A Note on Inference

Inference is the act of drawing conclusions from a model, be it making a prediction about a concentration at a particular time, such as the maximal concentration at the end of an infusion, or the average of some pharmacokinetic parameter, like clearance. These inferences are referred to as point estimates because they are estimates of the true value. Since these estimates are not known with certainty they have some error associated with them. For this reason confidence intervals, prediction intervals, or simply the error of the point estimate are included to show what the degree of precision was in the estimation. With models that are developed iteratively until some final optimal model is developed, the estimate of the error associated with inference is conditional on the final model. When inferences from a model are drawn, modelers typically act as though this were the true model. However, because the final model is uncertain (there may be other equally valid models, just this particular one was chosen) all point estimates error predicated on the final model will be underestimated (Chatfield, 1995). As such, the confidence interval or prediction interval around some estimate will be overly optimistic, as will the standard error of all parameters in a model. 

Unfortunately there is nothing in statistical theory that allows determination of the correct error estimate taking into account model uncertainty. Bayesian model averaging has been advocated as one such solution, but this methodology is not without criticism and is not an adequate solution at this point in time. At this point the only advice that can be given is to be aware of model uncertainty and recognize it as a limitation of iterative model development. 

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