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Numerical Analysis and Computation Commons™
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Articles 1 - 11 of 11
Full-Text Articles in Numerical Analysis and Computation
Optimization And Simulation Of An Evolving Kidney Paired Donation (Kpd) Program, Yijiang Li, Jack Kalbfleisch, Peter Xuekun Song, Yan Zhou, Alan Leichtman, Michael Rees
Optimization And Simulation Of An Evolving Kidney Paired Donation (Kpd) Program, Yijiang Li, Jack Kalbfleisch, Peter Xuekun Song, Yan Zhou, Alan Leichtman, Michael Rees
The University of Michigan Department of Biostatistics Working Paper Series
The old concept of barter exchange has extended to the modern area of living-donor kidney transplantation, where one incompatible donor-candidate pair is matched to another pair with a complementary incompatibility, such that the donor from one pair gives an organ to a compatible candidate in the other pair and vice versa. Kidney paired donation (KPD) programs provide a unique and important platform for living incompatible donor-candidate pairs to exchange organs in order to achieve mutual benefit. We propose a novel approach to organizing kidney exchanges in an evolving KPD program with advantages, including (i) it allows for a more exible …
A Hybrid Newton-Type Method For The Linear Regression In Case-Cohort Studies, Menggang Yu, Bin Nan
A Hybrid Newton-Type Method For The Linear Regression In Case-Cohort Studies, Menggang Yu, Bin Nan
The University of Michigan Department of Biostatistics Working Paper Series
Case-cohort designs are increasingly commonly used in large epidemiological cohort studies. Nan, Yu, and Kalbeisch (2004) provided the asymptotic results for censored linear regression models in case-cohort studies. In this article, we consider computational aspects of their proposed rank based estimating methods. We show that the rank based discontinuous estimating functions for case-cohort studies are monotone, a property established for cohort data in the literature, when generalized Gehan type of weights are used. Though the estimating problem can be formulated to a linear programming problem as that for cohort data, due to its easily uncontrollable large scale even for a …
Survival Analysis Using Auxiliary Variables Via Nonparametric Multiple Imputation, Chiu-Hsieh Hsu, Jeremy Taylor, Susan Murray, Daniel Commenges
Survival Analysis Using Auxiliary Variables Via Nonparametric Multiple Imputation, Chiu-Hsieh Hsu, Jeremy Taylor, Susan Murray, Daniel Commenges
The University of Michigan Department of Biostatistics Working Paper Series
We develop an approach, based on multiple imputation, that estimates the marginal survival distribution in survival analysis using auxiliary variable to recover information for censored observations. To conduct the imputation, we use two working survival model to define the nearest neighbor imputing risk set. One model is for the event times and the other for the censoring times. Based on the imputing risk set, two nonparametric multiple imputation methods are considered: risk set imputation, and Kaplan-Meier estimator. For both methods a future event or censoring time is imputed for each censored observation. With a categorical auxiliary variable, we show that …
A Bayesian Mixture Model Relating Dose To Critical Organs And Functional Complication In 3d Conformal Radiation Therapy, Tim Johnson, Jeremy Taylor, Randall K. Ten Haken, Avraham Eisbruch
A Bayesian Mixture Model Relating Dose To Critical Organs And Functional Complication In 3d Conformal Radiation Therapy, Tim Johnson, Jeremy Taylor, Randall K. Ten Haken, Avraham Eisbruch
The University of Michigan Department of Biostatistics Working Paper Series
A goal of radiation therapy is to deliver maximum dose to the target tumor while minimizing complications due to irradiation of critical organs. Technological advances in 3D conformal radiation therapy has allowed great strides in realizing this goal, however complications may still arise. Critical organs may be adjacent to tumors or in the path of the radiation beam. Several mathematical models have been proposed that describe a relationship between dose and observed functional complication, however only a few published studies have successfully fit these models to data using modern statistical methods which make efficient use of the data. One complication …
A Bayesian Method For Finding Interactions In Genomic Studies, Wei Chen, Debashis Ghosh, Trivellore E. Raghuanthan, Sharon Kardia
A Bayesian Method For Finding Interactions In Genomic Studies, Wei Chen, Debashis Ghosh, Trivellore E. Raghuanthan, Sharon Kardia
The University of Michigan Department of Biostatistics Working Paper Series
An important step in building a multiple regression model is the selection of predictors. In genomic and epidemiologic studies, datasets with a small sample size and a large number of predictors are common. In such settings, most standard methods for identifying a good subset of predictors are unstable. Furthermore, there is an increasing emphasis towards identification of interactions, which has not been studied much in the statistical literature. We propose a method, called BSI (Bayesian Selection of Interactions), for selecting predictors in a regression setting when the number of predictors is considerably larger than the sample size with a focus …
Finding Cancer Subtypes In Microarray Data Using Random Projections, Debashis Ghosh
Finding Cancer Subtypes In Microarray Data Using Random Projections, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
One of the benefits of profiling of cancer samples using microarrays is the generation of molecular fingerprints that will define subtypes of disease. Such subgroups have typically been found in microarray data using hierarchical clustering. A major problem in interpretation of the output is determining the number of clusters. We approach the problem of determining disease subtypes using mixture models. A novel estimation procedure of the parameters in the mixture model is developed based on a combination of random projections and the expectation-maximization algorithm. Because the approach is probabilistic, our approach provides a measure for the number of true clusters …
Resampling Methods For Estimating Functions With U-Statistic Structure, Wenyu Jiang, Jack Kalbfleisch
Resampling Methods For Estimating Functions With U-Statistic Structure, Wenyu Jiang, Jack Kalbfleisch
The University of Michigan Department of Biostatistics Working Paper Series
Suppose that inference about parameters of interest is to be based on an unbiased estimating function that is U-statistic of degree 1 or 2. We define suitable studentized versions of such estimating functions and consider asymptotic approximations as well as an estimating function bootstrap (EFB) method based on resampling the estimated terms in the estimating functions. These methods are justified asymptotically and lead to confidence intervals produced directly from the studentized estimating functions. Particular examples in this class of estimating functions arise in La estimation as well as Wilcoxon rank regression and other related estimation problems. The proposed methods are …
Maximum Likelihood Estimation Of Ordered Multinomial Parameters , Nicholas P. Jewell, Jack Kalbfleisch
Maximum Likelihood Estimation Of Ordered Multinomial Parameters , Nicholas P. Jewell, Jack Kalbfleisch
The University of Michigan Department of Biostatistics Working Paper Series
The pool-adjacent violator-algorithm (Ayer et al., 1955) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see, Barlow et al., 1972). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of ‘ordered’ multinomial parameters pi = (p1i, p2i, . . . , pmi) for 1 < = I < = k, where ordered means that pj1 < = pj2 < = .. . < = pjk for each j with 1 < = j < = m-1. The data consist of k independent observations X1, . . . ,Xk where Xi has a multinomial distribution with probability parameter pi and known index ni > = 1. By making use of variants of the pool adjacent violator algorithm, …
A Population Pharmacokinetic Model With Time-Dependent Covariates Measured With Errors, Lang Lil, Xihong Lin, Mort B. Brown, Suneel Gupta, Kyung-Hoon Lee
A Population Pharmacokinetic Model With Time-Dependent Covariates Measured With Errors, Lang Lil, Xihong Lin, Mort B. Brown, Suneel Gupta, Kyung-Hoon Lee
The University of Michigan Department of Biostatistics Working Paper Series
We propose a population pharmacokinetic (PK) model with time-dependent covariates measured with errors. This model is used to model S-oxybutynin's kinetics following an oral administration of Ditropan, and allows the distribution rate to depend on time-dependent covariates blood pressure and heart rate, which are measured with errors. We propose two two-step estimation methods: the second order two-step method with numerical solutions of differential equations (2orderND), and the second order two-step method with closed form approximate solutions of differential equations (2orderAD). The proposed methods are computationally easy and require fitting a linear mixed model at the first step and a nonlinear …
An Extended General Location Model For Causal Inference From Data Subject To Noncompliance And Missing Values, Yahong Peng, Rod Little, Trivellore E. Raghuanthan
An Extended General Location Model For Causal Inference From Data Subject To Noncompliance And Missing Values, Yahong Peng, Rod Little, Trivellore E. Raghuanthan
The University of Michigan Department of Biostatistics Working Paper Series
Noncompliance is a common problem in experiments involving randomized assignment of treatments, and standard analyses based on intention-to treat or treatment received have limitations. An attractive alternative is to estimate the Complier-Average Causal Effect (CACE), which is the average treatment effect for the subpopulation of subjects who would comply under either treatment (Angrist, Imbens and Rubin, 1996, henceforth AIR). We propose an Extended General Location Model to estimate the CACE from data with non-compliance and missing data in the outcome and in baseline covariates. Models for both continuous and categorical outcomes and ignorable and latent ignorable (Frangakis and Rubin, 1999) …
Maximization By Parts In Likelihood Inference, Peter Xuekun Song, Yanqin Fan, Jack Kalbfleisch
Maximization By Parts In Likelihood Inference, Peter Xuekun Song, Yanqin Fan, Jack Kalbfleisch
The University of Michigan Department of Biostatistics Working Paper Series
This paper presents and examines a new algorithm for solving a score equation for the maximum likelyhood estimate in certain problems of practical interest. The method circumvents the need to compute second order derivaties of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log likelihood from a simply analyzed model and the second part is used to update estimates from the first. Convergence properties of this fixed point algorithm are examined and asymptotics are derived for estimators obtained …