Statistical Models Commons^™

Linear Life Expectancy Regression With Censored Data, Ying Qing Chen, Su-Chun Cheng

U.C. Berkeley Division of Biostatistics Working Paper Series

Life expectancy, i.e., mean residual life function, has been of important practical and scientific interests to characterise the distribution of residual life. Regression models are often needed to model the association between life expectancy and its covariates. In this article, we consider a linear mean residual life model and further developed some inference procedures in presence of censoring. The new model and proposed inference procedure will be demonstrated by numerical examples and application to the well-known Stanford heart transplant data. Additional semiparametric efficiency calculation and information bound are also considered.

The Optimal Confidence Region For A Random Parameter, Hajime Uno, Lu Tian, L.J. Wei

Harvard University Biostatistics Working Paper Series

Under a two-level hierarchical model, suppose that the distribution of the random parameter is known or can be estimated well. Data are generated via a fixed, but unobservable realization of this parameter. In this paper, we derive the smallest confidence region of the random parameter under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is appealing when one deals with data generated under a highly parallel structure, for example, data from a trial with a large number of clinical centers involved or genome-wide …

A Note On Empirical Likelihood Inference Of Residual Life Regression, Ying Qing Chen, Yichuan Zhao

U.C. Berkeley Division of Biostatistics Working Paper Series

Mean residual life function, or life expectancy, is an important function to characterize distribution of residual life. The proportional mean residual life model by Oakes and Dasu (1990) is a regression tool to study the association between life expectancy and its associated covariates. Although semiparametric inference procedures have been proposed in the literature, the accuracy of such procedures may be low when the censoring proportion is relatively large. In this paper, the semiparametric inference procedures are studied with an empirical likelihood ratio method. An empirical likelihood confidence region is constructed for the regression parameters. The proposed method is further compared …

Semiparametric Quantitative-Trait-Locus Mapping: I. On Functional Growth Curves, Ying Qing Chen, Rongling Wu

U.C. Berkeley Division of Biostatistics Working Paper Series

The genetic study of certain quantitative traits in growth curves as a function of time has recently been of major scientific interest to explore the developmental evolution processes of biological subjects. Various parametric approaches in the statistical literature have been proposed to study the quantitative-trait-loci (QTL) mapping of the growth curves as multivariate outcomes. In this article, we view the growth curves as functional quantitative traits and propose some semiparametric models to relax the strong parametric assumptions which may not be always practical in reality. Appropriate inference procedures are developed to estimate the parameters of interest which characterise the possible …

Semiparametric Quantitative-Trait-Locus Mapping: Ii. On Censored Age-At-Onset, Ying Qing Chen, Chengcheng Hu, Rongling Wu

U.C. Berkeley Division of Biostatistics Working Paper Series

In genetic studies, the variation in genotypes may not only affect different inheritance patterns in qualitative traits, but may also affect the age-at-onset as quantitative trait. In this article, we use standard cross designs, such as backcross or F2, to propose some hazard regression models, namely, the additive hazards model in quantitative trait loci mapping for age-at-onset, although the developed method can be extended to more complex designs. With additive invariance of the additive hazards models in mixture probabilities, we develop flexible semiparametric methodologies in interval regression mapping without heavy computing burden. A recently developed multiple comparison procedures is adapted …

Nonparametric Methods For Analyzing Replication Origins In Genomewide Data, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

Due to the advent of high-throughput genomic technology, it has become possible to globally monitor cellular activities on a genomewide basis. With these new methods, scientists can begin to address important biological questions. One such question involves the identification of replication origins, which are regions in chromosomes where DNA replication is initiated. In addition, one hypothesis regarding replication origins is that their locations are non-random throughout the genome. In this article, we develop methods for identification of and cluster inference regarding replication origins involving genomewide expression data. We compare several nonparametric regression methods for the identification of replication origin locations. …

The False Discovery Rate: A Variable Selection Perspective, Debashis Ghosh, Wei Chen, Trivellore E. Raghuanthan

The University of Michigan Department of Biostatistics Working Paper Series

In many scientific and medical settings, large-scale experiments are generating large quantities of data that lead to inferential problems involving multiple hypotheses. This has led to recent tremendous interest in statistical methods regarding the false discovery rate (FDR). Several authors have studied the properties involving FDR in a univariate mixture model setting. In this article, we turn the problem on its side; in this manuscript, we show that FDR is a by-product of Bayesian analysis of variable selection problem for a hierarchical linear regression model. This equivalence gives many Bayesian insights as to why FDR is a natural quantity to …

Semiparametric Regression Analysis Of Mean Residual Life With Censored Survival Data, Ying Qing Chen, Su-Chun Cheng

U.C. Berkeley Division of Biostatistics Working Paper Series

As a function of time t, mean residual life is the remaining life expectancy of a subject given survival up to t. The proportional mean residual life model, proposed by Oakes & Dasu (1990), provides an alternative to the Cox proportional hazards model to study the association between survival times and covariates. In the presence of censoring, we develop semiparametric inference procedures for the regression coefficients of the Oakes-Dasu model using martingale theory for counting processes. We also present simulation studies and an application to the Veterans' Administration lung cancer data.

Nonparametric And Semiparametric Inference For Models Of Tumor Size And Metastasis, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

There has been some recent work in the statistical literature for modelling the relationship between the size of primary cancers and the occurrences of metastases. While nonparametric methods have been proposed for estimation of the tumor size distribution at which metastatic transition occurs, their asymptotic properties have not been studied. In addition, no testing or regression methods are available so that potential confounders and prognostic factors can be adjusted for. We develop a unified approach to nonparametric and semiparametric analysis of modelling tumor size-metastasis data in this article. An equivalence between the models considered by previous authors with survival data …

Semiparametic Models And Estimation Procedures For Binormal Roc Curves With Multiple Biomarkers, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

In diagnostic medicine, there is great interest in developing strategies for combining biomarkers in order to optimize classification accuracy. A popular model that has been used for receiver operating characteristic (ROC) curve modelling when one biomarker is available is the binormal model. Extension of the model to accommodate multiple biomarkers has not been considered in this literature. Here, we consider a multivariate binormal framework for combining biomarkers using copula functions that leads to a natural multivariate extension of the binormal model. Estimation in this model will be done using rank-based procedures. We show that the Van der Waerden rank score …

On Corrected Score Approach For Proportional Hazards Model With Covariate Measurement Error, Xiao Song, Yijian Huang

UW Biostatistics Working Paper Series

In the presence of covariate measurement error with the proportional hazards model, several functional modeling methods have been proposed. These include the conditional score estimator (Tsiatis and Davidian, 2001), the parametric correction estimator (Nakamura, 1992) and the nonparametric correction estimator (Huang and Wang, 2000, 2003) in the order of weaker assumptions on the error. Although they are all consistent, each suffers from potential difficulties with small samples and substantial measurement error. In this article, upon noting that the conditional score and parametric correction estimators are asymptotically equivalent in the case of normal error, we investigate their relative finite sample performance …

Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms In Estimation, Sandra E. Sinisi, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In van der Laan and Dudoit (2003) we propose and theoretically study a unified loss function based statistical methodology, which provides a road map for estimation and performance assessment. Given a parameter of interest which can be described as the minimizer of the population mean of a loss function, the road map involves as important ingredients cross-validation for estimator selection and minimizing over subsets of basis functions the empirical risk of the subset-specific estimator of the parameter of interest, where the basis functions correspond to a parameterization of a specified subspace of the complete parameter space. In this article we …

Robust Likelihood-Based Analysis Of Multivariate Data With Missing Values, Rod Little, An Hyonggin

The University of Michigan Department of Biostatistics Working Paper Series

The model-based approach to inference from multivariate data with missing values is reviewed. Regression prediction is most useful when the covariates are predictive of the missing values and the probability of being missing, and in these circumstances predictions are particularly sensitive to model misspecification. The use of penalized splines of the propensity score is proposed to yield robust model-based inference under the missing at random (MAR) assumption, assuming monotone missing data. Simulation comparisons with other methods suggest that the method works well in a wide range of populations, with little loss of efficiency relative to parametric models when the latter …

Unified Cross-Validation Methodology For Selection Among Estimators And A General Cross-Validated Adaptive Epsilon-Net Estimator: Finite Sample Oracle Inequalities And Examples, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

In Part I of this article we propose a general cross-validation criterian for selecting among a collection of estimators of a particular parameter of interest based on n i.i.d. observations. It is assumed that the parameter of interest minimizes the expectation (w.r.t. to the distribution of the observed data structure) of a particular loss function of a candidate parameter value and the observed data structure, possibly indexed by a nuisance parameter. The proposed cross-validation criterian is defined as the empirical mean over the validation sample of the loss function at the parameter estimate based on the training sample, averaged over …

Estimating Predictors For Long- Or Short-Term Survivors, Lu Tian, Wei Wang, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Smooth Quantile Ratio Estimation With Regression: Estimating Medical Expenditures For Smoking Attributable Diseases, Francesca Dominici, Scott L. Zeger

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper we introduce a semi-parametric regression model for estimating the difference in the expected value of two positive and highly skewed random variables as a function of covariates. Our method extends Smooth Quantile Ratio Estimation (SQUARE), a novel estimator of the mean difference of two positive random variables, to a regression model.

The methodological development of this paper is motivated by a common problem in econometrics where we are interested in estimating the difference in the average expenditures between two populations, say with and without a disease, taking covariates into account. Let Y1 and Y2 be two positive …

A Nonparametric Comparison Of Conditional Distributions With Nonnegligible Cure Fractions, Yi Li, Jin Feng

Harvard University Biostatistics Working Paper Series

No abstract provided.

Survival Analysis With Heterogeneous Covariate Measurement Error, Yi Li, Louise Ryan

Harvard University Biostatistics Working Paper Series

No abstract provided.

Loss Function Based Ranking In Two-Stage, Hierarchical Models, Rongheng Lin, Thomas A. Louis, Susan M. Paddock, Greg Ridgeway

Johns Hopkins University, Dept. of Biostatistics Working Papers

Several authors have studied the performance of optimal, squared error loss (SEL) estimated ranks. Though these are effective, in many applications interest focuses on identifying the relatively good (e.g., in the upper 10%) or relatively poor performers. We construct loss functions that address this goal and evaluate candidate rank estimates, some of which optimize specific loss functions. We study performance for a fully parametric hierarchical model with a Gaussian prior and Gaussian sampling distributions, evaluating performance for several loss functions. Results show that though SEL-optimal ranks and percentiles do not specifically focus on classifying with respect to a percentile cut …

Joint Modeling And Estimation For Recurrent Event Processes And Failure Time Data, Chiung-Yu Huang, Mei-Cheng Wang

Johns Hopkins University, Dept. of Biostatistics Working Papers

Recurrent event data are commonly encountered in longitudinal follow-up studies related to biomedical science, econometrics, reliability, and demography. In many studies, recurrent events serve as important measurements for evaluating disease progression, health deterioration, or insurance risk. When analyzing recurrent event data, an independent censoring condition is typically required for the construction of statistical methods. Nevertheless, in some situations, the terminating time for observing recurrent events could be correlated with the recurrent event process and, as a result, the assumption of independent censoring is violated. In this paper, we consider joint modeling of a recurrent event process and a failure time …

Semi-Parametric Box-Cox Power Transformation Models For Censored Survival Observations, Tianxi Cai, Lu Tian, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Unification Of Variance Components And Haseman-Elston Regression For Quantitative Trait Linkage Analysis, Wei-Min Chen, Karl W. Broman, Kung-Yee Liang

Johns Hopkins University, Dept. of Biostatistics Working Papers

Two of the major approaches for linkage analysis with quantitative traits in humans include variance components and Haseman-Elston regression. Previously, these have been viewed as quite separate methods. We describe a general model, fit by use of generalized estimating equations (GEE), for which the variance components and Haseman-Elston methods (including many of the extensions to the original Haseman-Elston method) are special cases, corresponding to different choices for a working covariance matrix. We also show that the regression-based test of Sham et al.(2002) is equivalent to a robust score statistic derived from our GEE approach. These results have several important implications. …

Smooth Quantile Ratio Estimation, Francesca Dominici, Leslie Cope, Daniel Q. Naiman, Scott L. Zeger

Johns Hopkins University, Dept. of Biostatistics Working Papers

In a study of health care expenditures attributable to smoking, we seek to compare the distribution of medical costs for persons with lung cancer or chronic obstructive pulmonary disease (cases) to those without (controls) using a national survey which includes hundreds of cases and thousands of controls. The distribution of costs is highly skewed toward larger values, making estimates of the mean from the smaller sample dependent on a small fraction of the biggest values. One approach to deal with the smaller sample is to rely on a simple parametric model such as the log-normal, but this makes the undesirable …

Statistical Inferences Based On Non-Smooth Estimating Functions, Lu Tian, Jun S. Liu, Mary Zhao, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

On The Cox Model With Time-Varying Regression Coefficients, Lu Tian, David Zucker, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Nonparametric Estimation Of The Bivariate Recurrence Time Distribution, Chiung-Yu Huang, Mei-Cheng Wang

Johns Hopkins University, Dept. of Biostatistics Working Papers

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution …

Efficient Semiparametric Marginal Estimation For Longitudinal/Clustered Data, Naisyin Wang, Raymond J. Carroll, Xihong Lin

The University of Michigan Department of Biostatistics Working Paper Series

We consider marginal generalized semiparametric partially linear models for clustered data. Lin and Carroll (2001a) derived the semiparametric efficinet score funtion for this problem in the mulitvariate Gaussian case, but they were unable to contruct a semiparametric efficient estimator that actually achieved the semiparametric information bound. We propose such an estimator here and generalize the work to marginal generalized partially liner models. Asymptotic relative efficincies of the estimation or throughout are investigated. The finite sample performance of these estimators is evaluated through simulations and illustrated using a longtiudinal CD4 count data set. Both theoretical and numerical results indicate that properly …

Equivalent Kernels Of Smoothing Splines In Nonparametric Regression For Clustered/Longitudinal Data, Xihong Lin, Naisyin Wang, Alan H. Welsh, Raymond J. Carroll

The University of Michigan Department of Biostatistics Working Paper Series

We compare spline and kernel methods for clustered/longitudinal data. For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, the recent work of Welsh, et al. (2002) shows that the same is not true for clustered/longitudinal data. First, conventional kernel methods fail to account for the within- cluster correlation, while spline methods are able to account for this correlation. Second, kernel methods and spline methods were found to have different local behavior, with conventional kernels being local and splines being non-local. To resolve these differences, we show that a smoothing …

Measuring Treatment Effects Using Semiparametric Models, Zhuo Yu, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In order to estimate the causal effect of treatments on an outcome of interest, one has to account for the effect of confounding factors which covary with the treatments and also contribute to the outcome of interest. In this paper, we use the semiparametric regression model to estimate the causal parameters. We assume the causal effect of the treatments can be described by the parametric component of the semiparametric regression model. Following the general methodology which was developed in van der Laan and Robins (2002) we give the orthogonal complement of the nuisance tangent space which identifies all the estimating …

Asymptotically Optimal Model Selection Method With Right Censored Outcomes, Sunduz Keles, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

Over the last two decades, non-parametric and semi-parametric approaches that adapt well known techniques such as regression methods to the analysis of right censored data, e.g. right censored survival data, became popular in the statistics literature. However, the problem of choosing the best model (predictor) among a set of proposed models (predictors) in the right censored data setting have not gained much attention. In this paper, we develop a new cross-validation based model selection method to select among predictors of right censored outcomes such as survival times. The proposed method considers the risk of a given predictor based on the …