titer adjusted for baseline CD4+ cell count, RNA in plasma, and PBMC titer, respectively. Regression of responses on exposure demonstrated an exposure effect for saquinavir which was significant for the maximum increase in CD4+ cell count and the decrease in RNA in plasma. For the PBMC titer, no significant relationship could be demonstrated but the results suggested a trend similar to that of the other response variables. For all three response variables, the slope of the saquinavir exposure response was greater with the triple combination (saquinavir, zidovudine, and zalcitabine) than with the combination of saquinavir and zidovudine, suggesting possible synergism between saquinavir and zalcitabine.

A pooled analysis of CD4 response to zidovudine and zalcitabine treatment in patients with AIDS and AIDS-related complex.

INTRODUCTION: This article reports a meta-analysis focused on the efficacy of zalcitabine and zidovudine alone or in combination as reported by three AIDS Clinical Trial Group trials. We analyzed the log CD4 count (LCD4) response to therapy up to 1 year after the beginning of therapy. One of the purposes of this article was to illustrate a meta-analysis method that permits pooling of original data from trials with different designs. METHODS: To effectively eliminate obvious differences due to design, we first estimated complete (1 year) individual LCD4 versus time curves using a sophisticated smoothing technique. Then several summary descriptors were computed from the completed LCD4 curves. Those descriptors were corrected for baseline covariate differences, and the corrected values were then related to measures of drug exposure. RESULTS: Significant baseline covariates were LCD4 baseline count and AIDS-related complex or AIDS diagnosis. The predictor, corrected for baseline covariates, that correlated best with drug exposure was intensity, the initial rate of rise of LCD4, estimated as the slope of LCD4 between pretreatment and peak LCD4. CONCLUSION: Using intensity as a single response measure, we found weak evidence for synergism of zalcitabine and zidovudine: combination therapy increased response by 20% over that expected from a purely additive interaction.

A semiparametric method for describing noisy population pharmacokinetic data.

We propose a semiparametric method to estimate model-independent pharmacokinetic (PK) measures such as area under concentration-time, peak concentration and time to peak concentration (Tpeak), for noisy population PK data from a sparsely sampled prospectively designed trial. The method is developed within the mixed-effect model framework, for the single-dose and steady-state case. We describe individual concentration vs. time using a longitudinal spline, consisting of a template spline, common to all individuals, and an individual-specific distortion spline accounting for individual differences. We impose a number of constraints on the longitudinal spline, including (i) it has a decreasing tail, (ii) its typical Tpeak is near the modal Tpeak observed in the population data, and (iii) its value is zero at time zero (single dose), or the same nonzero value at the beginning and end of a dosing interval (steady state). We test our method using simulated data and compare its performance to that of a parametric and a nonparametric method. An actual data example is also shown. The performance of the method is as good or better than that of a standard nonparametric method, and when the analysis model is misspecified, the method is superior to a standard parametric one. Since it is often not apparent that an analysis model is correct, we propose this approach as a general method for analysis.

Modeling a bivariate control system: LH and testosterone response to the GnRH antagonist antide.

A pharmacodynamic analysis of the input-response relationship between the gonadotropin-releasing hormone antagonist antide and luteinizing hormone (LH) and testosterone concentrations is presented. A control compartmental model is developed using pharmacokinetic and pharmacodynamic data from experiments in which different short intravenous antide infusions were given to healthy male volunteers. Because of the control interdependence between serum LH and testosterone a separation principle similar to one we have used previously to analyze physiological pharmacokinetic data is used for model exploration: testosterone and LH are first modeled separately, conditioning on the other observed response. This reveals that the LH effect on testosterone depends on previous LH exposure and that LH depends not on current but on previous testosterone exposure, resulting in an LH overshoot after antide-induced suppression. Both submodels are combined into one global model, which in addition includes a model for testosterone circadian variation. This model describes the data well and can be used to predict responses for some nonstudied antide dosages. However, the sensitivity of predictions to model assumptions limits the range of valid extrapolation, and this, too, is illustrated.