Statistical Models Commons^™

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 …

Mean Response Models Of Repeated Measurements In Presence Of Varying Effectiveness Onset, Ying Qing Chen, Su-Chun Cheng

U.C. Berkeley Division of Biostatistics Working Paper Series

Repeated measurements are often collected over time to evaluate treatment efficacy in clinical trials. Most of the statistical models of the repeated measurements have been focusing on their mean response as function of time. These models usually assume that the treatment has persistent effect of constant additivity or multiplicity on the mean response functions throughout the observation period of time. In reality, however, such assumption may be confounded by the potential existence of the so-called effectiveness action onset, although they are often unobserved or difficult to obtain. Instead of including nonparametric time-varying coefficients in the mean response models, we propose …

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.

Regulatory Motif Finding By Logic Regression, Sunduz Keles, Mark J. Van Der Laan, Chris Vulpe

U.C. Berkeley Division of Biostatistics Working Paper Series

Multiple transcription factors coordinately control transcriptional regulation of genes in eukaryotes. Although multiple computational methods consider the identification of individual transcription factor binding sites (TFBSs), very few focus on the interactions between these sites. We consider finding transcription factor binding sites and their context specific interactions using microarray gene expression data. We devise a hybrid approach called LogicMotif composed of a TFBS identification method combined with the new regression methodology logic regression of Ruczinski et al. (2003). LogicMotif has two steps: First potential binding sites are identified from transcription control regions of genes of interest. Various available methods can be …

A Statistical Method For Constructing Transcriptional Regulatory Networks Using Gene Expression And Sequence Data , Biao Xing, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Transcriptional regulation is one of the most important means of gene regulation. Uncovering transcriptional regulatory network helps us to understand the complex cellular process. In this paper, we describe a comprehensive statistical approach for constructing the transcriptional regulatory network using data of gene expression, promoter sequence, and transcription factor binding sites. Our simulation studies show that the overall and false positive error rates in the estimated transcriptional regulatory network are expected to be small if the systematic noise in the constructed feature matrix is small. Our analysis based on 658 microarray experiments on yeast gene expression programs and 46 transcription …

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 …

Comparison Of The Inverse Probability Of Treatment Weighted (Iptw) Estimator With A Naïve Estimator In The Analysis Of Longitudinal Data With Time-Dependent Confounding: A Simulation Study, Thaddeus Haight, Romain Neugebauer, Ira B. Tager, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

A simulation study was conducted to compare estimates from a naïve estimator, using standard conditional regression, and an IPTW (Inverse Probability of Treatment Weighted) estimator, to true causal parameters for a given MSM (Marginal Structural Model). The study was extracted from a larger epidemiological study (Longitudinal Study of Effects of Physical Activity and Body Composition on Functional Limitation in the Elderly, by Tager et. al [accepted, Epidemiology, September 2003]), which examined the causal effects of physical activity and body composition on functional limitation. The simulation emulated the larger study in terms of the exposure and outcome variables of interest-- physical …

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 …

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 …

Tree-Based Multivariate Regression And Density Estimation With Right-Censored Data , Annette M. Molinaro, Sandrine Dudoit, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a unified strategy for estimator construction, selection, and performance assessment in the presence of censoring. This approach is entirely driven by the choice of a loss function for the full (uncensored) data structure and can be stated in terms of the following three main steps. (1) Define the parameter of interest as the minimizer of the expected loss, or risk, for a full data loss function chosen to represent the desired measure of performance. Map the full data loss function into an observed (censored) data loss function having the same expected value and leading to an efficient estimator …

Supervised Detection Of Regulatory Motifs In Dna Sequences, Sunduz Keles, Mark J. Van Der Laan, Sandrine Dudoit, Biao Xing, Michael B. Eisen

U.C. Berkeley Division of Biostatistics Working Paper Series

Identification of transcription factor binding sites (regulatory motifs) is a major interest in contemporary biology. We propose a new likelihood based method, COMODE, for identifying structural motifs in DNA sequences. Commonly used methods (e.g. MEME, Gibbs sampler) model binding sites as families of sequences described by a position weight matrix (PWM) and identify PWMs that maximize the likelihood of observed sequence data under a simple multinomial mixture model. This model assumes that the positions of the PWM correspond to independent multinomial distributions with four cell probabilities. We address supervising the search for DNA binding sites using the information derived from …

A Semiparametric Model Selection Criterion With Applications To The Marginal Structural Model, M. Alan Brookhart, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Estimators for the parameter of interest in semiparametric models often depend on a guessed model for the nuisance parameter. The choice of the model for the nuisance parameter can affect both the finite sample bias and efficiency of the resulting estimator of the parameter of interest. In this paper we propose a finite sample criterion based on cross validation that can be used to select a nuisance parameter model from a list of candidate models. We show that expected value of this criterion is minimized by the nuisance parameter model that yields the estimator of the parameter of interest with …

Rank Regression In Stability Analysis, Ying Qing Chen, Annpey Pong, Biao Xing

U.C. Berkeley Division of Biostatistics Working Paper Series

Stability data are often collected to determine the shelf-life of certain characteristics of a pharmaceutical product, for example, a drug's potency over time. Statistical approaches such as the linear regression models are considered as appropriate to analyze the stability data. However, most of these regression models in both theory and practice rely heavily on their underlying parametric assumptions, such as normality of the continuous characteristics or their transformations. In this article, we propose and study some rank-based regression procedures for the stability data when the linear regression models are semiparametric with unspecified error structure. Numerical studies including Monte Carlo simulations …

Recurrent Events Analysis In The Presence Of Time Dependent Covariates And Dependent Censoring, Maja Miloslavsky, Sunduz Keles, Mark J. Van Der Laan, Steve Butler

U.C. Berkeley Division of Biostatistics Working Paper Series

Recurrent events models have lately received a lot of attention in the literature. The majority of approaches discussed show the consistency of parameter estimates under the assumption that censoring is independent of the recurrent events process of interest conditional on the covariates included into the model. We provide an overview of available recurrent events analysis methods, and present an inverse probability of censoring weighted estimator for the regression parameters in the Andersen-Gill model that is commonly used for recurrent event analysis. This estimator remains consistent under informative censoring if the censoring mechanism is estimated consistently, and generally improves on the …

Analysis Of Longitudinal Marginal Structural Models , Jennifer F. Bryan, Zhuo Yu, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator is used as an initial estimator and the corresponding treatment-orthogonalized, one-step estimator is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. A simulation study demonstrates that the the treatment-orthogonalized, one-step estimator is superior to the IPTW estimator in terms …

Locally Efficient Estimation With Bivariate Right Censored Data , Christopher M. Quale, Mark J. Van Der Laan, James M. Robins

U.C. Berkeley Division of Biostatistics Working Paper Series

Estimation for bivariate right censored data is a problem that has had much study over the past 15 years. In this paper we propose a new class of estimators for the bivariate survivor function based on locally efficient estimation. The locally efficient estimator takes bivariate estimators Fn and Gn of the distributions of the time variables T1,T2 and the censoring variables C1,C2, respectively, and maps them to the resulting estimator. If Fn and Gn are consistent estimators of F and G, respectively, then the resulting estimator will be nonparametrically efficient (thus the term ``locally efficient''). However, if either Fn or …

An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In non-randomized treatment studies a significant problem for statisticians is determining how best to adjust for confounders. Marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators are useful in analyzing the causal effect of treatment in observational studies. Given an IPTW estimator a doubly robust augmented IPTW (AIPTW) estimator orthogonalizes it resulting in a more e±cient estimator than the IPTW estimator. One purpose of this paper is to make a practical comparison between the IPTW estimator and the doubly robust AIPTW estimator via a series of Monte- Carlo simulations. We also consider the selection of the optimal …

Accelerated Hazards Model: Method, Theory And Applications, Ying Qing Chen, Nicholas P. Jewell, Jingrong Yang

U.C. Berkeley Division of Biostatistics Working Paper Series

In an accelerated hazards model, the hazard functions of a failure time are related through the time scale-change, which is often a function of covariates and associated parameters. When the hazard functions have special properties, such as monotonicity in time, the parameters may be clinically meaningful in measuring a treatment effect. This paper reviews methodological and theoretical development of this model. Applications of the accelerated hazards model including sample size calculation in clinical trials, are also explored.

Locally Efficient Estimation Of Regression Parameters Using Current Status Data, Chris Andrews, Mark J. Van Der Laan, James M. Robins

U.C. Berkeley Division of Biostatistics Working Paper Series

In biostatistics applications interest often focuses on the estimation of the distribution of a time-variable T. If one only observes whether or not T exceeds an observed monitoring time C, then the data structure is called current status data, also known as interval censored data, case I. We consider this data structure extended to allow the presence of both time-independent covariates and time-dependent covariate processes that are observed until the monitoring time. We assume that the monitoring process satisfies coarsening at random.

Our goal is to estimate the regression parameter beta of the regression model T = Z*beta+epsilon where the …

Why Prefer Double Robust Estimates? Illustration With Causal Point Treatment Studies, Romain Neugebauer, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In point treatment marginal structural models with treatment A, outcome Y and covariates W, causal parameters can be estimated under the assumption of no unobserved confounders. Three estimates can be used: the G-computation, Inverse Probability of Treatment Weighted (IPTW) or Double Robust (DR) estimates. The properties of the IPTW and DR estimates are known under an assumption on the treatment mechanism that we name "Experimental Treatment Assignment" (ETA) assumption. We show that the DR estimating function is unbiased when the ETA assumption is violated if the model used to regress Y on A and W is correctly specified. The practical …

Semiparametric Regression Analysis On Longitudinal Pattern Of Recurrent Gap Times, Ying Qing Chen, Mei-Cheng Wang, Yijian Huang

U.C. Berkeley Division of Biostatistics Working Paper Series

In longitudinal studies, individual subjects may experience recurrent events of the same type over a relatively long period of time. The longitudinal pattern of the gaps between the successive recurrent events is often of great research interest. In this article, the probability structure of the recurrent gap times is first explored in the presence of censoring. According to the discovered structure, we introduce the proportional reverse-time hazards models with unspecified baseline functions to accommodate heterogeneous individual underlying distributions, when the ongitudinal pattern parameter is of main interest. Inference procedures are proposed and studied by way of proper riskset construction. The …

Inference For Proportional Mean Residual Life Model In The Presence Of Censoring, Ying Q. Chen, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

As a function of time t, mean residual life is defined as remaining life expectancy of a subject given its survival to t. It plays an important role in many research areas to characterise stochastic behavior of survival over time. Similar to the Cox proportional hazard model, the proportional mean residual life model were proposed in statistical literature to study association between the mean residual life and individual subject's explanatory covariates. In this article, we will study this model and develop appropriate inference procedures in presence of censoring. Numerical studies including simulation and real data analysis are presented as well.

Regression Analysis Of Recurrent Gap Times With Time-Dependent Covariates, Ying Qing Chen, Mei-Cheng Wang, Yijian Huang

U.C. Berkeley Division of Biostatistics Working Paper Series

Individual subjects may experience recurrent events of same type over a relatively long period of time in a longitudinal study. Researchers are often interested in the distributional pattern of gaps between the successive recurrent events and their association with certain concomitant covariates as well. In this article, their probability structure is investigated in presence of censoring. According to the identified structure, we introduce the proportional reverse-time hazards models that allow arbitrary baseline function for every individual in the study, when the time-dependent covariates effect is of main interest. Appropriate inference procedures are proposed and studied to estimate the parameters of …

Estimating Causal Parameters In Marginal Structural Models With Unmeasured Confounders Using Instrumental Variables, Tanya A. Henneman, Mark Johannes Van Der Laan, Alan E. Hubbard

U.C. Berkeley Division of Biostatistics Working Paper Series

For statisticians analyzing medical data, a significant problem in determining the causal effect of a treatment on a particular outcome of interest, is how to control for unmeasured confounders. Techniques using instrumental variables (IV) have been developed to estimate causal parameters in the presence of unmeasured confounders. In this paper we apply IV methods to both linear and non-linear marginal structural models. We study a specific class of generalized estimating equations that is appropriate to these data, and compare the performance of the resulting estimator to the standard IV method, a two-stage least squares procedure. Our results are applied to …

Marginal Regression Of Gaps Between Recurrent Events, Yijian Huang, Ying Qing Chen

U.C. Berkeley Division of Biostatistics Working Paper Series

Recurrent event data typically exhibit the phenomenon of intra-individual correlation, owing to not only observed covariates but also random effects. In many applications, the population can be reasonably postulated as a heterogeneous mixture of individual renewal processes, and the inference of interest is the effect of individual-level covariates. In this article, we suggest and investigate a marginal proportional hazards model for gaps between recurrent events. A connection is established between observed gap times and clustered survival data, however, with informative cluster size. We then derive a novel and general inference procedure for the latter, based on a functional formulation of …

Identification Of Regulatory Elements Using A Feature Selection Method, Sunduz Keles, Mark J. Van Der Laan, Michael B. Eisen

U.C. Berkeley Division of Biostatistics Working Paper Series

Many methods have been described to identify regulatory motifs in the transcription control regions of genes that exhibit similar patterns of gene expression across a variety of experimental conditions. Here we focus on a single experimental condition, and utilize gene expression data to identify sequence motifs associated with genes that are activated under this experimental condition. We use a linear model with two way interactions to model gene expression as a function of sequence features (words) present in presumptive transcription control regions. The most relevant features are selected by a feature selection method called stepwise selection with monte carlo cross …

Mixture Hazards Models With Additive Random Effects Accounting For Treatment Effectiveness Lag Time, Ying Qing Chen, C. A. Rohde, M.-C. Wang

U.C. Berkeley Division of Biostatistics Working Paper Series

In many clinical trials to evaluate treatment efficacy, it is believed that there may exist latent treatment effectiveness lag times after which medical treatment procedure or chemical compound would be in full effect. In this article, semiparametric regression models are proposed and studied for estimating the treatment effect accounting for such latent lag times. The new models take advantage of the invariance property of the additive hazards model in marginalising over an additive latent variable; parameters in the models are thus easily estimated and interpreted, while the flexibility of not having to specify the baseline hazard function is preserved. Monte …

A Class Of Semiparametric Scale-Change Hazards Regression Models And Its Adequacy For Censored Survival Data, Ying Qing Chen

U.C. Berkeley Division of Biostatistics Working Paper Series

A class of semiparametric hazards regression models called the accelerated hazards models was introduced to identify the covariate effect characterized by the scale-change between hazard functions. In this article, we compare the accelerated hazards models with several other popular classes of regression models in statistical literature for censored survival data. We also propose and study some test statistics to assess the models' adequacy. Simulation studies are conducted to evaluate the performance of the test statistics. Actual clinical trials data are analyzed to demonstrate the proposed models and test statistics.