Nonparametric Testing Methods for Treatment-Biomarker Interaction based on Local Partial-Likelihood
MetadataShow full item record
A fair amount of research has been done on the interactions between treatment and biomarkers hoping to avoid failure to recognize effective agents which benefit only a subset of patients in traditional clinical designs and analysis, such as (Bonetti, 2004), (Bonetti et al., 2009), and (Royston and Sauerbrei, 2004). Particularly, Fan et al. (Fan et al., 2006) assumed the treatment effect is an unknown function of a putative biomarker, and proposed techniques to give the local partial likelihood estimation (LPLE) of this treatment effect function using local linear techniques (Fan and Chen, 1999). However, no methods were developed for assessing whether the treatment effect is indeed a function of the biomarker (interaction exists) or just a constant (no interactions). Based on the idea of LPLE, a new nonparametric hypothesis testing methodology, which we call local partial likelihood bootstrap (LPLB) test, is proposed in this work to identify the differences in treatment effects among subgroups of patients with different values of biomarkers in a Phase III clinical trials study. A bootstrap technique is used to evaluate the significance of the test. Meanwhile, the proposed method can also be applied to identify the interactions between a putative biomarker and a collection of covariates (covariate vectors) that are discrete or continuous. Numerical studies show that the LPLB test can provide a substantial improvement in the power of the interaction detection compared with the commonly used method, especially for interactions of complex form. The LPLB test is also applied to a prostate cancer trial with the serum prostatic acid phosphatase (AP) biomarker.