Recursive Partitioning in the Health Sciences by Heping Zhang, Burton Singer (auth.)

By Heping Zhang, Burton Singer (auth.)

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Sample text

For example, in the study of Goldman et al. 2 Determination of Terminal Nodes 33 predict whether a patient with chest pain suffers from a serious heart disease based on the information available within a few hours of admission. To this end, we first classify a node T to either class 0 (normal) or 1 (abnormal), and we predict the outcome of an individual based on the membership of the node to which the individual belongs. Unfortunately, we always make mistakes in such a classification, because some of the normal subjects will be predicted as diseased and vice versa.

3. For any risk threshold r (0 :::; r :::; 1), we calculate the empirical true and false positive probabilities respectively as TPP = the number of preterm deliveries for which Oi > r the total number of preterm deliveries and F P P = the number of term deliveries for which Oi > r. 1. In the medical literature, the true positive and negative probabilities are commonly referred to as sensitivity and specificity. 1 indicates that the final logistic regression model improves the predictive precision over a random prediction model.

P. Then, the odds ratio for subjects i and k to be abnormal is ()d (1 - ()i) ()k/(I - ()k) = exp({3d· Taking the logarithm of both sides, we see that {3l is the log odds ratio of the response resulting from two such subjects when their first covariate differs by one unit and the other covariates are the same. In the health sciences, exp({3d is referred to as the adjusted odds ratio attributed to Xl while controlling for X2, •.. , xp- The remaining {3's have similar interpretations. This useful interpretation may become invalid, however, in the presence of interactive effects among covariates.

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