Abstract
Individuals differ in how they respond to a given treatment. In an effort to predict the treatment response and analyze the heterogeneity of treatment effect, we propose a general modeling framework by identifying treatment-covariate interactions honoring a hierarchical condition. We construct a single-step (Formula presented.) norm penalty procedure that maintains the hierarchical structure of interactions in the sense that a treatment-covariate interaction term is included in the model only when either the covariate or both the covariate and treatment have nonzero main effects. We developed a constrained Lasso approach with two parameterization schemes that enforce the hierarchical interaction restriction differently. We solved the resulting constrained optimization problem using a spectral projected gradient method. We compared our methods to the unstructured Lasso using simulation studies including a scenario that violates the hierarchical condition (misspecified model). The simulations showed that our methods yielded more parsimonious models and outperformed the unstructured Lasso for correctly identifying nonzero treatment-covariate interactions. The superior performance of our methods are also corroborated by an application to a large randomized clinical trial data investigating a drug for treating congestive heart failure (N = 2569). Our methods provide a well-suited approach for doing secondary analysis in clinical trials to analyze heterogeneous treatment effects and to identify predictive biomarkers.
Original language | English (US) |
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Pages (from-to) | 5417-5433 |
Number of pages | 17 |
Journal | Statistics in Medicine |
Volume | 40 |
Issue number | 25 |
DOIs | |
State | Published - Nov 10 2021 |
Keywords
- Lasso
- heterogeneity of treatment effect
- hierarchical interaction
- treatment-covariate interaction
ASJC Scopus subject areas
- Epidemiology
- Statistics and Probability