Survival Analysis Commons^™

Nonparametric Regression Using Local Kernel Estimating Equations For Correlated Failure Time Data, Zhangsheng Yu, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Semiparametric Maximum Likelihood Estimation In Normal Transformation Models For Bivariate Survival Data, Yi Li, Ross L. Prentice, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Note On Targeted Maximum Likelihood And Right Censored Data, Mark J. Van Der Laan, Daniel Rubin

U.C. Berkeley Division of Biostatistics Working Paper Series

A popular way to estimate an unknown parameter is with substitution, or evaluating the parameter at a likelihood based fit of the data generating density. In many cases, such estimators have substantial bias and can fail to converge at the parametric rate. van der Laan and Rubin (2006) introduced targeted maximum likelihood learning, removing these shackles from substitution estimators, which were made in full agreement with the locally efficient estimating equation procedures as presented in Robins and Rotnitzsky (1992) and van der Laan and Robins (2003). This note illustrates how targeted maximum likelihood can be applied in right censored data …

Empirical Efficiency Maximization, Daniel B. Rubin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

It has long been recognized that covariate adjustment can increase precision, even when it is not strictly necessary. The phenomenon is particularly emphasized in clinical trials, whether using continuous, categorical, or censored time-to-event outcomes. Adjustment is often straightforward when a discrete covariate partitions the sample into a handful of strata, but becomes more involved when modern studies collect copious amounts of baseline information on each subject.

The dilemma helped motivate locally efficient estimation for coarsened data structures, as surveyed in the books of van der Laan and Robins (2003) and Tsiatis (2006). Here one fits a relatively small working model …

Survival Analysis With Large Dimensional Covariates: An Application In Microarray Studies, David A. Engler, Yi Li

Harvard University Biostatistics Working Paper Series

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time …

Spatial Cluster Detection For Censored Outcome Data, Andrea J. Cook, Diane Gold, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

Doubly Robust Censoring Unbiased Transformations, Daniel Rubin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We consider random design nonparametric regression when the response variable is subject to right censoring. Following the work of Fan and Gijbels (1994), a common approach to this problem is to apply what has been termed a censoring unbiased transformation to the data to obtain surrogate responses, and then enter these surrogate responses with covariate data into standard smoothing algorithms. Existing censoring unbiased transformations generally depend on either the conditional survival function of the response of interest, or that of the censoring variable. We show that a mapping introduced in another statistical context is in fact a censoring unbiased transformation …

The Two-Sample Problem For Failure Rates Depending On A Continuous Mark: An Application To Vaccine Efficacy, Peter B. Gilbert, Ian W. Mckeague, Yanqing Sun

UW Biostatistics Working Paper Series

The efficacy of an HIV vaccine to prevent infection is likely to depend on the genetic variation of the exposing virus. This paper addresses the problem of using data on the HIV sequences that infect vaccine efficacy trial participants to 1) test for vaccine efficacy more powerfully than procedures that ignore the sequence data; and 2) evaluate the dependence of vaccine efficacy on the divergence of infecting HIV strains from the HIV strain that is contained in the vaccine. Because hundreds of amino acid sites in each HIV genome are sequenced, it is natural to treat the divergence (defined in …

Evaluating Prediction Rules For T-Year Survivors With Censored Regression Models, Hajime Uno, Tianxi Cai, Lu Tian, L.J. Wei

Harvard University Biostatistics Working Paper Series

Suppose that we are interested in establishing simple, but reliable rules for predicting future t-year survivors via censored regression models. In this article, we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models we derive consistent estimators for the above measures via substitution and cross validation estimation procedures. Furthermore, we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, …

Designed Extension Of Survival Studies: Application To Clinical Trials With Unrecognized Heterogeneity, Yi Li, Mei-Chiung Shih, Rebecca A. Betensky

Harvard University Biostatistics Working Paper Series

It is well known that unrecognized heterogeneity among patients, such as is conferred by genetic subtype, can undermine the power of randomized trial, designed under the assumption of homogeneity, to detect a truly beneficial treatment. We consider the conditional power approach to allow for recovery of power under unexplained heterogeneity. While Proschan and Hunsberger (1995) confined the application of conditional power design to normally distributed observations, we consider more general and difficult settings in which the data are in the framework of continuous time and are subject to censoring. In particular, we derive a procedure appropriate for the analysis of …

Mixture Cure Survival Models With Dependent Censoring, Yi Li, Ram C. Tiwari, Subharup Guha

Harvard University Biostatistics Working Paper Series

A number of authors have studies the mixture survival model to analyze survival data with nonnegligible cure fractions. A key assumption made by these authors is the independence between the survival time and the censoring time. To our knowledge, no one has studies the mixture cure model in the presence of dependent censoring. To account for such dependence, we propose a more general cure model which allows for dependent censoring. In particular, we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time using a class of Archimedean …

Semiparametric Normal Transformation Models For Spatially Correlated Survival Data, Yi Li, Xihong Lin

Harvard University Biostatistics Working Paper Series

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich …

Inference On Survival Data With Covariate Measurement Error - An Imputation-Based Approach, Yi Li, Louise Ryan

Harvard University Biostatistics Working Paper Series

We propose a new method for fitting proportional hazards models with error-prone covariates. Regression coefficients are estimated by solving an estimating equation that is the average of the partial likelihood scores based on imputed true covariates. For the purpose of imputation, a linear spline model is assumed on the baseline hazard. We discuss consistency and asymptotic normality of the resulting estimators, and propose a stochastic approximation scheme to obtain the estimates. The algorithm is easy to implement, and reduces to the ordinary Cox partial likelihood approach when the measurement error has a degenerative distribution. Simulations indicate high efficiency and robustness. …

Linear Regression Of Censored Length-Biased Lifetimes, Ying Qing Chen, Yan Wang

UW Biostatistics Working Paper Series

Length-biased lifetimes may be collected in observational studies or sample surveys due to biased sampling scheme. In this article, we use a linear regression model, namely, the accelerated failure time model, for the population lifetime distributions in regression analysis of the length-biased lifetimes. It is discovered that the associated regression parameters are invariant under the length-biased sampling scheme. According to this discovery, we propose the quasi partial score estimating equations to estimate the population regression parameters. The proposed methodologies are evaluated and demonstrated by simulation studies and an application to actual data set.

New Statistical Paradigms Leading To Web-Based Tools For Clinical/Translational Science, Knut M. Wittkowski

COBRA Preprint Series

As the field of functional genetics and genomics is beginning to mature, we become confronted with new challenges. The constant drop in price for sequencing and gene expression profiling as well as the increasing number of genetic and genomic variables that can be measured makes it feasible to address more complex questions. The success with rare diseases caused by single loci or genes has provided us with a proof-of-concept that new therapies can be developed based on functional genomics and genetics.

Common diseases, however, typically involve genetic epistasis, genomic pathways, and proteomic pattern. Moreover, to better understand the underlying biologi-cal …

Robust Inferences For Covariate Effects On Survival Time With Censored Linear Regression Models, Larry Leon, Tianxi Cai, L. J. Wei

Harvard University Biostatistics Working Paper Series

Various inference procedures for linear regression models with censored failure times have been studied extensively. Recent developments on efficient algorithms to implement these procedures enhance the practical usage of such models in survival analysis. In this article, we present robust inferences for certain covariate effects on the failure time in the presence of "nuisance" confounders under a semiparametric, partial linear regression setting. Specifically, the estimation procedures for the regression coefficients of interest are derived from a working linear model and are valid even when the function of the confounders in the model is not correctly specified. The new proposals are …

Multiple Testing Procedures: R Multtest Package And Applications To Genomics, Katherine S. Pollard, Sandrine Dudoit, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

The Bioconductor R package multtest implements widely applicable resampling-based single-step and stepwise multiple testing procedures (MTP) for controlling a broad class of Type I error rates, in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics. The current version of multtest provides MTPs for tests concerning means, differences in means, and regression parameters in linear and Cox proportional hazards models. Procedures are provided to control Type I error rates defined as tail probabilities for arbitrary functions of the numbers of false positives and rejected hypotheses. These error rates include tail probabilities …

Choice Of Monitoring Mechanism For Optimal Nonparametric Functional Estimation For Binary Data, Nicholas P. Jewell, Mark J. Van Der Laan, Stephen Shiboski

U.C. Berkeley Division of Biostatistics Working Paper Series

Optimal designs of dose levels in order to estimate parameters from a model for binary response data have a long and rich history. These designs are based on parametric models. Here we consider fully nonparametric models with interest focused on estimation of smooth functionals using plug-in estimators based on the nonparametric maximum likelihood estimator. An important application of the results is the derivation of the optimal choice of the monitoring time distribution function for current status observation of a survival distribution. The optimal choice depends in a simple way on the dose response function and the form of the functional. …

Semiparametric Binary Regression Under Monotonicity Constraints, Moulinath Banerjee, Pinaki Biswas, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

Summary: We study a binary regression model where the response variable $\Delta$ is the indicator of an event of interest (for example, the incidence of cancer) and the set of covariates can be partitioned as $(X,Z)$ where $Z$ (real valued) is the covariate of primary interest and $X$ (vector valued) denotes a set of control variables. For any fixed $X$, the conditional probability of the event of interest is assumed to be a monotonic function of $Z$. The effect of the control variables is captured by a regression parameter $\beta$. We show that the baseline conditional probability function (corresponding to …

Deletion/Substitution/Addition Algorithm For Partitioning The Covariate Space In Prediction, Annette Molinaro, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a new method for predicting censored (and non-censored) clinical outcomes from a highly-complex covariate space. Previously we suggested a unified strategy for predictor construction, selection, and performance assessment. Here we introduce a new algorithm which generates a piecewise constant estimation sieve of candidate predictors based on an intensive and comprehensive search over the entire covariate space. This algorithm allows us to elucidate interactions and correlation patterns in addition to main effects.

Semiparametric Methods For Semi-Competing Risks Problem With Censoring And Truncation, Hongyu Jiang, Jason Fine, Richard J. Chappell

Harvard University Biostatistics Working Paper Series

Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Since mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. Firstly, we develop a novel estimator …

Censored Linear Regression For Case-Cohort Studies, Bin Nan, Menggang Yu, Jack Kalbfleisch

The University of Michigan Department of Biostatistics Working Paper Series

Right censored data from a classical case-cohort design and a stratified case-cohort design are considered. In the classical case-cohort design, the subcohort is obtained as a simple random sample of the entire cohort, whereas in the stratified design, the subcohort is selected by independent Bernoulli sampling with arbitrary selection probabilities. For each design and under a linear regression model, methods for estimating the regression parameters are proposed and analyzed. These methods are derived by modifying the linear ranks tests and estimating equations that arise from full-cohort data using methods that are similar to the "pseudo-likelihood" estimating equation that has been …

Estimating A Survival Distribution With Current Status Data And High-Dimensional Covariates, Mark J. Van Der Laan, Aad Van Der Vaart

U.C. Berkeley Division of Biostatistics Working Paper Series

We consider the inverse problem of estimating a survival distribution when the survival times are only observed to be in one of the intervals of a random bisection of the time axis. We are particularly interested in the case that high-dimensional and/or time-dependent covariates are available, and/or the survival events and censoring times are only conditionally independent given the covariate process. The method of estimation consists of regularizing the survival distribution by taking the primitive function or smoothing, estimating the regularized parameter by using estimating equations, and finally recovering an estimator for the parameter of interest.

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.

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 …

Asymptotic Results For Simultaneous Group Sequential Analysis Of Rank-Based And Weighted Kaplan-Meier Tests With Paired Survival Data In The Presence Of Censoring. Technical Report, Adin-Cristian Andrei, Susan Murray

The University of Michigan Department of Biostatistics Working Paper Series

This research sequentially monitors paired survival differences using a new class of non-parametric tests based on functionals of standardized paired weighted log-rank (PWLR) and standardized paired weighted Kaplan-Meier (PWKM) tests. During a trial these tests may alternately assume the role of the more extreme statistic. By monitoring PEMAX, the maximum between the absolute values of the standardized PWLR and PWKM, one combines advantages of rank-based and non rank-based paired testing paradigms. Simulations show that monitoring treatment differences using PEMAX maintains type I error and is nearly as powerful as using the more advantageous of the two tests, in proportional hazards …

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 …