MAXIMUM LIKELIHOOD ESTIMATION

A dose-response model depends on adjustable parameters that can be systematically varied in order to give a best fit relative to a specific estimation criterion.  The best fit means a specific member of the specified family of dose-response models that most closely corresponds to the data when closeness is measured in terms of the specified estimation criterion.  The most widely used estimation criterion is maximum likelihood estimation. 

The maximum likelihood estimates of the adjustable parameters in a dose-response model are the values of these parameters which maximize the likelihood of observing the dose-response data that was in fact observed.  Computer codes have been written to efficiently search all possible parameter values for the combination of parameter values that maximize the likelihood of observing the specific dose-response outcomes that were observed.  The set of parameter values that maximizes the likelihood function (that gives the largest likelihood of actually observing the empirical data, given all the other possibilities and given the initial choice for the dose-response model) is referred to as the maximum likelihood estimates (MLE's) of parameter values.  The dose-response model that incorporates the maximum likelihood estimate of the set of parameter values provides the best estimates of the probability that an individual will develop the specified response when exposed to a specified dose.