Grace Wahba, Yuedong Wang, Chong Gu, Ronald Klein, MD, Barbara Klein, MD
We describe the use of smoothing spline analysis of variance (SS(cid:173) ANOVA) in the penalized log likelihood context, for learning (estimating) the probability p of a '1' outcome, given a train(cid:173) ing set with attribute vectors and outcomes. p is of the form pet) = eJ(t) /(1 + eJ(t)), where, if t is a vector of attributes, f is learned as a sum of smooth functions of one attribute plus a sum of smooth functions of two attributes, etc. The smoothing parameters governing f are obtained by an iterative unbiased risk or iterative GCV method. Confidence intervals for these estimates are available.
In medical risk factor analysis records of attribute vectors and outcomes (0 or 1) for each example (patient) for n examples are available as training data. Based on the training data, it is desired to estimate the probability p of the 1 outcome for any