Nonparametric Expectation Maximization Research Articles

Faulds: A Non-Parametric Iterative Classifier for Internet-Wide OS Fingerprinting

Recent work in OS fingerprinting has focused on overcoming random distortion in network and user features during Internet-scale SYN scans. These classification techniques work under an assumption that all parameters of the profiled network are known a-priori – the likelihood of packet loss, the popularity of each OS, the distribution of network delay, and the probability of user modification to each default TCP/IP header value. However, it is currently unclear how to obtain realistic versions of these parameters for the public Internet and/or customize them to a particular network being analyzed. To address this issue, we derive a non-parametric Expectation-Maximization (EM) estimator, which we call <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Faulds</i> , for the unknown distributions involved in single-probe OS fingerprinting and demonstrate its significantly higher robustness to noise compared to methods in prior work. We apply Faulds to a new scan of 67M webservers and discuss its findings.

Nonparametric estimation of recursive point processes with application to mumps in Pennsylvania.

The self-exciting Hawkes point process model (Hawkes, 1971) has been used to describe and forecast communicable diseases. A variant of the Hawkes model, called the recursive model, was proposed by Schoenberg etal. (2019) and has been shown to fit well to various epidemic disease datasets. Unlike the Hawkes model, the recursive model allows the productivity to vary as the overall rate of incidence of the disease varies. Here, we extend the data-driven nonparametric expectation-maximization method of Marsan and Lengliné (2008) in order to fit the recursive model without assuming a particular functional form for the productivity. The nonparametric recursive model is trained to fit to weekly reported cases of mumps in Pennsylvania during the January 1970-September 1990 time frame and then assessed using one week forecasts for the October 1990-December 2001 time period. Both its training and predictive ability are evaluated compared to that of other candidate models, such as Hawkes and SVEILR (susceptible, vaccinated, exposed, infected, lightly infected, recovered) compartmentalmodels.

Estimation of Beauty Contest Auctions

Beauty contests are auction mechanisms used to buy or sell differentiated products where the auctioneer does not specify a decision rule to pick the winning bidder. Beauty contests are widely used in procuring welfare-to-work projects, freelance services, selling online ads, real estate transactions, and hiring, dating/marriage decisions. Unlike price-only auctions, beauty contests have no closed-form bidding strategies and suffer from nonmultiplicatively separable unobserved auction heterogeneity, which makes their estimation challenging. To address these challenges, we formulate beauty contests as incomplete information games and present a two-step estimator. A key contribution of our method is its ability to account for common-knowledge auction-specific unobservables using finite unobserved types. We show that unobserved auction types and distributions of bids are nonparametrically identified and recoverable in the first step using a nonparametric Expectation-Maximization (EM)-like algorithm, and that these can then be used in the second step to recover cost distributions. We present an application of our method in the online freelancing context. We find that seller margins in this marketplace are around 15% of the bid, and that not accounting for unobserved heterogeneity can significantly bias cost estimates in this setting. Based on our estimates, we run counterfactual simulations and provide guidelines to managers of freelance firms.Data, as supplemental material, are available at http://dx.doi.org/10.1287/mksc.2015.0929 .

Estimation of Beauty Contest Auctions

Beauty contests are auction mechanisms used to buy or sell differentiated products where the auctioneer does not specify a decision rule to pick the winning bidder. Beauty contests are widely used in procuring welfare-to-work projects, freelance services, selling online ads, real estate transactions, and hiring, dating/marriage decisions. Unlike price-only auctions, beauty contests have no closed-form bidding strategies and suffer from nonmultiplicatively separable unobserved auction heterogeneity, which makes their estimation challenging. To address these challenges, we formulate beauty contests as incomplete information games and present a two-step estimator. A key contribution of our method is its ability to account for common-knowledge auction-specific unobservables using finite unobserved types. We show that unobserved auction types and distributions of bids are nonparametrically identified and recoverable in the first step using a nonparametric Expectation-Maximization (EM)-like algorithm, and that ...

Noised image segmentation based on rough set and orthogonal polynomial density model

In order to segment a noised image, a method is proposed based on the rough set and orthogonal polynomial density model, in which the nonparametric mixture model can accurately fit the image gray distribution and the rough set can deal with the inaccuracy and uncertainty problems. First, the nonparametric mixture density model is constructed based on the upper and lower approximations of the rough set which can address the problem of over-relying on the prior presumption. Second, the nonparametric expectation-maximization is used to estimate the mixture model parameters. Finally, image pixels are classified according to Bayesian criterion. Experiments on different datasets show that our method is effective in solving the problem of model mismatch, restraining the noise, and preserving the boundary for the noised image segmentation.

Performance of a Divided-Load Intravenous Vancomycin Dosing Strategy for Critically Ill Patients

Current guidelines recommend vancomycin trough concentrations 15 to 20 µg/mL in complicated infections and all trough concentrations above 10 µg/mL. We assessed the performance of a novel divided-load protocol designed to attain target trough concentrations within 24 hours of initiation and prevent doses given at concentrations above the target range, in critically ill patients. The protocol was evaluated in 79 critically ill patients through retrospective medical record review. Vancomycin serum concentrations were drawn before the third dose after initiation and after any dosing change. Steady-state concentrations were drawn before the fifth or sixth doses. Vancomycin concentrations before the second dose were predicted using a nonparametric expectation maximization algorithm. Sixty-nine of 79 patients received scheduled doses, and 62 (90%) of the scheduled-dose patients attained therapeutic target concentrations 12 to 24 hours after therapy initiation. Eight scheduled-dose patients weighed > 150% of ideal body weight (IBW) and were significantly more likely to exhibit supratherapeutic trough concentrations before the fifth or sixth doses (P = .0004) compared with patients weighing ≤150% of IBW. Ten of 79 patients (8 dialysis dependent and 2 experiencing acute kidney injury) were dosed in response to measured serum drug concentrations drawn according to the divided-load protocol. All the 8 dialysis-dependent patients (100%) attained therapeutic concentrations 12 hours after therapy initiation. The divided-load vancomycin dosing strategy achieved measured trough concentrations 15 to 20 µg/mL for most critically ill patients within 24 hours of initial dosing, without allowing doses given during supratherapeutic concentrations.

A Nonparametric Joint Assortment and Price Choice Model

The selection of products and prices offered by a firm significantly impacts its profits. Existing approaches do not provide flexible models that capture the joint effect of assortment and price. We propose a nonparametric framework in which each customer is represented by a particular price threshold and a particular preference list over the alternatives. The customers follow a two-stage choice process; they consider the set of products with prices less than the threshold and choose the most preferred product from the set considered. We develop a tractable nonparametric expectation maximization (EM) algorithm to fit the model to the aggregate transaction data and design an efficient algorithm to determine the profit-maximizing combination of offer set and price. We also identify classes of pricing structures of increasing complexity, which determine the computational complexity of the estimation and decision problems. Our pricing structures are naturally expressed as business constraints, allowing a manager to trade off pricing flexibility with computational burden.This paper was accepted by Yinyu Ye, optimization.

A Two-Stage Model of Consideration Set and Choice: Learning, Revenue Prediction, and Applications

The selection of products and prices offered by a firm significantly impacts its profits. Existing approaches do not provide flexible models that capture the joint effect of assortment and price. We propose a nonparametric framework in which each customer is represented by a particular price threshold and a particular preference list over the alternatives. The customers follow a two-stage choice process; they consider the set of products with prices less than the threshold and choose the most preferred product from the set considered. We develop a tractable nonparametric expectation-maximization (EM) algorithm to fit the model to the aggregate transaction data and design an efficient algorithm to determine the profit-maximizing combination of offer set and price. We also identify classes of pricing structures of increasing complexity, which determine the computational complexity of the estimation and decision problems. Our pricing structures are naturally expressed as business constraints, allowing a manager to trade off pricing flexibility with computational burden.

Inferring synaptic inputs given a noisy voltage trace via sequential Monte Carlo methods

We discuss methods for optimally inferring the synaptic inputs to an electrotonically compact neuron, given intracellular voltage-clamp or current-clamp recordings from the postsynaptic cell. These methods are based on sequential Monte Carlo techniques ("particle filtering"). We demonstrate, on model data, that these methods can recover the time course of excitatory and inhibitory synaptic inputs accurately on a single trial. Depending on the observation noise level, no averaging over multiple trials may be required. However, excitatory inputs are consistently inferred more accurately than inhibitory inputs at physiological resting potentials, due to the stronger driving force associated with excitatory conductances. Once these synaptic input time courses are recovered, it becomes possible to fit (via tractable convex optimization techniques) models describing the relationship between the sensory stimulus and the observed synaptic input. We develop both parametric and nonparametric expectation-maximization (EM) algorithms that consist of alternating iterations between these synaptic recovery and model estimation steps. We employ a fast, robust convex optimization-based method to effectively initialize the filter; these fast methods may be of independent interest. The proposed methods could be applied to better understand the balance between excitation and inhibition in sensory processing in vivo.

Non-parametric and region-based image fusion with Bootstrap sampling

Image fusion refers to the techniques that integrate complementary information from multiple image sensors’ data in a way that makes the new images more suitable for human visual perception and reduces computation processing tasks. In this paper, we propose a non-parametric and region-based image fusion based on the Bootstrap sampling (BS) principle, which reduces the dependence effect of pixels in real images and minimizes the fusion time. Given an original image, we randomly select a small representative set of pixels. In the statistical image formation model, image sensors are described as the true scene corrupted by additive non-Gaussian distortion. Then, a Non-parametric Expectation–Maximization (NEM) algorithm would be used to estimate both the model parameters and the fused image. The non-parametric aspect comes from the use of the orthogonal series’ estimator. Obtained results show that the BS method gives better results than the classical one, both for fused image quality as well as for computation time.

Unsupervised Bayesian image segmentation using orthogonal series

This paper deals with the problem of unsupervised image segmentation which consists in first mixture identification phase and second a Bayesian decision phase. During the mixture identification phase, the conditional probability density function (pdf) and the a priori class probabilities must be estimated. The most difficult part is the estimation of the number of pixel classes or in other words the estimation of the number of density mixture components. To resolve this problem, we propose here a Stochastic and Nonparametric Expectation-Maximization (SNEM) algorithm. The algorithm finds the most likely number of classes, their associated model parameters and generates a segmentation of the image by classifying the pixels into these classes. The non-parametric aspect comes from the use of the orthogonal series estimator. Experimental results are promising, we have obtained accurate results on a variety of real images.

Population pharmacokinetic modelling of carbamazepine in epileptic elderly patients: implications for dosage

Proper use of antiepileptic drugs in the elderly involves knowledge of their pharmacokinetics to ensure a patient-specific balance between efficacy and toxicity. However, populations of epileptic patients on chronic carbamazepine (CBZ) therapy which have been studied have included data of relatively few elderly patients. The aim of the present study was to evaluate the population pharmacokinetics of CBZ in elderly patients on chronic monotherapy. We have used the non-parametric expectation maximization (NPEM) program in the USC*PACK collection of PC programs to estimate individual and population post-induction pharmacokinetics of CBZ in epileptic elderly patients who received chronic CBZ monotherapy. Age-related changes of CBZ population pharmacokinetics were evaluated from routine therapeutic drug monitoring (TDM) data of 37 elderly and 35 younger patients with epilepsy. As a 'historical control' we used previously published population modelling results from 99 young epileptic patients on chronic CBZ monotherapy. In that control group, TDM was performed in the same pharmacokinetic (PK) laboratory, using the same sampling strategy as in the present study, and the same PK population modelling software was used for data analysis. A poor correlation was found between daily CBZ dose and serum concentrations in the elderly patients (r=0.2, P=0.25). Probably statistically significant difference in the median values of the CBZ metabolic rate constant (P<0.001) between elderly and relatively young epileptic patients was found. Our results showed that age-related influences in CBZ pharmacokinetics in elderly patients should be considered in the optimal planning of CBZ dosage regimens. Most elderly patients with epilepsy will usually need CBZ dosages lower than those based on the median population PK parameter values obtained from younger patients. The present population model is also uniquely well suited for the new 'multiple model' design of dosage regimens to hit target therapeutic goals with maximum precision.

Parametric and Nonparametric Population Methods

This study examined parametric and nonparametric population modelling methods in three different analyses. The first analysis was of a real, although small, clinical dataset from 17 patients receiving intramuscular amikacin. The second analysis was of a Monte Carlo simulation study in which the populations ranged from 25 to 800 subjects, the model parameter distributions were Gaussian and all the simulated parameter values of the subjects were exactly known prior to the analysis. The third analysis was again of a Monte Carlo study in which the exactly known population sample consisted of a unimodal Gaussian distribution for the apparent volume of distribution (V(d)), but a bimodal distribution for the elimination rate constant (k(e)), simulating rapid and slow eliminators of a drug. For the clinical dataset, the parametric iterative two-stage Bayesian (IT2B) approach, with the first-order conditional estimation (FOCE) approximation calculation of the conditional likelihoods, was used together with the nonparametric expectation-maximisation (NPEM) and nonparametric adaptive grid (NPAG) approaches, both of which use exact computations of the likelihood. For the first Monte Carlo simulation study, these programs were also used. A one-compartment model with unimodal Gaussian parameters V(d) and k(e) was employed, with a simulated intravenous bolus dose and two simulated serum concentrations per subject. In addition, a newer parametric expectation-maximisation (PEM) program with a Faure low discrepancy computation of the conditional likelihoods, as well as nonlinear mixed-effects modelling software (NONMEM), both the first-order (FO) and the FOCE versions, were used. For the second Monte Carlo study, a one-compartment model with an intravenous bolus dose was again used, with five simulated serum samples obtained from early to late after dosing. A unimodal distribution for V(d) and a bimodal distribution for k(e) were chosen to simulate two subpopulations of 'fast' and 'slow' metabolisers of a drug. NPEM results were compared with that of a unimodal parametric joint density having the true population parameter means and covariance. For the clinical dataset, the interindividual parameter percent coefficients of variation (CV%) were smallest with IT2B, suggesting less diversity in the population parameter distributions. However, the exact likelihood of the results was also smaller with IT2B, and was 14 logs greater with NPEM and NPAG, both of which found a greater and more likely diversity in the population studied. For the first Monte Carlo dataset, NPAG and PEM, both using accurate likelihood computations, showed statistical consistency. Consistency means that the more subjects studied, the closer the estimated parameter values approach the true values. NONMEM FOCE and NONMEM FO, as well as the IT2B FOCE methods, do not have this guarantee. Results obtained by IT2B FOCE, for example, often strayed visibly away from the true values as more subjects were studied. Furthermore, with respect to statistical efficiency (precision of parameter estimates), NPAG and PEM had good efficiency and precise parameter estimates, while precision suffered with NONMEM FOCE and IT2B FOCE, and severely so with NONMEM FO. For the second Monte Carlo dataset, NPEM closely approximated the true bimodal population joint density, while an exact parametric representation of an assumed joint unimodal density having the true population means, standard deviations and correlation gave a totally different picture. The smaller population interindividual CV% estimates with IT2B on the clinical dataset are probably the result of assuming Gaussian parameter distributions and/or of using the FOCE approximation. NPEM and NPAG, having no constraints on the shape of the population parameter distributions, and which compute the likelihood exactly and estimate parameter values with greater precision, detected the more likely greater diversity in the parameter values in the population studied. In the first Monte Carlo study, NPAG and PEM had more precise parameter estimates than either IT2B FOCE or NONMEM FOCE, as well as much more precise estimates than NONMEM FO. In the second Monte Carlo study, NPEM easily detected the bimodal parameter distribution at this initial step without requiring any further information. Population modelling methods using exact or accurate computations have more precise parameter estimation, better stochastic convergence properties and are, very importantly, statistically consistent. Nonparametric methods are better than parametric methods at analysing populations having unanticipated non-Gaussian or multimodal parameter distributions.

Methotrexate pharmacokinetics and survival in osteosarcoma.

The aim of this study was to analyze the relationship between exposure to high-dose methotrexate (HDMTX) and tumor response in terms of survival in children with osteosarcoma. This study included 44 patients (479 courses) who received a median dose of 5.92 g/m2 of MTX (interquartile range (IQR) 2.37 g/m2) in a 4-hr infusion. The mean area under the concentration-time curve (AUC) estimated by parametric methods (non-parametric expectation maximization, NPEM), and the mean concentration at the end of the infusion were considered to be the exposure parameters. Tumor response was recorded as disease-free survival (DFS), overall survival (OS), and histologic tumor response. The relationship between MTX exposure and survival parameters was analyzed by Cox regression. The group of 11 patients who were the least exposed to MTX (AUC <2,400 micromol/L hr) presented a high DFS, probably due to the shorter interval of time between MTX courses that led to a higher dose density. In patients with AUC >2,400 micromol/L hr, an increase in the AUC was related to an increase in the DFS. Significant differences were observed in the DFS between patients whose mean AUC was below or above 4,000 micromol/L hr (P=0.024), such that 4,000 micromol/L hr was considered as the minimum AUC to be aimed at for future patients. Dose density seems to be an important factor in osteosarcoma response, but this must be confirmed in further studies. In order to improve the response to osteosarcoma in children, it is recommended that the dose of MTX to be increased such as to obtain an AUC higher than 4,000 micromol/L hr.

Non-parametric and unsupervised Bayesian classification with Bootstrap sampling

In this paper, we propose a non-parametric and unsupervised Bayesian classification based on the principle of Bootstrap sampling (BS) which reduces the dependence effect of pixels in real images, and reduces the classification time. Given an original image, we randomly select a small representative set of pixels. Then, a Non-parametric Expectation-Maximization (NEM) algorithm is used for image segmentation. The non-parametric aspect comes from the use of the orthogonal probability density function (pdf) estimation, which is reduced to the estimation of the first Fourier coefficients (FC's) of the pdf with respect to a given orthogonal basis. The results we obtain show that the BS method gives better results than the classical one, both in the quality of the segmented image and the computing time.

Pharmacokinetics and pharmacodynamics of cefepime in patients with various degrees of renal function.

This study evaluated the pharmacokinetics of cefepime in 36 patients with different levels of renal function. Pharmacokinetic and pharmacodynamic parameters were calculated using samples obtained at steady state. Patients with creatinine clearance (CL(CR)) of >100 ml/min had more rapid clearance (CL) and a lower minimum concentration in serum (C(min)). C(min) in this group was found to be 3.3 +/- 3.6 mg/liter (mean and standard deviation), compared to 19.5 +/- 21.5 mg/liter in patients with a CL(CR) of between 60 and 100 ml/min (P = 0.025) and 14.0 +/- 11.5 mg/liter in patients with a CL(CR) of <60 ml/min (P = 0.009). Patient data were also analyzed by the nonparametric expectation maximization method and Bayesian forecasting. The median volume of distribution in the central compartment was 27.08 liters. CL and CL(CR) were highly correlated (P = 0.00033) according to the equation CL= 0.324 liters/h + (0.0551 x CL(CR)). The median rate constants from the central compartment to the peripheral compartment and from the peripheral compartment to the central compartment were 12.58 and 41.09 h(-1), respectively. The time-concentration profiles for 1,000 patients (CL(CR)s, 120, 60, and 30 ml/min) each receiving various dosing regimens were simulated by using Monte Carlo simulations. Standard dosing resulted in a C(min) that was greater than or equal to the MIC in more than 80% of the simulated profiles with MICs < or = 2 mg/liter. Current dosing recommendations may be suboptimal for monotherapy of infections due to less susceptible pathogens (e.g., those for which MICs are > or = 4 mg/liter), particularly when CL(CR) exceeds 120 ml/min.

Pharmacokinetics of vancomycin in (pre)term neonates and influence of covariates

In order to optimize the dosage regimen of vancomycin in neonates, we investigated the population pharmacokinetics and the influence of covariates on the individual pharmacokinetic parameters. Data from 105 preterm and term neonates were analyzed retrospectively. Their Post Conceptional Age (PCA) ranged from 26.5 to 44.1 weeks. Post Natal Age (PNA) was 13.7 (8.2) (mean (s.d.), range: 4–54 days. Plasma vancomycin trough and peak concentration pairs were routinely obtained around the second dose and on several days thereafter (mean 5.8 concentrations/infant). Routine gentamicin drug monitoring, immediately preceding the vancomycin course, was available in 65 infants (mean 4 concentrations/infant). Both population and individual pharmacokinetic parameters of vancomycin were calculated according to a one-compartment open model with a non-parametric expectation maximization algorithm (NPEM2, USCPACK 10.7; University SC, USA). Calculations were also performed with an iterative Bayesian fitting procedure and maximum a posteriori Bayesian fitting (MW\PHARM 3.50, Mediware, The Netherlands). The influence of several demographic and clinical covariates was calculated using stepwise multiple regression analysis with SPSS 10.0 software (Chicago, IL, USA). Recent literature indicates that serum creatinine in the first 2 weeks of life does not reflect glomerular filtration rate [1]. Therefore we also calculated the correlation between Kel gentamicin and Kel vancomycin. Three subgroups were defined: < 30, ≥ 30 and < 37, and ≥ 37 weeks’ PCA. Their population parameters (median + mean DF50+DF95) are reported in the same order: Kel (h−1): 0.0889 (0.0229), 0.1090 (0.0249), 0.1634 (0.0458) and V/W (lkg−1): 0.5487 (0.1362), 0.4950 (0.1368), 0.4229 (0.0914). Results obtained with NPEM2 and MW/PHARM were almost identical. A significant (P < 0.001) correlation was found between Kel of gentamicin and vancomycin (r = 0.579) and between serum creatinine and Kel of vancomycin (r = −0.563). Stepwise multiple linear regression analysis yielded the following statistically significant equations: A significant correlation was demonstrated between vancomycin elimination rate and serum creatinine concentrations. The correlation with gentamicin kinetics could be used in practice if plasma creatinine concentrations are not available or biased. The predictive value of the observed correlations has to be validated prospectively in clinical practice.

An unsupervised and non-parametric bayesian classifier

We propose here an unsupervised Bayesian classifier based on a non-parametric expectation-maximization algorithm. The non-parametric aspect comes from the use of the orthogonal probability density function (pdf) estimation, which is reduced to the estimation of the first Fourier coefficients of the pdf with respect to a given orthogonal basis. So, the mixture identification step based on the maximization of the likelihood can be realized without hypothesis on the conditional pdf’s distribution. This means that for the unsupervised image segmentation example we do not need any assumption for the gray level image pixels distribution. The generalization to the multivariate case can be obtained by considering the multidimensional orthogonal function basis. In this paper, we give some simulation results for the determination of the smoothing parameter and to compute the error of classification.

Pharmacokinetics of Rifampin Under Fasting Conditions, With Food, and With Antacids

Determine the intrasubject and intersubject variability in, and the effects of food or antacids on, the pharmacokinetics of rifampin (RIF). Randomized, four-period crossover phase I study. Fourteen healthy male and female volunteers. Subjects ingested single doses of RIF, 600 mg, under fasting conditions twice, with a high-fat meal, and with aluminum-magnesium antacid. They also received standard doses of isoniazid, pyrazinamide, and ethambutol. Serum was collected for 48 h and assayed by high-pressure liquid chromatography. Data were analyzed using noncompartmental methods and a compartmental analysis using nonparametric expectation maximization. Both fasting conditions produced similar results: a mean RIF maximal serum concentration (Cmax) of 10.54+/-3.18 microg/mL, the time at which it occurred (Tmax) of 2.42+/-1.32 h, and the area under the curve from time zero to infinity (AUC0-infinity) of 57.15+/-13.41 microg x h/mL. These findings are similar to those reported previously. Antacids did not alter these parameters (Cmax of 10.89+/-5.22 microg/mL, Tmax of 2.36+/-1.28 h, and AUC0-infinity of 58.37+/-18.49 microg x h/mL). In contrast, the Food and Drug Administration high-fat meal reduced RIF Cmax by 36% (7.27+/-2.29 microg/mL), nearly doubled Tmax (4.43+/-1.09 h), but reduced AUC0-infinity by only 6% (55.20+/-14.48 microg x h/mL). These changes in Cmax, Tmax, and AUC0-infinity can be avoided by giving RIF on an empty stomach whenever possible.

Levofloxacin population pharmacokinetics and creation of a demographic model for prediction of individual drug clearance in patients with serious community-acquired infection.

Population pharmacokinetic modeling is a useful approach to obtaining estimates of both population and individual pharmacokinetic parameter values. The potential for relating pharmacokinetic parameters to pharmacodynamic outcome variables, such as efficacy and toxicity, exists. A logistic regression relationship between the probability of a successful clinical and microbiological outcome and the peak concentration-to-MIC ratio (and also the area under the plasma concentration-time curve [AUC]/MIC ratio) has previously been developed for levofloxacin; however, levofloxacin assays for determination of the concentration in plasma are not readily available. We attempted to derive and validate demographic variable models to allow prediction of the peak concentration in plasma and clearance (CL) from plasma for levofloxacin. Two hundred seventy-two patients received levofloxacin intravenously for the treatment of community-acquired infection of the respiratory tract, skin or soft tissue, or urinary tract, and concentrations in plasma, guided by optimal sampling theory, were obtained. Patient data were analyzed by the Non-Parametric Expectation Maximization approach. Maximum a posteriori probability Bayesian estimation was used to generate individual parameter values, including CL. Peak concentrations were simulated from these estimates. The first 172 patients were used to produce demographic models for the prediction of CL and the peak concentration. The remaining 100 patients served as the validation group for the model. A median bias and median precision were calculated. A two-compartment model was used for the population pharmacokinetic analysis. The mean CL and the mean volume of distribution of the central compartment (V1) were 9.27 liters/h and 0.836 liter/kg, respectively. The mean values for the intercompartmental rate constants, the rate constant from the central compartment to the peripheral compartment (Kcp) and the rate constant from the peripheral compartment to the central compartment (Kpc), were 0.487 and 0.647 h(-1), respectively. The mean peak concentration and the mean AUC values normalized to a dosage of 500 mg every 24 h were 8.67 microg/ml and 72.53 microg x h/ml, respectively. The variables included in the final model for the prediction of CL were creatinine clearance (CLCR), race, and age. The median bias and median precision were 0.5 and 18.3%, respectively. Peak concentrations were predicted by using the demographic model-predicted parameters of CL, V1, Kcp and Kpc, in the simulation. The median bias and the median precision were 3.3 and 21.8%, respectively. A population model of the disposition of levofloxacin has been developed. Population demographic models for the prediction of peak concentration and CL from plasma have also been successfully developed. However, the performance of the model for the prediction of peak concentration was likely insufficient to be of adequate clinical utility. The model for the prediction of CL was relatively robust, with acceptable bias and precision, and explained a reasonable amount of the variance in the CL of levofloxacin from plasma in the population (r2 = 0.396). Estimated CLCR, age, and race were the final model covariates, with CLCR explaining most of the population variance in the CL of levofloxacin from plasma. This model can potentially optimize the benefit derived from the pharmacodynamic relationships previously developed for levofloxacin.