Browsing by Author "Rosner, Gary L."

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    A dynamic model for survival data with longitudinal covariates
    (2006) Rudnicki, Krzysztof Janusz; Rosner, Gary L.
    Analyses involving both longitudinal and time-to-event data are quite common in medical research. The primary goal of such studies may be to simultaneously study the effect of treatment on both the longitudinal covariate and survival, but secondary objectives, such as understanding the within-patients patterns of change of the time-dependent marker, or the relationship between the marker's profiles and the occurrence of the event of interest, are often considered. Currently available methods of analyzing survival and longitudinal data usually introduce many undesirable and sometimes unreasonable assumptions. We introduce two flexible Bayesian hierarchical modeling approaches for analyzing these two types of data by use of dynamic models and survival analysis methods. In both approaches the longitudinal covariate is modeled via dynamic hierarchical models which allow the shapes of the longitudinal trajectories to be determined by the data rather than by the assumed parametric model. The trajectories are patient specific, and the link between them is provided by the hierarchical structure of the model, allowing borrowing of strength across patients. In the survival part of the model, the first method, referred to as 2-Stage model, uses the estimates of the longitudinal trajectories obtained in the first stage of the analysis, as a time-dependent covariate in the Cox PH model, to find the estimates of the corresponding survival model parameters. The second approach, called the joint model, assumes the piecewise exponential distribution for the event times of the patients and uses a discretized version of the Cox PH model. Some of the parameters of this survival model are also allowed to change over time, and again, dynamic models provide the description of the stochastic evolution of these parameters. A combination of various MCMC techniques is used to obtain a sample from the joint posterior distributions of all the model parameters. This distribution combines the likelihood of the longitudinal and survival data and the prior knowledge about the parameters. Simulation studies provide the measure of the quality of the method and both models are compared to one of the currently existing approaches.
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    Bayesian optimal design for phase II screening trials
    (2006) Ding, Meichun; Rosner, Gary L.
    Rapid progress in biomedical research necessitates clinical evaluation that identifies promising innovations quickly and efficiently. Rapid evaluation is especially important if the number of innovations is large compared to the supply of suitable study patients. Most phase II screening designs available in the literature consider one treatment at a time. Each study is considered in isolation. We propose a more systematic decision-making approach to the phase II screening process. The sequential study design allows for more efficiency and greater learning about treatments. The approach incorporates a Bayesian hierarchical model that allows combining information across several related studies in a formal way and improves estimation in small data sets by borrowing strength from other treatments. The underlying probability model is a hierarchical probit regression model that also allows for treatment-specific covariates. The design criterion is to maximize the utility for the new treatment, a sampling cost per patient, and the possible demonstration of a significant treatment benefit in a future randomized clinical trial. Computer simulations show that, this method has high probabilities of discarding treatments with low success rates and moving treatments with high success rates to phase III trial. Compared to the fully sequential design proposed by Wang and Leung's in 1998 Biometrics, this method provides a smaller number of patients required to screen out the first promising treatment and has better design characteristics.
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    Effect on Prediction When Modeling Covariates in Bayesian Nonparametric Models
    (Springer Nature, 2013) Cruz-Marcelo, Alejandro; Rosner, Gary L.; Müller, Peter; Stewart, Clinton F.; Center for Computational Finance and Economic Systems
    In biomedical research, it is often of interest to characterize biologic processes giving rise to observations and to make predictions of future observations. Bayesian nonparamric methods provide a means for carrying out Bayesian inference making as few assumptions about restrictive parametric models as possible. There are several proposals in the literature for extending Bayesian nonparametric models to include dependence on covariates. In this article, we examine the effect on fitting and predictive performance of incorporating covariates in a class of Bayesian nonparametric models by one of two primary ways: either in the weights or in the locations of a discrete random probability measure. We show that different strategies for incorporating continuous covariates in Bayesian nonparametric models can result in big differences when used for prediction, even though they lead to otherwise similar posterior inferences. When one needs the predictive density, as in optimal design, and this density is a mixture, it is better to make the weights depend on the covariates. We demonstrate these points via a simulated data example and in an application in which one wants to determine the optimal dose of an anticancer drug used in pediatric oncology.
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    Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds
    (Taylor & Francis, 2011) Cruz-Marcelo, Alejandro; Ensor, Katherine B.; Rosner, Gary L.
    The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material.
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    Modeling Covariates with Nonparametric Bayesian Methods
    (SSRN, 2010) Cruz-Marcelo, Alejandro; Rosner, Gary L.; Mueller, Peter; Stewart, Clinton; Center for Computational Finance and Economic Systems
    A research problem that has received increased attention in recent years is extending Bayesian nonparametric methods to include dependence on covariates. Limited attention, however, has been directed to the following two aspects. First, analyzing how the performance of such extensions differs, and second, understanding which features are worthwhile in order to produce better results. This article proposes answers to those questions focusing on predictive inference and continuous covariates. Specifically, we show that 1) nonparametric models using different strategies for modeling continuous covariates can show noteworthy differences when they are being used for prediction, even though they produce otherwise similar posterior inference results, and 2) when the predictive density is a mixture, it is convenient to make the weights depend on the covariates in order to produce sensible estimators. Such claims are supported by comparing the Linear DDP (an extension of the Sethuraman representation) and the Conditional DP (which augments the nonparametric distribution to include the covariates). Unlike the Conditional DP, the weights in the predictive mixture density of the Linear DDP are not covariate-dependent. This results in poor estimators of the predictive density. Specifically, in a simulation example, the Linear DDP wrongly introduces an additional mode into the predictive density, while in an application to a pharmacokinetic study, it produces unrealistic concentration-time curves.