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"Schumitzky, Alan"
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Analysis of Combination Drug Therapy to Develop Regimens with Shortened Duration of Treatment for Tuberculosis
Tuberculosis remains a worldwide problem, particularly with the advent of multi-drug resistance. Shortening therapy duration for Mycobacterium tuberculosis is a major goal, requiring generation of optimal kill rate and resistance-suppression. Combination therapy is required to attain the goal of shorter therapy.
Our objective was to identify a method for identifying optimal combination chemotherapy. We developed a mathematical model for attaining this end. This is accomplished by identifying drug effect interaction (synergy, additivity, antagonism) for susceptible organisms and subpopulations resistant to each drug in the combination.
We studied the combination of linezolid plus rifampin in our hollow fiber infection model. We generated a fully parametric drug effect interaction mathematical model. The results were subjected to Monte Carlo simulation to extend the findings to a population of patients by accounting for between-patient variability in drug pharmacokinetics.
All monotherapy allowed emergence of resistance over the first two weeks of the experiment. In combination, the interaction was additive for each population (susceptible and resistant). For a 600 mg/600 mg daily regimen of linezolid plus rifampin, we demonstrated that >50% of simulated subjects had eradicated the susceptible population by day 27 with the remaining organisms resistant to one or the other drug. Only 4% of patients had complete organism eradication by experiment end.
These data strongly suggest that in order to achieve the goal of shortening therapy, the original regimen may need to be changed at one month to a regimen of two completely new agents with resistance mechanisms independent of the initial regimen. This hypothesis which arose from the analysis is immediately testable in a clinical trial.
Journal Article
Analyzing Pharmacodynamic Count Data That Rapidly Decrease to Zero
We present a framework for maximum likelihood analysis on count observations that begin high and quickly drop to zero, for example, from hollow fiber drug comparison studies. This simulation study focuses on treating observed counts as Poisson or normally distributed for the purpose of estimating infection rebound after effective treatment. CFU profiles were simulated from inoculation to 96 h post‐treatment. The PK‐PD link was an Emax inhibitory model. Random parameters were pathogen growth and natural decay rates, drug concentration for half‐maximal effect, and drug pathogen kill rate. Other parameters, including PK, were fixed. Parameters were adjusted to attain 67% efficacy at 24 h. Random parameter values were optimized for profiles observed at 24, 48, 72, and 96 h assuming each of four probability assumptions: (1) all CFU measurements were Poisson distributed (truth); (2) CFU < 128 were Poisson, higher values were normally distributed; (3) all observations were normally distributed; and (4) observations were normally distributed but CFU < 10 were censored. CFU‐time profiles were re‐simulated using the optimized parameter densities. Rebound percentage (CFU ≥ 10 at 24 h post‐treatment) was best predicted using strategy 2, above. For limited periodically collected time series count data that quickly fall to 0, the true proportion reaching 0 (lack of rebound) was best modeled by assuming Poisson distribution at low counts. At higher counts (≥ 128), assuming normality is reasonable. Censoring observations leads to biased models.
Journal Article
RPEM: Randomized Monte Carlo parametric expectation maximization algorithm
Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis–Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi‐Random Parametric Expectation Maximization (QRPEM) for a realistic two‐compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log‐normal cases.
Journal Article
An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics
Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.
Journal Article
Combination Treatment With Meropenem Plus Levofloxacin Is Synergistic Against Pseudomonas aeruginosa Infection in a Murine Model of Pneumonia
Background. Meropenem plus levofloxacin treatment was shown to be a promising combination in our in vitro hollow fiber infection model. We strove to validate this finding in a murine Pseudomonas pneumonia model. Methods. A dose-ranging study with meropenem and levofloxacin alone and in combination against Pseudomonas aeruginosa was performed in a granulocytopenic murine pneumonia model. Meropenem and levofloxacin were administered to partially humanize their pharmacokinetic profiles in mouse serum. Total and resistant bacterial populations were estimated after 24 hours of therapy. Pharmacokinetic profiling of both drugs was performed in plasma and epithelial lining fluid, using a population model. Results. Meropenem and levofloxacin penetrations into epithelial lining fluid were 39.3% and 64.3%, respectively. Both monotherapies demonstrated good exposure responses. An innovative combination-therapy analytic approach demonstrated that the combination was statistically significantly synergistic (α = 2.475), as was shown in the hollow fiber infection model. Bacterial resistant to levofloxacin and meropenem was seen in the control arm. Levofloxacin monotherapy selected for resistance to itself. No resistant subpopulations were observed in any combination therapy arm. Conclusions. The combination of meropenem plus levofloxacin was synergistic, producing good bacterial kill and resistance suppression. Given the track record of safety of each agent, this combination may be worthy of clinical trial.
Journal Article
Two general methods for population pharmacokinetic modeling: non-parametric adaptive grid and non-parametric Bayesian
Population pharmacokinetic (PK) modeling methods can be statistically classified as either parametric or nonparametric (NP). Each classification can be divided into maximum likelihood (ML) or Bayesian (B) approaches. In this paper we discuss the nonparametric case using both maximum likelihood and Bayesian approaches. We present two nonparametric methods for estimating the unknown joint population distribution of model parameter values in a pharmacokinetic/pharmacodynamic (PK/PD) dataset. The first method is the NP Adaptive Grid (NPAG). The second is the NP Bayesian (NPB) algorithm with a stick-breaking process to construct a Dirichlet prior. Our objective is to compare the performance of these two methods using a simulated PK/PD dataset. Our results showed excellent performance of NPAG and NPB in a realistically simulated PK study. This simulation allowed us to have benchmarks in the form of the true population parameters to compare with the estimates produced by the two methods, while incorporating challenges like unbalanced sample times and sample numbers as well as the ability to include the covariate of patient weight. We conclude that both NPML and NPB can be used in realistic PK/PD population analysis problems. The advantages of one versus the other are discussed in the paper. NPAG and NPB are implemented in R and freely available for download within the
Pmetrics
package from
www.lapk.org
.
Journal Article
A non-parametric optimal design algorithm for population pharmacokinetics
This paper introduces a non-parametric estimation algorithm designed to effectively estimate the joint distribution of model parameters with application to population pharmacokinetics. Our research group has previously developed the non-parametric adaptive grid (NPAG) algorithm, which while accurate, explores parameter space using an ad-hoc method to suggest new support points. In contrast, the non-parametric optimal design (NPOD) algorithm uses a gradient approach to suggest new support points, which reduces the amount of time spent evaluating non-relevant points and by this the overall number of cycles required to reach convergence. In this paper, we demonstrate that the NPOD algorithm achieves similar solutions to NPAG across two datasets, while being significantly more efficient in both the number of cycles required and overall runtime. Given the importance of developing robust and efficient algorithms for determining drug doses quickly in pharmacokinetics, the NPOD algorithm represents a valuable advancement in non-parametric modeling. Further analysis is needed to determine which algorithm performs better under specific conditions.
Paper
NPSA: Nonparametric Simulated Annealing for Global Optimization
In this paper we describe NPSA, the first parallel nonparametric global maximum likelihood optimization algorithm using simulated annealing (SA). Unlike the nonparametric adaptive grid search method NPAG, which is not guaranteed to find a global optimum solution, and may suffer from the curse of dimensionality, NPSA is a global optimizer and it is free from these grid related issues. We illustrate NPSA by a number of examples including a pharmacokinetics (PK) model for Voriconazole and show that NPSA may be taken as an upgrade to the current grid search based nonparametric methods.
Paper
RPEM: Randomized Monte Carlo Parametric Expectation Maximization Algorithm
Inspired from quantum Monte Carlo, by using unbiased estimators all the time and sampling discrete and continuous variables at the same time using Metropolis algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). In particular, we compared RPEM with Monolix's SAEM and Certara's QRPEM for a realistic two-compartment Voriconazole model with ordinary differential equations (ODEs) and using simulated data. We show that RPEM is 3 to 4 times faster than SAEM and QRPEM, and more accurate than them in reconstructing the population parameters.
Paper