Deriving Optimal Composite Scores: Relating Observational/Longitudinal Data with a Primary Endpoint

In numerous clinical/experimental studies, multiple endpoints are measured on each subject. It is often not clear which of these endpoints should be designated as of primary importance. The desirability function approach is a way of combining multiple responses into a single unitless composite score. The response variables may include multiple types of data: binary, ordinal, count, interval data. Each response variable is transformed to a 0 to1 unitless scale with zero representing a completely undesirable response and one representing the ideal value. In desirability function methodology, weights on individual components can be incorporated to allow different levels of importance to be assigned to different outcomes. The assignment of the weight values are subjective and based on individual or group expert opinion. In this dissertation, it is our goal to find the weights or response variable transformations that optimize an external empirical objective criterion. For example, we find the optimal weights/transformations that minimize the generalized variance of a prediction regression model relating the score and response of an external variable in pre-clinical and clinical data. For application of the weighting/transformation scheme, initial weighting or transformation values must be obtained then calculation of the corresponding value of the composite score follows. Based on the selected empirical model for the analyses, parameter estimates are found using the usual iterative algorithms (e.g., Gauss Newton). A direct search algorithm (e.g., the Nelder-Mead simplex algorithm) is then used for the minimization of a given objective criterion i.e. generalized variance. The finding of optimal weights/transformations can also be viewed as a model building process. Here relative importance levels are given to each variable in the score and less important variables are minimized and essentially eliminated