Physical Sciences and Mathematics Commons^™

A General Approach To Goodness Of Fit For U Processes, Debashis Ghosh, Youngjoo Cho

Debashis Ghosh

Goodness of fit procedures are essential tools for assessing model adequacy in statistics. In this work, we present a general theory and approach to goodness of fit techniques based on U-processes for the accelerated failure time (AFT) model. Many of the examples will focus on U-statistics of order 2. While many authors have proposed goodness of fit tests for U-statistics of order one, less has been developed for higher order U-statistics. In this paper, we propose goodness of fit tests for U-statistics of order 2 by using theoretical results from Nolan and Pollard (1987) and Nolan and Pollard (1988). We …

Hypothesis Testing For An Extended Cox Model With Time-Varying Coefficients, Takumi Saegusa, Chongzhi Di, Ying Qing Chen

Chongzhi Di

In many randomized clinical trials, the log-rank test has routinely been used to detect a treatment effect under the Cox proportional hazards model for censored time-to-event outcomes. However, it may lose power substantially when the proportional hazards assumption does not hold. There are approaches to testing the proportionality, such as the smoothing spline-based score test by Lin, Zhang and Davidian (2006). In this paper, we consider an extended Cox model assuming time-varying treatment effect. We then use smoothing splines to model the time-varying treatment effect, and we propose spline-based score tests for the overall treatment effect. Our proposed tests take …

A Causal Framework For Surrogate Endpoints With Semi-Competing Risks Data, Debashis Ghosh

Debashis Ghosh

In this note, we address the problem of surrogacy using a causal modelling framework that differs substantially from the potential outcomes model that pervades the biostatistical literature. The framework comes from econometrics and conceptualizes direct effects of the surrogate endpoint on the true endpoint. While this framework can incorporate the so-called semi-competing risks data structure, we also derive a fundamental non-identifiability result. Relationships to existing causal modelling frameworks are also discussed.

Meta-Analysis For Surrogacy: Accelerated Failure Time Models And Semicompeting Risks Modelling, Debashis Ghosh, Jeremy M. Taylor, Daniel J. Sargent

Debashis Ghosh

There has been great recent interest in the medical and statistical literature in the assessment and validation of surrogate endpoints as proxies for clinical endpoints in medical studies. More recently, authors have focused on using meta-analytical methods for quanti cation of surrogacy. In this article, we extend existing procedures for analysis based on the accelerated failure time model to this setting. An advantage of this approach relative to proportional hazards model is that it allows for analysis in the semi-competing risks setting, where we constrain the surrogate endpoint to occur before the true endpoint. A novel principal components procedure is …

Combining Multiple Models With Survival Data: The Phase Algorithm, Debashis Ghosh, Zheng Yuan

Debashis Ghosh

In many scientic studies, one common goal is to develop good prediction rules based on a set of available measurements. This paper proposes a model averaging methodology using proportional hazards regression models to construct new estimators of predicted survival probabilities. A screening step based on an adaptive searching algorithm is used to handle large numbers of covariates. The nite-sample properties of the proposed methodology is assessed using simulation studies. Application of the method to a cancer biomarker study is also given.

Composite Endpoint Analysis For Assessing Surrogacy With Censored Data, Debashis Ghosh

Debashis Ghosh

Background: There is great interest in the development of surrogate endpoints using new technologies in medical research. The promise of such endpoints is that they would allow for faster completion of clinical trials and would be potentially cost-effective.

Purpose: In determining surrogacy, it is important to distinguish the roles of surrogate from the true endpoint. The latter should be thought of as the gold standard. We discuss a framework in which the utility of a surrogate endpoint is based on whether or not as part of a composite endpoint, it yields treatment effects that associate with that on the true …