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Full-Text Articles in Physical Sciences and Mathematics
The Predictive Hazard Ratio For Biomarker Evaluation Studies, Debashis Ghosh
The Predictive Hazard Ratio For Biomarker Evaluation Studies, Debashis Ghosh
Debashis Ghosh
There is tremendous scientific and medical interest in the use of biomarkers to better facilitate medical decision making. In this article, we present a simple framework for assessing the predictive ability of a biomarker. The methodology requires use of techniques from a subfield of survival analysis termed semicompeting risks; results are presented to make the article self-contained. A crucial parameter for evaluating is the predictive hazard ratio, which is different from the usual hazard ratio from Cox regression models for right-censored data. This quantity will be defined; its estimation, inference and adjustment for covariates will be discussed. Aspects of censoring …
On The Spectral Decomposition For Kernel Machines, Debashis Ghosh
On The Spectral Decomposition For Kernel Machines, Debashis Ghosh
Debashis Ghosh
Recently, a class of machine learning-inspired procedures, termed kernel machine methods, has been extensively developed in the statistical literature. It has been shown to have large power for a wide class of problems and applications in genomics and brain imaging. Many authors have exploited an equivalence between kernel machines and mixed effects models and used attendant estimation and inferential procedures. In this note, we explore the theoretical foundations of the kernel machine using a spectral decomposition. This leads to simple characterizations of the kernel machine procedure and its bias and variance properties. In addition, we construct a so-called `adaptively minimax' …
Penalized Regression Procedures For Variable Selection In The Potential Outcomes Framework, Debashis Ghosh, Yeying Zhu, Donna L. Coffman
Penalized Regression Procedures For Variable Selection In The Potential Outcomes Framework, Debashis Ghosh, Yeying Zhu, Donna L. Coffman
Debashis Ghosh
A recent topic of much interest in causal inference is model selection. In this article, we describe a framework in which to consider penalized regression approaches to variable selection for causal effects. The framework leads to a simple `impute, then select' class of procedures that is agnostic to the type of imputation algorithm as well as penalized regression used. It also clarifies how model selection involves a multivariate regression model, and that these methods can be applied for identifying subgroups in which treatment effects are homogeneous. Analogies and links with the literature on machine learning methods, missing data and imputation …
A Data-Adaptive Strategy For Inverse Weighted Estimation Of Causal Effects, Yeying Zhu, Debashis Ghosh, Bhramar Mukherjee, Nandita Mitra
A Data-Adaptive Strategy For Inverse Weighted Estimation Of Causal Effects, Yeying Zhu, Debashis Ghosh, Bhramar Mukherjee, Nandita Mitra
Debashis Ghosh
In most nonrandomized observational studies, differences between treatment groups may arise not only due to the treatment but also because of the effect of confounders. Therefore, causal inference regarding the treatment effect is not as straightforward as in a randomized trial. To adjust for confounding due to measured covariates, the average treatment effect is often estimated by using propensity scores. In this article, we focus on the use of inverse probability weighted (IPW) estimation methods. Typically, propensity scores are estimated by logistic regression. More recent suggestions have been to employ nonparametric classification algorithms from machine learning. In this article, we …