Ordinal response prediction using bootstrap aggregation, with application to a high-throughput methylation data set

Abstract

Many investigators conducting translational research are performing high-throughput genomic experiments and then developing multigenic classifiers using the resulting high-dimensional data set. In a large number of applications, the class to be predicted may be inherently ordinal. Examples of ordinal outcomes include tumor-node-metastasis (TNM) stage (I, II, III, IV); drug toxicity evaluated as none, mild, moderate, or severe; and response to treatment classified as complete response, partial response, stable disease, or progressive disease. While one can apply nominal response classification methods to ordinal response data, in doing so some information is lost that may improve the predictive performance of the classifier. This study examined the effectiveness of alternative ordinal splitting functions combined with bootstrap aggregation for classifying an ordinal response. We demonstrate that the ordinal impurity and ordered twoing methods have desirable properties for classifying ordinal response data and both perform well in comparison to other previously described methods. Developing a multigenic classifier is a common goal for microarray studies, and therefore application of the ordinal ensemble methods is demonstrated on a high-throughput methylation data set.

Figure 1

Candidate split s divides node t it into left (t_L) and right (t_R) descendant nodes such that a proportion p_L of the cases in t go into t_L and a proportion of cases p_R go into t_R.

Figure 2

Right-hand figure: Boxplots of misclassification rates for each of the five impurity methods calculated using out-of-bag observations from the simulation study. Left-hand figure: Boxplots of the gamma statistic for each of the five impurity methods calculated using out-of-bag observations from the simulation study.

Figure 3

Right-hand figure: Boxplots of misclassification rates for each of the four impurity methods calculated using out-of-bag observations from the case application. Left-hand figure: Boxplots of the gamma statistic for each of the four impurity methods calculated using out-of-bag observations from the case application.