Nonparametric Inference on Treatment-biomarker Interaction Based on Probability Index

In precision medicine, an important task is identifying subgroups of patients who may benefit m ore f rom a t reatment b ased o n a c linical variable or biomarker.In this paper, we propose a non-parametric treatment-biomarker interaction measure using a probabilistic index to assess differences in treatment effects b etween s ubgroups f ormed b y d ichotomizing a b iomarker a t a cutpoint.When the cutpoint is prespecified, null hypothesis of no interaction is tested using Wilcoxon-type statistics.When the cutpoint is not prespecified, t he s ame null hypothesis is tested across a range of cutpoint values by taking the supremum of Wilcoxon-type statistics with p-value calculated by a bootstrap procedure.It is shown that the sizes of the proposed tests converge to the nominal level in both cases.If the null hypothesis is rejected in the case of unspecified cutpoint, a profile e stimator f or t he c utpoint t hat m aximizes t he d ifference in treatment effects i s p roposed.W e s how t hat t he e stimator h as c ubic-rate c onvergence and asymptotically follows a scaled Chernoff's d istribution.F urthermore, w e introduce an m-out-of-n bootstrap procedure to estimate the unknown scaling factor in the asymptotic distribution.Extensive simulation studies support our theory,