Logistic models

Equation (3.14.2.11) predicts the cell dry weight concentration with respect to time. The model shows the cell dry weight concentration (x) is independent of substrate concentration. However, the logistic model includes substrate inhibition, which is not clearly seen from Equation (3.14.2.11). 

Figure 3.7 shows the growth of R. rubrum in a batch fermentation process using a gaseous carbon source (CO). The data shown follow the logistic model as fitted by (3.14.2.11) with the solid lines, which also represent an unstructured rate model without any lag phase. The software Sigma Plot was used to fit model (3.14.2.11) to the experimental data. An increase in concentration of acetate in the prepared culture media did not improve the cell dry weight at values of 2.5 and 3 gT-1 acetate, as shown in Figure 3.7. However, the exponential growth rates were clearly observed with acetate concentrations of 0.5-2 g-F1 hi the culture media.

Liquid-liquid extraction, 172, 183 Logistic model, 55, 56 Lyophilisation, 172 Lysine, 1, 8, 202, 339, 340... 

The dose-response relahonship in a quantal model can be analyzed with the help of a logistic model where we calculate probability of an event at a given concentrahon or AUC or dose ... 

Construct a concentration-effect plot as in O Figure 13-5, and determine the IC50 value by fitting a logistic model to the data. 

A number of issues influenced the selection of the dose-response model form and the treatment of the data prior to fitting the model. First, shoot weight and shoot length are continuous response measurements therefore, use of a standardized logistic model form is not appropriate. Second, the natural variation in plant growth often resulted in apparent increased shoot weight and shoot length measurements relative to the control at low herbicide application rates. A dose-response model needs to perform well even when some measurements in treatment levels exceed the controls. 

This was a multi-centre, pan-European, randomised double-blind placebo-controlled clinical trial in acute stroke to evaluate the effect of ancrod, a natural defribrinogenating agent (Hennerici et al. (2006)). The primary endpoint was based on the Barthel Index a favourable score of 95 or 100 or a return to the pre-stroke level at three months was viewed as a success. The primary method of statistical analysis was based on a logistic model including terms for treatment, age category, baseline Scandinavian Stroke Scale and centre. 

Logistic Models. This model is based upon the assumption of a logistic distribution of the logarithms of the individual tolerances. 

The empirical models are based on mathematical functions that mimic the distribution of the standards measured in the assay. They can be based on point to point (interpolation) methods or regression methods. The most widely used empirical models that have been applied to MIP-ILAs include the log-logit model and the four-parameter logistic model. 

The 4-parameter logistic model is considered the most versatile one for fitting the dose-response curves in immunoassays [42]. The fitting equation is given by [22, 23, 41]... 

In contrast, an ECx that produces a specific percent reduction (e.g., x = 10, 20 or 50%) in ceriodaphnid reproduction can be calculated by adjusting a logistic model derived from the Hill equation to the test results (Vindimian et ah, 1983). This model is characterized by the following equation ... 

Where Y is the observed total number of live young ceriodaphnids per replicate, C is the concentration being tested, Ymax is the adjusted value of live young ceriodaphnids expected in the control, EC50 is the estimated concentration which causes 50% of reproduction inhibition and Hn is the estimated Hill number corresponding to the slope of the sigmoid curve. Then, the ECx can be estimated by an equation directly derived from the logistic model, as follows ... 

Segreti A, Vocci FJ, Dewey WL. 1979. Antagonism of barium chloride lethality by atropine and naloxone Analysis by a multivariate logistic model. Toxicol Appl Pharmacol 50 25-30. 

Piegorsch WW, Weinberg CR, Taylor JA (1994) Non-hierarchical logistic models and case-only designs for assessing susceptibility in population-based case-control studies. 

Due to the complexity of the optimisation problem, a solution in a closed form is not feasible and for this reason simulation methodologies are usually used. The respective tools utilise logistic models of the power components and are based on... 

For calibration, a seven-point standard curve ranging from 2-32 ng/mL in rat or dog EDTA plasma was used. The four-parameter logistic model was used to describe the relationship between the OD readings and nominal concentration (CONC) of the analyte (DeLean et al. 1978) ... 

As an example we may present logistic model of growth (8), where F = N - current value of population number r - Malthusian parameter Fa, =N00 - capacity of medium (limited value of N). 

The initial analysis showed that sex had no significant effect on either TK or dose-limiting toxicity, and subsequently sex was excluded from the model. Table 17.2 summarizes the statistical analysis for correlation between mortality and plasma AUC or Cmax. The logistic model shown in Table 17.2 was fitted... 

Moore and Caux (1997), in the same paper examining the relationships between hypothesis testing and effects levels, also characterized some important properties of the regression approach. One of the critical questions is which model to use and how much of a difference it makes. Logistic, probit, Weibull, and three parameter logistic models incorporating a slope parameter were compared in these data sets. The differences in using these models for extrapolation depend upon the structure of the data set. 

TABLE 14-1 The Four-Para meter Logistic Model Expressed in Three Different Forms... 

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