Pharmacokinetics which describes the time course of drug absorption, distribution, metabolism, and excretion in the body is critical in formulating drug therapy. Nonlinear Mixed Effects (NLME) models are popularly used in many longitudinal studies, including human immunodeficiency viral dynamics, pharmacokinetic analyses, and studies of growth and decay.This work aimed to develop efficient NLME models for analyzing Theophylline concentration data within the pharmacokinetics framework. The data consisted of Theophylline concentration (mg/L) measurements of 12 asthmatic patients who were treated with oral Theophylline. The serum concentrations were measured at 11 times per subject over 25 hours periods. Hence, a total of 132 observations were obtained. Six different pharmacokinetics models were fitted in a step-wise manner to these data within the framework of NLME techniques. The best of these models that yielded the most efficient estimates of the physiological factors such as absorption rate ( ), elimination rate ( ), and clearance ( ) in the patients was determined using suitable model selection criteria. The results showed that the clearance and absorption rate have mixed effects with estimated values of = 0.0397 and = 1.54203 (for fixed effects) while the effect of the elimination rate in all the patients is fixed with the estimated value of =0.0860. Also, the low estimated standard deviations of the random effects components of (0.1699) and (0.6384)over the entire samples is a clear evidence that the fitted model was quite consistent and efficient.Results from this study would further serve as useful guides to clinicians and drug developers in the proper formulation and administration of Theophylline therapy on patients suffering from respiratory diseases.Keywords: Pharmacokinetics; theophylline concentration; nonlinear mixed effects model; compartmental model ÖZET Vücutta zamanla meydana gelen ilaç emilimi, dağılımı, metabolizması ve boşaltımını tanımlayan farmakokinetikler, ilaç terapi formüllerinde çok önemlidir. Doğrusal olmayan karışık etki (DOKE) modelleri, büyüme ve çürüme çalışmaları, farmakokinetik analizler ve insan immün yetmezliği viral dinamiklerini kapsayan birçok longitudinal çalışmada popüler olarak kullanılmaktadır. Bu çalışmada farmakokinetik yapı için teofilin konsantrasyon verisi analiz edilerek etkili DOKE modelleri geliştirmek amaçlanmaktadır. Veri seti, ağızdan teofilin ile tedavi edilen 12 astım hastasının teofilin konsantrasyon ölçümlerini içermektedir. Serum konsantrasyonları, 25 saatlik periyotlarla her hastadan 11 kez ölçülmüştür. Dolayısıyla 132 gözlem elde edilmiştir. DOKE teknikleri çerçevesinde bu veri seti için altı farklı farmakokinetik model aşamalı olarak tahmin edilmiştir. Hastalarda emilim hızı ( ), eleme hızı ( ) ve aralık ( ) gibi fizyolojik faktörlerin en etkili tahminini sağlayan en iyi modeller uygun model seçim kriteri kullanılarak belirlenmiştir. Sonuçlar, eleme hızının tüm hastalarda = 0.0860 tahmin değeri ile sabit olmasına rağmen, aralık ve emilim hız...

The Poisson regression is popularly used to model count data. However, real data often do not satisfy the assumption of equality of the mean and variance which is an important property of the Poisson distribution. The Poisson – Gamma (Negative binomial) distribution and the recent Conway-Maxwell-Poisson (COM-Poisson) distributions are some of the proposed models for over- and under-dispersion respectively. Nevertheless, the parameterization of the COM-Poisson distribution still remains a major challenge in practice as the location parameter of the original COM-Poisson distribution rarely represents the mean of the distribution. As a result, this paper proposes a new parameterization of the COM-Poisson distribution via the central location (mean) so that more easily-interpretable models and results can be obtained.  The parameterization involves solving nonlinear equations which do not have analytical solutions. The nonlinear equations are solved using the efficient and fast derivative free spectral algorithm. Implementation of the parameterization in R (R Core Team, 2018) is used to present useful numerical results concerning the relationship between the mean of the COM-Poisson distribution and the location parameter in the original COM-Poisson parameterization. The proposed technique is further used to fit COM-Poisson probability models to real life datasets. It was found that obtaining estimates via this parameterization makes the estimation easier and faster compared to directly maximizing the likelihood function of the standard COM-Poisson distribution.

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Overweight and obesity which are known to pose serious health problems are becoming increasingly prevalent in Nigeria which is a sub-Saharan African country. This study utilized the 2018 Nigeria Demographic Health Survey to examine demographic and socio-economic risk factors of overweight and obesity among Nigerian women aged 15-49 years. Exploratory analysis was used to provide basic description of the data while a semiparametric structured additive models was used to describe the relationship between the presumed factors and overweight and obesity status while also accounting for spatial effects at state level. The national prevalence of overweight and obesity among Nigerian women was found to be 27.4%. Increased risk of overweight and obesity among Nigerian women was found to be strongly associated with being older, high educational level, being rich, living in an urban area, having many children, being pregnant, and residing in southern part of Nigeria. In respect to ethnicity and religion, the Fulani tribe and Islamic religion were associated with lower prevalence of overweight and obesity. Overweight and obesity were found to be significantly more prevalent in the Southern parts compared to the Northern parts of Nigeria. The highest and lowest prevalence of overweight and obesity were observed in Anambra and Yobe states respectively. Prevalence of overweight and obesity was higher among Muslim women compared to Christian women since most Northern women are Muslims and most Southern women are Christians. Random (unstructured) spatial effects were significant indicating that overweigh/obesity was influenced by unobserved state specific factors

A new mixed Poisson model is proposed as a better alternative for modelling count data in the presence of overdispersion and/or heavy-tail. The mathematical properties of the model were derived. The maximum likelihood estimation method is employed to estimate the model’s parameters and its applications to the three real data sets discussed. The model is used to model sets of frequencies that have been used in different literature on the subject. The results of the new model were compared with Poisson, Negative Binomial and Generalized Poisson-Sujatha distributions (POD, NBD and GPSD, respectively). The parameter estimates expected frequencies and the goodness-of-fit statistics under each model are computed using R software. The results show that the proposed PSD fits better than POD, NBD and GPSD for all the data sets considered. Hence, PSD is a better alternative provided to model count data exhibiting overdispersion property.