Log-normal regression modeling through recursive partitioning

This article discusses a method for fitting log-normal regression models to censored survival data through binary decision trees. Recursive partitioning is performed by analysis of the distributions of residuals and cross-validation estimates of the average squared error. Several forms of strata selection and bootstrapping are examined to study their relative effectiveness. If the Newton - Raphson method for determining the maximum likelihood estimates fails because of heavy censoring, a method relying only on the first derivatives of the log likelihood function is used. The proposed method helps to identify the local effect of the covariates. The methods are illustrated with real and simulated data. Especially, a data set having categorical variables and missing values is used for modeling the tree-structured log-normal regression.