Optimal Scaling, A Wonderful Method for Analysing Clinical Trials with Imperfect Data

Abstract

Context: In clinical trials the research question is often measured with multiple variables, and multiple regression is commonly used for analysis. The problem with multiple regression is that consecutive levels of the variables are assumed to be equal, while in practice this is virtually never true. Optimal scaling is a method designed to maximize the relationship between a predictor and an outcome variable by adjusting their scales. Aims: To assess the performance of optimal scaling in clinical research. Settings and design: A simulated example of a drug efficacy trial was used. The SPSS module Optimal Scaling with ridge regression, lasso and elastic net regression was used. Results: The ridge optimal scaling model produced eight p-values < 0.01, while traditional regression and unregularized optimal scaling produced only 3 and 2 p-values < 0.01. Lasso optimal scaling eliminated 4 of 12 predictors from the analysis, while, of the remainder, only two were significant at p < 0.01. Similarly elastic net optimal scaling did not provide additional benefit. Conclusions: 1/ Optimal scaling shows similarly sized effects compared to traditional regression. In order to benefit from optimal scaling a regularization procedure for the purpose of correcting overdispersion is needed. 2/ Ridge optimal scaling performed much better than did traditional regression giving rise to many more statistically significant predictors. 3/ Lasso optimal scaling shrinks some b-values to zero, and is particularly suitable if you are looking for a limited number of strong predictors. 4/ Elastic net optimal scaling works better than lasso if the number of predictors is larger than the number of observations.