Semiparametric single-index models for optimal treatment regimens with censored outcomes

Jin Wang (), Donglin Zeng () and D. Y. Lin ()
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Jin Wang: University Of North Carolina
Donglin Zeng: University Of North Carolina
D. Y. Lin: University Of North Carolina

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2022, vol. 28, issue 4, No 11, 744-763

Abstract: Abstract There is a growing interest in precision medicine, where a potentially censored survival time is often the most important outcome of interest. To discover optimal treatment regimens for such an outcome, we propose a semiparametric proportional hazards model by incorporating the interaction between treatment and a single index of covariates through an unknown monotone link function. This model is flexible enough to allow non-linear treatment-covariate interactions and yet provides a clinically interpretable linear rule for treatment decision. We propose a sieve maximum likelihood estimation approach, under which the baseline hazard function is estimated nonparametrically and the unknown link function is estimated via monotone quadratic B-splines. We show that the resulting estimators are consistent and asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound. The optimal treatment rule follows naturally as a linear combination of the maximum likelihood estimators of the model parameters. Through extensive simulation studies and an application to an AIDS clinical trial, we demonstrate that the treatment rule derived from the single-index model outperforms the treatment rule under the standard Cox proportional hazards model.

Keywords: B-spline; Nonparametric maximum likelihood; Precision medicine; Proportional hazards; Survival data; Treatment decision (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10985-022-09566-4

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