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Analysis of kinetic data


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Analysis of kinetic data

  2. 2. INTRODUCTION Population pharmacokinetics: study of drug absorption and disposition characteristics in a population or distinct subset of population. The information obtained is then summarized using mathematical models. Population models address variability arising from o Inter-individual variability o Explainable o Unexplainable o Intra-individual variability o Measurement errors
  3. 3. POPULATION PHARMACOKINETIC METHODS TRADITIONAL METHODS 1. Start with the individuals then progress NEWER METHODS 1. to the population. 2. evaluating the individuals. Random errors from all sources are combined (inter-individual Goes directly to the population without 2. variability, Separate the unexplainable inter- individual variability from the residual intra-individual variability, measurement random errors. errors). 3. E.g. Traditional standard two stage Method, Naïve pooling method 3. E.g. Parametric method: Mixed effect modelling Non parametric method: NPML, NPEM, SNP, I2S
  5. 5. TRADITIONAL STANDARD TWO STAGE METHOD It is a traditional method. It involves study of relatively small number of individuals subjected to intense sampling. The period of the study is short, since the individuals are usually instutionalised.
  6. 6. It consists of two stages: Stage 1: Each individuals data is analysed on a case by case basis using weighed or extended nonlinear least square regression to determine the individual pharmacokinetic parameters. Stage 2: The individual pharmacokinetic parameters are pooled to determine measures of central tendency and variability for the population. The association between specific pharmacokinetic parameters and demographic characters are studied.
  7. 7. ADVANTAGES It provides reliable and robust estimates when extensive numbers of samples are available for each individual. It is a simple method. It is a well tried and straightforward method to implement. Many software packages are available for this method. Statistics are straightforward and are familiar to the investigators. It is capable of producing estimates of typical values for members of a population that are similar to those found with direct population approaches. It is considered to be the golden standard in case of rich data.
  8. 8. DISADVANTAGES Being a controlled study design, it is very expensive and requires careful planning and implementation. It gives unreliable results in case of sparse data. It is difficult to study a sufficiently large number of individuals to adequately represent the population. There are ethical issues to obtain extensive samples from a fragile subpopulation.
  9. 9. NAIVE POOLING METHOD It is a traditional method. In this method, the data from all individuals are pooled and analysed simultaneously without consideration of the individual from whom the specific data were obtained.
  10. 10. ADVANTAGES It may be the only viable approach in certain situations, for e.g. in case on animal data, where each animal provides only one data point.
  11. 11. DISADVANTAGES This method is generally considered the least favourable. It is susceptible to bias. It produces inaccurate estimates of pharmacokinetic parameters.
  13. 13. MIXED EFFECT MODELLING Mixed effect modelling is a parametric method which assumes a specific distribution of pharmacokinetic parameters prior to estimation. It is considered as the optimum population model method.
  14. 14. It is a direct method in which the population parameters are determined in a single stage of analysis applied simultaneously to the data from many individuals. This method recognises which data arise from the same individual and which do not.
  15. 15. “Effects” are factors that contribute to the variability of the measured observation. They are of two types: o fixed o random
  16. 16. E.g. Cp = D/Vd . e –Cl/Vdt Cp = concentration of drug in the plasma (dependent variable) D = dose (fixed effect) t = time
  17. 17. Fixed effects are components of the structural pharmacokinetic model. They do not include any unexplainable variation either between or within individuals. Fixed effect parameters are represented by the symbol theta.
  18. 18. Each individual in a population will have a specific value for their pharmacokinetic parameter, which will differ from the population typical value due to unexplainable variability. This variability is represented by the symbol eta (?).
  19. 19. The manner in which an individual’s eta relates the individual’s pharmacokinetic parameter to the population typical value is given by the error model. A variety of error models can be chosen, depending upon the visual inspection of data, experience, trial and error.
  20. 20. The most well-known method for applying mixed effect method in NONMEM (non linear mixed effect modelling). The output from NONMEM includes estimates of mean variances and covariances of the parameters.
  21. 21. ADVANTAGES It is useful for sparse and randomly collected data. It is able to derive population models when only a few samples are available from each individual. Individuals are still identifiable, which permits repeated measures for individuals in spite of the data being pooled into a single data set. Inclusion of covariates during elimination procedure offsets unbalanced data. It is ideal for studying population such as very old, very young or very sick which are difficult to study using STS.
  22. 22. DISADVANTAGES Study design does not call for collection of samples at specific times, resulting in imprecise estimates. Therefore some thought should be given to the optimal collection time. Biased estimates have been reported especially when data contain large amount of random error.
  23. 23. NON PARAMETRIC METHODS Non parametric methods do not assume any specific distribution of parameters about the population values, but rather allow for many possible distributions. In this method, the entire population distribution of each parameter is estimated from the population data. This permits visual inspection of distribution before committing to one.
  24. 24. Different non parametric methods are: Non parametric maximum likelihood [NPML] Non parametric expectation maximization [NPEM] Semi/ smooth non parametric method [SNP]
  25. 25. NON PARAMETRIC MAXIMUM LIKELIHOOD [NPML] This method permits all forms of distributions including those containing sharp changes, such as discontinuities and kinks. It uses maximum likelihood as estimator.
  26. 26. NON PARAMETRIC EXPECTATION MAXIMIZATION [NPEM] This method is preferred to any parametric method when there is an unexpected multimodal or nonnormal distribution of atleast one of the nodal parameters. It eliminates the need for initial guesses which are required for nonlinear least square procedure. It is preferable to traditional method in case of sparse data. It uses expectation maximization as the estimator.
  27. 27. SEMI/ SMOOTH NON PARAMETRIC METHOD [SNP] This method places some restrictions on the type of parametric distributions considered. Functions that are not permitted include those containing sharp edges and discontinuities.
  28. 28. ITERATIVE TWO STAGE METHOD I2S method may be used with rich data, a mixture of rich and sparse data or only sparse data. To initiate the procedure an approximate prior population model is required. Source for these population value include literature, naïve pooled data method, STS method etc.
  29. 29. This population model is subjected to Bayesian estimation of individual parameters for all patients, both rich and sparse in data (stage 1). The population parameters are recalculated with these new individual parameters in order to form new set of priori distribution (stage 2).
  30. 30. The Bayesian estimation step is performed again using the new population model to find more accurate estimates of individual parameters. This is carried out until the difference between the new and old prior distribution is essentially zero. This method yields both individual and population parameters.
  32. 32. PRE APPROVAL PHASE (drug development phase) Development of dosage regimen. Determination of dosage requirements in special populations Predicting outcomes of various forms of drug administration like multiple doses, special patient groups, and controlled release formulations. Investigating potential disease and drug interactions. Studying drug concentration- acute toxic effect relationships. Construction of population pharmacokinetic model. Evaluating pharmacokinetic versus pharmacodynamics variability.
  33. 33. POST APPROVAL PHASE Application of the population average dose for an individual, depending on the variability of pharmacokinetic and pharmacodynamics parameters. Dose individualisation for individuals whose pharmacokinetic parameters are most likely to deviate from the population typical values. Dose individualisation for drugs with narrow therapeutic index. Stochastic control of drug therapy.