document: 1-dimensional splines as building blocks for improving accuracy of risk outcomes models Transformation of both the response variable and the predictors is commonly used in fitting regression models . However , these transformation methods do not always provide the maximum linear correlation between the response variable and the predictors , especially when there are non-linear relationships between predictors and the response such as the medical data set used in this study . A spline based transformation method is proposed that is second order smooth , continuous , and minimizes the mean squared error between the response and each predictor . Since the computation time for generating this spline is O ( n ) , the processing time is reasonable with massive data sets . In contrast to cubic smoothing splines , the resulting transformation equations also display a high level of efficiency for scoring . Data used for predicting health outcomes contains an abundance of non-linear relationships between predictors and the outcomes requiring an algorithm for modeling them accurately . Thus , a transformation that fits an adaptive cubic spline to each of a set of variables is proposed . These curves are used as a set of transformation functions on the predictors . A case study of how the transformed variables can be fed into a simple linear regression model to predict risk outcomes is presented . The results show significant improvement over the performance of the original variables in both linear and non-linear models .
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