Prastyo, Dedy Dwi (2008) Pemodelan Farmakokinetika Populasi Dan Individu Menggunakan Algoritma EM-Nonparametrik dan Analisis Bayesian. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Proses absorsi, distribusi, metabolisme, dan ekskresi suatu obat di dalam sistem biologi sangat kompleks, namun dapat disederhanakan ke model farmakokinetik. Setiap individu diukur konsentrasi obat di dalam tubuhnya beberapa kali. Jika ada n individu, data pengamatan dinyatakan dalam vektor random (Y1, Y2 , ... , Yn) . Setiap (\i) memiliki vektor parameter farmakokinetik {fq. Nilai Yi dapat diamati dan distribusi bersyarat p(\j 19i) diketahui bentuknya. Nilai parameter 9i tidak diketahui (hanya dapat ditaksir) dan dianggap sebagai variabel tidak teramati. Fungsi distribusi prior gabungan, F* ( 9i), tidak diketahui bentuknya atau bersifat nonparametrik. Algoritma Ekspektasi Maksimisasi Nonparametrik (EMNP) digunakan untuk menaksir distribusi prior gabungan apabila 9 = 9i (identik) dan data (Yi, Y2 , .. ., Y0 ) diketahui nilainya. Algoritma EMNP selalu menaikkan nilai loglikelihood dari Fk(9) pada setiap iterasi ke-k dan limit Fk(9) konvergen ke F* ( 9) untuk k ~ oo . Penaksiran parameter farmakokinetika populasi dilanjutkan dengan penaksiran parameter farmakokinetika untuk setiap individu. Algoritma Nelder-Mead simpleks digunakan untuk menaksir parameter farmakokinetik individu dengan meminimumkan Maximum a Posteriory Probability (MAP). Algoritma EMNP dan MAP dapat menaksir parameter farmakokinetik populasi dan individu dengan baik walaupun data pengamatan sedikit, bahkan tunggal. Pemodelan farmakokinetik populasi dan individu diterapkan pada kasus bedah urologi.
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The process of absorption, distribution, metabolism, and excretion of medicine in biology system are very complex. The complexity system can be simplified by pharmacokinetics model. The concentration of medicine in the body of patients usually are measured several times. Consider a sequence repetitive experiments of n individual, (Y1, Y2 , .. ., Y0 ), and each individual (\i) will be estimated its pharmacokinetic parameters ( 9i) . So, each experiment is represented by a pair of random vector(Yi,9i). Random vector Yi is observed and density p(\j 19i) is known. However, random vector 9i is not observed (assumed as an unobserved variable) and its joint prior distribution function, F* ( 9i ) , is unknown (nonparametric ). Nonparametric Expectation-Maximization (NPEM) algorithm is used to estimate joint prior distribution if 9 = 9i (identic) given data (\I, Y2 , .. ., Y0 ). NPEM algorithm increases the log-likelihood of Fk{9) in every iteration k and limit F k ( 9) converge to F* ( 9) for k ~ oo . The next work is to estimate individual pharmacokinetic parameter .. Individual pharmacokinetic parameters are estimated by minimizing Maximum a Posteriory Probability (MAP) using Nelder-Mead simplex algorithm. NPEM algorithm and MAP could estimate population and individual pharmacokinetics parameter well, although for sparse data. Population and individual pharmacokinetics modelling are applied to the case of urology disease.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | RTSt 519.542 Pra p 2008 3100008031186 (WEEDING) |
| Uncontrolled Keywords: | Algoritma EMNP, Algoritma Nelder-Mead simpleks, Distribusi prior, MAP, Parameter farmakokinetik, NPEM algorithm, Nelder-Mead simplex algorithm, Pharmacokinetic parameter, Prior distribution. |
| Subjects: | Q Science > QA Mathematics > QA279.5 Bayesian statistical decision theory. Q Science > QA Mathematics > QA9.58 Algorithms |
| Divisions: | Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Anis Wulandari |
| Date Deposited: | 25 Feb 2026 05:03 |
| Last Modified: | 25 Feb 2026 05:03 |
| URI: | http://repository.its.ac.id/id/eprint/132596 |
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