Population models

Now consider a latticized version of this model. Populate a square lattice -which may represent a tissue sample in which the modeled immune reactions are assumed to occur - with each of the four cell types C, H, M and V and initialize the system so that a fraction po of each cell type is in its high (i.e. = 1) concentration state. Assign the value 1 to each site i,j) if the sum of the concentrations of its nearest neighbors that are of the same cell type as site (i, j) is nonzero. After all sites have been assigned new values in this manner, update the system according to equations 8.92. 

Data on antidepressant dmgs are available from a number of sources randomized, controlled clinical trials (RCTs) in both hospital and primary-care populations decision analytic models population-based naturalistic observational studies of usual... 

We can also use chemical kinetics to attempt to model populations of living systems such as single-celled organisms or plant, animal, and human populations. We describe the density of individuals (species A) as Ca, which might be in individualsA olume in a three-dimensional... 

Piotrovsky, V. Drug efficacy analysis as an exercise in dynamic (indirect-response) population PK-PD modelling. Population Approach Group... 

Himmelblau [32] and Himmelblau and Bischoff [33] have considered three types of model which are useful in process analysis, i.e. empirical models, population balance models and transport phenomena models. Empirical models involve mathematical relationships between dependent and independent variables, which are postulated either entirely a priori, or by considering the nature of the experimental data, or by analogies, etc. On the other hand, transport phenomena models are based on the laws of... 

Model populations or communities can be established in the laboratory or in the field which they simulate, but they do not exactly reproduce the real situation. They can be used to run controlled experiments with adequate replication and can demonstrate the effects of chemicals on ecological processes such as the carbon and nitrogen cycles discussed in Chapter 7. 

There are many approaches used for PPK model development in the literature. These range from modeling population pharmacokinetic data without exploratory data analysis to approaches that incorporate the latter. Excellent examples of population pharmacokinetic model development, which incorporate exploratory data analysis into population pharmacokinetic model development, can be found in the articles by Ette and Ludden and Mandema, Verotta, and Sheiner Excellent reviews on the validation of PPK models are available in the literature. Thus, validation will not be discussed. 

D. Type 1 Interaction Models Population Balance Techniques. 238... 

Once the statistical parameter to optimize is defined (e.g., maximizing by a leave-one-out validation procedure), along with the model population size P (for example, P = 100) and the maximum number L of allowed variables in a model (for example, L = 5) the minimum number of allowed variables is usually assumed equal to one. Moreover, a cross-over probability pc (usually high, for example, pc > 0.9) and a mutation probability Pm (usually small, for example, Pm < 0.1) must also be defined by the user. 

The model population is initially built by random models with a number of variables between 1 and L, and the models are ordered with respect to the selected statistical parameter - the quality of the model - (the best model is in first place, the worst model at position P) ... 

After a random generation of a model population, random mutations of one or a few variables are tried. If better models are obtained after a fixed number of trials, this procedure is repeated on the new generation of models otherwise random mutations of several variables becomes allowed. Also in this case, if better models are obtained after a fixed number of trials, the first procedure is repeated on the new generation of models otherwise systematic addition and elimination of the variables of the population models is performed. If better models are obtained, the procedure restarts from the first step otherwise, if all the variables are checked the procedure ends and the variables of the final population models are checked for their statistical significance and eventually eliminated. 

Population characteristics -h Measured in humans -h Large population size possible -h Full range of sensitive subpopulations possible + Measured in humans - Limited number of subjects + Possible to study sensitive subpopulations - Extrapolation to humans + Large group size possible - Homogeneity of animal model population and environmental factors-relevance to human ... 

Step 6. With the appropriate pharmacostatistical models, population model building is performed using covariates retained in step 5 with the covariate selection level set at a= 0.005. The backward elimination for covariate selection in applied to each of the 100 bootstrap samples. The covariates found to be important in explaining the variablilty in the parameter of interest are used to build the final population PM model. 

FIGURE 16.1 Final model population observed concentrations DV) versus predicted concentrations. The predicted concentrations appear to take a series of fixed values corresponding to the number of observation time points. 

Todeschini, R., Consonni, V. and Pavan, M. (2004c) A distance measure between models a tool for similarity/diversity analysis of model populations. Chemom. Intell. Lab. Syst., 70, 55-61. 

Doak D, Kareiva P, Kleptetka B. 1994. Modeling population viability for the desert tortoise in the western Mojave Desert. Ecol Appl 4 446 160. 

The investigated system is a certain model population of insects,... 

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