An alternative pruning based approach to unbiased recursive partitioning

Tree-based methods are a non-parametric modelling strategy that can be used in combination with generalized linear models or Cox proportional hazards models, mostly at an exploratory stage. Their popularity is mainly due to the simplicity of the technique along with the ease in which the resulting model can be interpreted. Variable selection bias from variables with many possible splits or missing values has been identified as one of the problems associated with tree-based methods. A number of unbiased recursive partitioning algorithms have been proposed that avoid this bias by using p-values in the splitting procedure of the algorithm. The final tree is obtained using direct stopping rules (pre-pruning strategy) or by growing a large tree first and pruning it afterwards (post-pruning). Some of the drawbacks of pre-pruned trees based on p-values in the presence of interaction effects and a large number of explanatory variables are discussed, and a simple alternative post-pruning solution is presented that allows the identification of such interactions. The proposed method includes a novel pruning algorithm that uses a false discovery rate (FDR) controlling procedure for the determination of splits corresponding to significant tests. The new approach is demonstrated with simulated and real-life examples.