Nonparametric Biomarker Based Treatment Selection With Reproducibility Data

We consider evaluating biomarkers for treatment selection under assay modification. Survival outcome, treatment, and Affymetrix gene expression data were attained from cancer patients. Consider migrating a gene expression biomarker to the Illumina platform. A recent novel approach allows a quick evaluation of the migrated biomarker with only a reproducibility study needed to compare the two platforms, achieved by treating the original biomarker as an error-contaminated observation of the migrated biomarker. However, its assumptions of a classical measurement error model and a linear predictor for the outcome may not hold. Ignoring such model deviations may lead to sub-optimal treatment selection or failure to identify effective biomarkers. To overcome such limitations, we adopt a nonparametric logistic regression to model the relationship between the event rate and the biomarker, and the deduced marker-based treatment selection is optimal. We further assume a nonparametric relationship between the migrated and original biomarkers and show that the error-contaminated biomarker leads to sub-optimal treatment selection compared to the error-free biomarker. We obtain the estimation via B-spline approximation. The approach is assessed by simulation studies and demonstrated through application to lung cancer data.