Development of a Compartmental Pharmacokinetic Model for Molecular Radiotherapy with 131I-CLR1404

Pharmacokinetic modeling of the radiopharmaceuticals used in molecular radiotherapy is an important step towards accurate radiation dosimetry of such therapies. In this paper, we present a pharmacokinetic model for CLR1404, a phospholipid ether analog that, labeled with 124I/131I, has emerged as a promising theranostic agent. We follow a systematic approach for the model construction based on a decoupling process applied to previously published experimental data, and using the goodness-of-fit, Sobol’s sensitivity analysis, and the Akaike Information Criterion to construct the optimal form of the model, investigate potential simplifications, and study factor prioritization. This methodology was applied to previously published experimental human time-activity curves for 9 organs. The resulting model consists of 17 compartments involved in the CLR1404 metabolism. Activity dynamics in most tissues are well described by a blood contribution plus a two-compartment system, describing fast and slow uptakes. The model can fit both clinical and pre-clinical kinetic data of 124I/131I. In addition, we have investigated how simple fits (exponential and biexponential) differ from the complete model. Such fits, despite providing a less accurate description of time-activity curves, may be a viable alternative when limited data is available in a practical case.

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A population-based method to determine the time-integrated activity in molecular radiotherapy

EJNMMI Physics ◽

10.1186/s40658-021-00427-x ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Deni Hardiansyah ◽

Ade Riana ◽

Peter Kletting ◽

Nouran R. R. Zaid ◽

Matthias Eiber ◽

...

Keyword(s):

Model Selection ◽

Goodness Of Fit ◽

Information Criterion ◽

Population Based ◽

Castration Resistant Prostate Cancer ◽

Planar Imaging ◽

Exponential Functions ◽

Akaike Weight ◽

Molecular Radiotherapy ◽

Function Selection

Abstract Background The calculation of time-integrated activities (TIAs) for tumours and organs is required for dosimetry in molecular radiotherapy. The accuracy of the calculated TIAs is highly dependent on the chosen fit function. Selection of an adequate function is therefore of high importance. However, model (i.e. function) selection works more accurately when more biokinetic data are available than are usually obtained in a single patient. In this retrospective analysis, we therefore developed a method for population-based model selection that can be used for the determination of individual time-integrated activities (TIAs). The method is demonstrated at an example of [177Lu]Lu-PSMA-I&T kidneys biokinetics. It is based on population fitting and is specifically advantageous for cases with a low number of available biokinetic data per patient. Methods Renal biokinetics of [177Lu]Lu-PSMA-I&T from thirteen patients with metastatic castration-resistant prostate cancer acquired by planar imaging were used. Twenty exponential functions were derived from various parameterizations of mono- and bi-exponential functions. The parameters of the functions were fitted (with different combinations of shared and individual parameters) to the biokinetic data of all patients. The goodness of fits were assumed as acceptable based on visual inspection of the fitted curves and coefficients of variation CVs < 50%. The Akaike weight (based on the corrected Akaike Information Criterion) was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit. Results The function $$A_{1} { }\beta { }e^{{ - \left( {\lambda_{1} + \lambda_{{{\text{phys}}}} } \right)t}} + A_{1} { }\left( {1 - \beta } \right){ }e^{{ - \left( {\lambda_{{{\text{phys}}}} } \right)t}}$$ A 1 β e - λ 1 + λ phys t + A 1 1 - β e - λ phys t with shared parameter $$\beta$$ β was selected as the function most supported by the data with an Akaike weight of 97%. Parameters $$A_{1}$$ A 1 and $$\lambda_{1}$$ λ 1 were fitted individually for every patient while parameter $$\beta { }$$ β was fitted as a shared parameter in the population yielding a value of 0.9632 ± 0.0037. Conclusions The presented population-based model selection allows for a higher number of parameters of investigated fit functions which leads to better fits. It also reduces the uncertainty of the obtained Akaike weights and the selected best fit function based on them. The use of the population-determined shared parameter for future patients allows the fitting of more appropriate functions also for patients for whom only a low number of individual data are available.

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Comparison of growth models to describe growth from birth to 6 years in a Beninese cohort of children with repeated measurements

BMJ Open ◽

10.1136/bmjopen-2019-035785 ◽

2020 ◽

Vol 10 (9) ◽

pp. e035785

Author(s):

Shukrullah Ahmadi ◽

Florence Bodeau-Livinec ◽

Roméo Zoumenou ◽

André Garcia ◽

David Courtin ◽

...

Keyword(s):

Growth Model ◽

Goodness Of Fit ◽

Growth Models ◽

Information Criterion ◽

Height Growth ◽

Sub Saharan Africa ◽

Individual Growth ◽

Secondary Outcome ◽

Growth Trajectories ◽

Best Fitting

ObjectiveTo select a growth model that best describes individual growth trajectories of children and to present some growth characteristics of this population.SettingsParticipants were selected from a prospective cohort conducted in three health centres (Allada, Sekou and Attogon) in a semirural region of Benin, sub-Saharan Africa.ParticipantsChildren aged 0 to 6 years were recruited in a cohort study with at least two valid height and weight measurements included (n=961).Primary and secondary outcome measuresThis study compared the goodness-of-fit of three structural growth models (Jenss-Bayley, Reed and a newly adapted version of the Gompertz growth model) on longitudinal weight and height growth data of boys and girls. The goodness-of-fit of the models was assessed using residual distribution over age and compared with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The best-fitting model allowed estimating mean weight and height growth trajectories, individual growth and growth velocities. Underweight, stunting and wasting were also estimated at age 6 years.ResultsThe three models were able to fit well both weight and height data. The Jenss-Bayley model presented the best fit for weight and height, both in boys and girls. Mean height growth trajectories were identical in shape and direction for boys and girls while the mean weight growth curve of girls fell slightly below the curve of boys after neonatal life. Finally, 35%, 27.7% and 8% of boys; and 34%, 38.4% and 4% of girls were estimated to be underweight, wasted and stunted at age 6 years, respectively.ConclusionThe growth parameters of the best-fitting Jenss-Bayley model can be used to describe growth trajectories and study their determinants.

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Prediction of successful de-cannulation of tracheostomised patients in medical intensive care units

Respiratory Research ◽

10.1186/s12931-021-01732-w ◽

2021 ◽

Vol 22 (1) ◽

Author(s):

Chul Park ◽

Ryoung-Eun Ko ◽

Jinhee Jung ◽

Soo Jin Na ◽

Kyeongman Jeon

Keyword(s):

Logistic Regression ◽

Regression Analysis ◽

Logistic Regression Analysis ◽

Goodness Of Fit ◽

Characteristic Curve ◽

Multivariable Logistic Regression Analysis ◽

Limited Data ◽

Underlying Malignancy ◽

Medical Intensive Care ◽

Good Calibration

Abstract Background Limited data are available on practical predictors of successful de-cannulation among the patients who undergo tracheostomies. We evaluated factors associated with failed de-cannulations to develop a prediction model that could be easily be used at the time of weaning from MV. Methods In a retrospective cohort of 346 tracheostomised patients managed by a standardized de-cannulation program, multivariable logistic regression analysis identified variables that were independently associated with failed de-cannulation. Based on the logistic regression analysis, the new predictive scoring system for successful de-cannulation, referred to as the DECAN score, was developed and then internally validated. Results The model included age > 67 years, body mass index < 22 kg/m2, underlying malignancy, non-respiratory causes of mechanical ventilation (MV), presence of neurologic disease, vasopressor requirement, and presence of post-tracheostomy pneumonia, presence of delirium. The DECAN score was associated with good calibration (goodness-of-fit, 0.6477) and discrimination outcomes (area under the receiver operating characteristic curve 0.890, 95% CI 0.853–0.921). The optimal cut-off point for the DECAN score for the prediction of the successful de-cannulation was ≤ 5 points, and was associated with the specificities of 84.6% (95% CI 77.7–90.0) and sensitivities of 80.2% (95% CI 73.9–85.5). Conclusions The DECAN score for tracheostomised patients who are successfully weaned from prolonged MV can be computed at the time of weaning to assess the probability of de-cannulation based on readily available variables.

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Model Selection in Peptide-receptor Radionuclide Therapy for an Accurate Determination of Time Integrated Activity Coefficients

Journal of Physics Conference Series ◽

10.1088/1742-6596/2019/1/012079 ◽

2021 ◽

Vol 2019 (1) ◽

pp. 012079

Author(s):

N Atikah ◽

A Riana ◽

A Dwi ◽

Z Anwari ◽

Misrawati ◽

...

Keyword(s):

Model Selection ◽

Activity Coefficients ◽

Radionuclide Therapy ◽

Goodness Of Fit ◽

Accurate Determination ◽

Peptide Receptor Radionuclide Therapy ◽

Information Criterion ◽

Selection Function ◽

Pharmacokinetic Data ◽

Peptide Receptor

Abstract Calculation of accurate time-integrated activity coefficients (TIACs) is desirable in nuclear medicine dosimetry. The accuracy of the calculated TIACs is highly dependent on the fit function. However, systematic studies of determining a good function for peptide-receptor radionuclide therapy (PRRT) in different patients have not been reported in the literature. The aim of this study was to individually determine the best function for the calculation of TIACs in tumor and kidneys using a model selection based on the goodness of fit criteria and Corrected Akaike Information Criterion (AICc). The data used in this study was pharmacokinetic data of 111In-DOTATATE in tumor and kidneys obtained from 4 PRRT patients. Eleven functions with various parameterizations were formulated to describe the biokinetic data of 111In-DOTATATE in tumor and kidneys. The model selection was performed by choosing the best function from the function with sufficient goodness of fit based on the smallest AICc. Based on the results of model selection, function A 1 -(λ 1+λphys )t was selected as the best function for all tumor and kidneys in patients with meningioma tumors. By using this function, the calculated of TIACs could be more accurate for future patients with meningioma tumor.

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Tornumonkpe Distribution: Statistical Properties and Goodness of Fit

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2021/v14i130318 ◽

2021 ◽

pp. 12-22

Author(s):

Barinaadaa John Nwikpe

Keyword(s):

Goodness Of Fit ◽

Real Life ◽

Mathematical Expression ◽

Information Criterion ◽

Moment Generating Function ◽

Data Sets ◽

The Moment ◽

The One ◽

Coefficient Of Skewness ◽

New Distribution

A new sole parameter probability distribution named the Tornumonkpe distribution has been derived in this paper. The new model is a blend of gamma (2, and gamma(3 distributions. The shape of its density for different values of the parameter has been shown. The mathematical expression for the moment generating function, the first three raw moments, the second and third moments about the mean, the distribution of order statistics, coefficient of variation and coefficient of skewness has been given. The parameter of the new distribution was estimated using the method of maximum likelihood. The goodness of fit of the Tornumonkpe distribution was established by fitting the distribution to three real life data sets. Using -2lnL, Bayesian Information Criterion (BIC), and Akaike Information Criterion(AIC) as criterial for selecting the best fitting model, it was revealed that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used.

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Longitudinal Pattern of Aerenchyma Formation Using the Ti-Gompertz Model in Rice Adventitious Roots

Frontiers in Plant Science ◽

10.3389/fpls.2021.776971 ◽

2021 ◽

Vol 12 ◽

Author(s):

Yun Chen ◽

Guoming Li ◽

Buhong Zhao ◽

Yajun Zhang ◽

Kun Liu ◽

...

Keyword(s):

Adventitious Roots ◽

Goodness Of Fit ◽

Gompertz Model ◽

Root Apex ◽

Information Criterion ◽

Ordinary Least Squares ◽

Parameter Estimates ◽

Aerenchyma Formation ◽

Root Aerenchyma ◽

Longitudinal Pattern

The longitudinal pattern of root aerenchyma formation of its relationship with the function of adventitious roots in rice remains unclear. In this study, the percentage of the aerenchyma area to the cross-sectional area (i.e., aerenchyma percentage) was fit with four non-linear models, namely, W0-Gompertz, Ti-Gompertz, logistic, and von Bertalanffy. Goodness-of-fit criteria such as the R2, the Akaike information criterion (AIC), and the Bayesian information criterion (BIC) were used to select the model. The bias of the parameters was evaluated using the difference between the ordinary least squares-based parameter estimates and the mean of 1,000 bootstrap-based parameter estimates and the symmetry of the distributions of these parameters. The results showed that the Ti-Gompertz model, which had a high goodness-of-fit with an R2 close to 1, lower AIC and BIC values, parameter estimates close to being unbiased, and good linear approximation, provided the best fit for the longitude pattern of rice aerenchyma formation with different root lengths among the competing models. Using the second- and third-order derivatives according to the distance from the root apex, the critical points of Ti-Gompertz were calculated. The rapid stage for aerenchyma formation was from the maximum acceleration point (1.38–1.76 cm from the root apex) to the maximum deceleration point (3.13–4.19 cm from the root apex). In this stage, the aerenchyma percentage increased by 5.3–15.7% per cm, suggesting that the cortical cells tended to die rapidly for the aerenchyma formation rather than for the respiration cost during this stage. Meanwhile, the volume of the aerenchyma of the entire roots could be computed using the integral function of the Ti-Gompertz model. We proposed that the longitudinal pattern of root aerenchyma formation modeled by the Ti-Gompertz model helped to deeply understand the relationship between the anatomical traits and physiological function in rice adventitious roots.

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Contrast response functions in the visual wulst of the alert burrowing owl: a single-unit study

Journal of Neurophysiology ◽

10.1152/jn.00505.2015 ◽

2016 ◽

Vol 116 (4) ◽

pp. 1765-1784 ◽

Cited By ~ 1

Author(s):

Pedro Gabrielle Vieira ◽

João Paulo Machado de Sousa ◽

Jerome Baron

Keyword(s):

Single Unit ◽

Goodness Of Fit ◽

Dynamic Range ◽

Information Criterion ◽

Future Research ◽

Response Functions ◽

Athene Cunicularia ◽

Low Contrast ◽

Burrowing Owl ◽

Contrast Response

The neuronal representation of luminance contrast has not been thoroughly studied in birds. Here we present a detailed quantitative analysis of the contrast response of 120 individual neurons recorded from the visual wulst of awake burrowing owls ( Athene cunicularia). Stimuli were sine-wave gratings presented within the cell classical receptive field and optimized in terms of eye preference, direction of drift, and spatiotemporal frequency. As contrast intensity was increased from zero to near 100%, most cells exhibited a monotonic response profile with a compressive, at times saturating, nonlinearity at higher contrasts. However, contrast response functions were found to have a highly variable shape across cells. With the view to capture a systematic trend in the data, we assessed the performance of four plausible models (linear, power, logarithmic, and hyperbolic ratio) using classical goodness-of-fit measures and more rigorous statistical tools for multimodel inferences based on the Akaike information criterion. From this analysis, we conclude that a high degree of model uncertainty is present in our data, meaning that no single descriptor is able on its own to capture the heterogeneous nature of single-unit contrast responses in the wulst. We further show that the generalizability of the hyperbolic ratio model established, for example, in the primary visual cortex of cats and monkeys is not tenable in the owl wulst mainly because most neurons in this area have a much wider dynamic range that starts at low contrast. The challenge for future research will be to understand the functional implications of these findings.

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Parameter Estimation Method of Mixture Distribution for Construction Machinery

Mathematical Problems in Engineering ◽

10.1155/2018/3124048 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9

Author(s):

Xinting Zhai ◽

Jixin Wang ◽

Jinshi Chen

Keyword(s):

Parameter Estimation ◽

Likelihood Function ◽

Estimation Method ◽

Mixture Distribution ◽

Information Criterion ◽

Working Environment ◽

Practical Case ◽

Chi Square ◽

Construction Machinery ◽

Parameter Estimation Method

Due to the harsh working environment of the construction machinery, a simple distribution cannot be used to approximate the shape of the rainflow matrix. In this paper, the Weibull-normal (W-n) mixture distribution is used. The lowest Akaike information criterion (AIC) value is employed to determine the components number of the mixture. A parameter estimation method based on the idea of optimization is proposed. The method estimates parameters of the mixture by maximizing the log likelihood function (LLF) using an intelligent optimization algorithm (IOA), genetic algorithm (GA). To verify the performance of the proposed method, one of the already existing methods is applied in the simulation study and the practical case study. The fitting effects of the fitted distributions are compared by calculating the AIC and chi-square (χ2) value. It can be concluded that the proposed method is feasible and effective for parameter estimation of the mixture distribution.

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Statistical Inference of Odd Fréchet Inverse Lomax Distribution with Applications

Complexity ◽

10.1155/2020/4658596 ◽

2020 ◽

Vol 2020 ◽

pp. 1-20

Author(s):

Ramadan A. ZeinEldin ◽

Muhammad Ahsan ul Haq ◽

Sharqa Hashmi ◽

Mahmoud Elsehety ◽

M. Elgarhy

Keyword(s):

Goodness Of Fit ◽

Continuous Distribution ◽

Information Criterion ◽

Value Theory ◽

Estimation Methods ◽

Parameter Distribution ◽

Monte Carlo Simulation Study ◽

Lifetime Distributions ◽

Lomax Distribution ◽

Inverse Lomax Distribution

In this article, we propose and study a new three-parameter distribution, called the odd Fréchet inverse Lomax (OFIL) distribution, derived by combining the odd Fréchet-G family and the inverse Lomax distribution. Since Fréchet is a continuous distribution with wide applicability in extreme value theory, the new model contains these properties as well as the characteristics of the inverse Lomax distribution which make it more flexible and provide a good alternative for some well-known lifetime distributions. We initially present a linear representation of its functions and discussion on density and hazard rate function. Then, we study its various mathematical properties. Different estimation methods are used to estimate parameters of OFIL. The Monte Carlo simulation study is carried out to compare the efficiencies of different methods of estimation. The maximum likelihood estimation (MLE) method is used to estimate the OFIL parameters by considering three practical data applications. We show that the related model is the best in comparisons based on Akaike information criterion (AIC), Bayesian information criterion (BIC), and other goodness-of-fit measures.

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Population Pharmacokinetic Study of Prophylactic Fluconazole in Preterm Infants for Prevention of Invasive Candidiasis

Antimicrobial Agents and Chemotherapy ◽

10.1128/aac.01960-18 ◽

2019 ◽

Vol 63 (6) ◽

Author(s):

Yu Kyong Kim ◽

Juyoung Lee ◽

Jaeseong Oh ◽

Su-jin Rhee ◽

Seung Han Shin ◽

...

Keyword(s):

Body Weight ◽

Preterm Infants ◽

Goodness Of Fit ◽

Pharmacokinetic Model ◽

Dose Interval ◽

Volume Of Distribution ◽

Population Pharmacokinetic ◽

Oral Fluconazole ◽

Systemic Fungal Infection ◽

Population Pharmacokinetic Study

ABSTRACT Fluconazole is an antifungal agent with reported evidence for its prophylactic effect against systemic fungal infection in preterm infants. The aim of this study was to build a population pharmacokinetic model to evaluate the pharmacokinetic characteristics of intravenous and oral fluconazole in preterm infants with the current prophylactic fluconazole dosing regimen. A pharmacokinetic model was developed using 301 fluconazole concentrations from 75 preterm infants with a baseline body weight (WT) ranging from 0.5 to 1.5 kg and an estimated glomerular filtration rate (eGFR) ranging from 12.9 to 58.5 ml/min/1.73 m2. Eligible infants received an intravenous or oral dose of 3 mg/kg of body weight of fluconazole, twice weekly with a ≥72-h dose interval, for 4 weeks. The model was qualified with basic goodness-of-fit diagnostics, visual predictive checks, and bootstrapping. The fluconazole pharmacokinetics was well described with a one-compartment linear model with a proportional residual error. The population clearance (CL) and volume of distribution (V) were derived as 0.0197 × (WT/1.00)0.746 × (eGFR/25.0)0.463 × exp(η) and 1.04 × WT × exp(η), respectively. Such covariate analyses augment the awareness of the need for personalized dosing in preterm infants. (This study has been registered at ClinicalTrials.gov under identifier NCT01683760.)

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