  In many biomedical problems, data are often heterogeneous, with samples
spanning multiple patient subgroups, where different subgroups may have
different disease subtypes, stages, or other medical contexts. These subgroups
may be related, but they are also expected to have differences with respect to
the underlying biology. The heterogeneous data presents a precious opportunity
to explore the heterogeneities and commonalities between related subgroups.
Unfortunately, effective statistical analysis methods are still lacking.
Recently, several novel methods based on integrative analysis have been
proposed to tackle this challenging problem. Despite promising results, the
existing studies are still limited by ignoring data contamination and making
strict assumptions of linear effects of covariates on response. As such, we
develop a robust nonparametric integrative analysis approach to identify
heterogeneity and commonality, as well as select important covariates and
estimate covariate effects. Possible data contamination is accommodated by
adopting the Cauchy loss function, and a nonparametric model is built to
accommodate nonlinear effects. The proposed approach is based on a sparse
boosting technique. The advantages of the proposed approach are demonstrated in
extensive simulations. The analysis of The Cancer Genome Atlas data on
glioblastoma multiforme and lung adenocarcinoma shows that the proposed
approach makes biologically meaningful findings with satisfactory prediction.
