Ordinal logistic model

FIGURE 11.13 A collection of 10 responses (ordinates) to a compound resulting from exposure of a biological preparation to 10 concentrations of the compound (abscissae, log scale). The dotted line indicates the mean total response of all of the concentrations. The sigmoidal curve indicates the best fit of a four-parameter logistic function to the data points. The data were fit to Emax = 5.2, n = 1, EC5o = 0.4 pM, and basal = 0.3. The value for F is 9.1, df=6, 10. This shows that the fit to the complex model is statistically preferred (the fit to the sigmoidal curve is indicated). 

When experiments results in ordinate categorical responses, say C categories, a general modeling approach based on logistic regression model can be described as... 

Another method of detecting a dose-response relationship is to fit the data to various models for dose-response curves. This method statistically determines whether or not a dose-response model (such as a Logistic function) fits the data points more accurately than simply the mean of the values this method is described fully in Chapter 12. The most simple model would be to assume no dose-response relationship and calculate the mean of the ordinate data as the response for each concentration of ligand (horizontal straight line parallel to the abscissal axis). A more complex model would be to fit the data to a sigmoidal dose-response function (Equation 11.2). A sum of squares can be calculated for the simple model (response — mean of all response) and then for a fit of the data set refit to the four parameter Logistic shown... 

Haines et al. (47) suggested including the criterion Bayesian D-optimality, which maximizes some concave function of the information matrix, which in essence is the minimization of the generalized variance of the maximum likelihood estimators of the two parameters of the logistic regression. The authors underline that toxicity is recorded as an ordinal variable and not a simple binary variable, and that the present design needs to be extended to proportional odds models. 

Another model for the co-ordination of complex networks that has been proposed is the idea of a 4PL or a lead logistics service provider. 

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