Abstract

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 is p roposed. We show that the estimator has cubic-rate convergence and

asymptotically follows a scaled Chernoff’s d istribution. Furthermore, we introduce an m-out-of-n bootstrap procedure to estimate the unknown scaling factor

in the asymptotic distribution. Extensive simulation studies support our theory,

and the proposed procedures are applied to a dataset from a clinical trial on

advanced colorectal cancer.

Information

Preprint No.SS-2025-0076
Manuscript IDSS-2025-0076
Complete AuthorsZehui Wang, Yanglei Song, Wenyu Jiang, Dongsheng Tu
Corresponding AuthorsDongsheng Tu
Emailsdtu@ctg.queensu.ca

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Supplementary Materials

The proofs and more simulation results are presented in the SMs.

Supplementary materials are available for download.