Statistics and Probability Commons^™

An Analysis Of Nonignorable Nonresponse In A Survey With A Rotating Panel Design, Caterina Giusti, Roderick J. Little

The University of Michigan Department of Biostatistics Working Paper Series

Missing values to income questions are common in survey data. When the probabilities of nonresponse are assumed to depend on the observed information and not on the underlining unobserved amounts, the missing income values are missing at random (MAR), and methods such as sequential multiple imputation can be applied. However, the MAR assumption is often considered questionable in this context, since missingness of income is thought to be related to the value of income itself, after conditioning on available covariates. In this article we describe a sensitivity analysis based on a pattern-mixture model for deviations from MAR, in the context …

Panel Count Data Regression With Informative Observation Times, Petra Buzkova

UW Biostatistics Working Paper Series

When patients are monitored for potentially recurrent events such as infections or tumor metastases, it is common for clinicians to ask patients to come back sooner for follow-up based on the results of the most recent exam. This means that subjects’ observation times will be irregular and related to subject-specific factors. Previously proposed methods for handling such panel count data assume that the dependence between the events process and the observation time process is time-invariant. This article considers situations where the observation times are predicted by time-varying factors, such as the outcome observed at the last visit or cumulative exposure. …

Likelihood Ratio Testing For Admixture Models With Application To Genetic Linkage Analysis, Chong-Zhi Di, Kung-Yee Liang

Johns Hopkins University, Dept. of Biostatistics Working Papers

We consider likelihood ratio tests (LRT) and their modifications for homogeneity in admixture models. The admixture model is a special case of two component mixture model, where one component is indexed by an unknown parameter while the parameter value for the other component is known. It has been widely used in genetic linkage analysis under heterogeneity, in which the kernel distribution is binomial. For such models, it is long recognized that testing for homogeneity is nonstandard and the LRT statistic does not converge to a conventional 2 distribution. In this paper, we investigate the asymptotic behavior of the LRT for …

Targeted Maximum Likelihood Method For Repeated Measures Semiparametric Regression: Discovery For Transcription Factor Activity, Catherine Tuglus, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In longitudinal and repeated measures data analysis, often the goal is to determine the effect of a treatment or aspect on a particular outcome (e.g. disease progression). We consider semiparametric repeated measures regression model, where the parametric component models effect of the variable of interest and any modification by other covariates. The expectation of this parametric component over the other covariates is a measure of variable importance. Here we present a targeted maximum likelihood estimator of the finite dimensional regression parameter, which is easily estimated using standard software for generalized estimating equations. The targeted maximum likelihood method provides double robust …

Graphical Procedures For Evaluating Overall And Subject-Specific Incremental Values From New Predictors With Censored Event Time Data, Hajime Uno, Tianxi Cai, Lu Tian, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Collaborative Targeted Maximum Likelihood For Time To Event Data, Ori M. Stitelman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Current methods used to analyze time to event data either, rely on highly parametric assumptions which result in biased estimates of parameters which are purely chosen out of convenience, or are highly unstable because they ignore the global constraints of the true model. By using Targeted Maximum Likelihood Estimation one may consistently estimate parameters which directly answer the statistical question of interest. Targeted Maximum Likelihood Estimators are substitution estimators, which rely on estimating the underlying distribution. However, unlike other substitution estimators, the underlying distribution is estimated specifically to reduce bias in the estimate of the parameter of interest. We will …

Doubly Regularized Reml For Estimation And Selection Of Fixed And Random Effects In Linear Mixed-Effects Models, Sijian Wang, Peter Xuewin Song, Ji Zhu

The University of Michigan Department of Biostatistics Working Paper Series

The linear mixed effects model (LMM) is widely used in the analysis of clustered or longitudinal data. In the practice of LMM, the inference on the structure of the random effects component is of great importance, not only to yield proper interpretation of subject-specific effects but also to draw valid statistical conclusions. This task of inference becomes significantly challenging when a large number of fixed effects and random effects are involved in the analysis. The difficulty of variable selection arises from the need of simultaneously regularizing both mean model and covariance structures, with possible parameter constraints between the two. In …

Multilevel Sparse Functional Principal Component Analysis, Chong-Zhi Di, Ciprian M. Crainiceanu

Johns Hopkins University, Dept. of Biostatistics Working Papers

The basic observational unit in this paper is a function. Data are assumed to have a natural hierarchy of basic units. A simple example is when functions are recorded at multiple visits for the same subject. Di et al. (2009) proposed Multilevel Functional Principal Component Analysis (MFPCA) for this type of data structure when functions are densely sampled. Here we consider the case when functions are sparsely sampled and may contain as few as 2 or 3 observations per function. As with MFPCA, we exploit the multilevel structure of covariance operators and data reduction induced by the use of principal …

A New Class Of Dantzig Selectors For Censored Linear Regression Models, Yi Li, Lee Dicker, Sihai Dave Zhao

Harvard University Biostatistics Working Paper Series

No abstract provided.

Targeting The Optimal Design In Randomized Clinical Trials With Binary Outcomes And No Covariate, Antoine Chambaz, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

This article is devoted to the asymptotic study of adaptive group sequential designs in the case of randomized clinical trials with binary treatment, binary outcome and no covariate. By adaptive design, we mean in this setting a clinical trial design that allows the investigator to dynamically modify its course through data-driven adjustment of the randomization probability based on data accrued so far, without negatively impacting on the statistical integrity of the trial. By adaptive group sequential design, we refer to the fact that group sequential testing methods can be equally well applied on top of adaptive designs. Prior to collection …

Targeted Maximum Likelihood Based Causal Inference, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Given causal graph assumptions, intervention-specific counterfactual distributions of the data can be defined by the so called G-computation formula, which is obtained by carrying out these interventions on the likelihood of the data factorized according to the causal graph. The obtained G-computation formula represents the counterfactual distribution the data would have had if this intervention would have been enforced on the system generating the data. A causal effect of interest can now be defined as some difference between these counterfactual distributions indexed by different interventions. For example, the interventions can represent static treatment regimens or individualized treatment rules that assign …

Bio-Creep In Non-Inferiority Clinical Trials, Siobhan P. Everson-Stewart, Scott S. Emerson

UW Biostatistics Working Paper Series

After a non-inferiority clinical trial, a new therapy may be accepted as effective, even if its treatment effect is slightly smaller than the current standard. It is therefore possible that, after a series of trials where the new therapy is slightly worse than the preceding drugs, an ineffective or harmful therapy might be incorrectly declared efficacious; this is known as “bio-creep.” Several factors may influence the rate at which bio-creep occurs, including the distribution of the effects of the new agents being tested and how that changes over time, the choice of active comparator, the method used to model the …

Estimates Of Information Growth In Longitudinal Clinical Trials, Abigail Shoben, Kyle Rudser, Scott S. Emerson

UW Biostatistics Working Paper Series

In group sequential clinical trials, it is necessary to estimate the amount of information present at interim analysis times relative to the amount of information that would be present at the final analysis. If only one measurement is made per individual, this is often the ratio of sample sizes available at the interim and final analyses. However, as discussed by Wu and Lan (1992), when the statistic of interest is a change over time, as with longitudinal data, such an approach overstates the information. In this paper, we discuss other problems that can result in overestimating the information, such as …

Robustness Of Approaches To Roc Curve Modeling Under Misspecification Of The Underlying Probability Model, Sean Devlin, Elizabeth Thomas, Scott S. Emerson

UW Biostatistics Working Paper Series

The receiver operating characteristic (ROC) curve is a tool of particular use in disease status classification with a continuous medical test (marker). A variety of statistical regression models have been proposed for the comparison of ROC curves for different markers across covariate groups. A full parametric modeling of the marker distribution has been generally found to be overly reliant on the strong parametric assumptions. Pepe (2003) has instead developed parametric models for the ROC curve that induce a semi-parametric model for the marker distributions. The estimating equations proposed for use in these ROC-GLM models may differ from commonly used estimating …

Simple, Efficient Estimators Of Treatment Effects In Randomized Trials Using Generalized Linear Models To Leverage Baseline Variables, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Models, such as logistic regression and Poisson regression models, are often used to estimate treatment effects in randomized trials. These models leverage information in variables collected before randomization, in order to obtain more precise estimates of treatment effects. However, there is the danger that model misspecification will lead to bias. We show that certain easy to compute, model-based estimators are asymptotically unbiased even when the working model used is arbitrarily misspecified. Furthermore, these estimators are locally efficient. As a special case of our main result, we consider a simple Poisson working model containing only main terms; in this case, we …

Targeted Maximum Likelihood Estimation Of The Parameter Of A Marginal Structural Model, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Targeted maximum likelihood estimation is a versatile tool for estimating parameters in semiparametric and nonparametric models. We work through an example applying targeted maximum likelihood methodology to estimate the parameter of a marginal structural model. In the case we consider, we show how this can be easily done by clever use of standard statistical software. We point out differences between targeted maximum likelihood estimation and other approaches (including estimating function based methods). The application we consider is to estimate the effect of adherence to antiretroviral medications on virologic failure in HIV positive individuals.

Penalized Functional Regression, Jeff Goldsmith, Jennifer Feder, Ciprian M. Crainiceanu, Brian Caffo, Daniel Reich

Johns Hopkins University, Dept. of Biostatistics Working Papers

We develop fast fitting methods for generalized functional linear models. An undersmooth of the functional predictor is obtained by projecting on a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression. Our method can be applied to many functional data designs including functions measured with and without error, sparsely or densely sampled. The methods also extend to the case of multiple functional predictors or functional predictors with a natural multilevel structure. Our approach can be implemented using standard mixed effects software and is computationally fast. Our methodology is motivated by a diffusion tensor imaging …

Regression Adjustment And Stratification By Propensty Score In Treatment Effect Estimation, Jessica A. Myers, Thomas A. Louis

Johns Hopkins University, Dept. of Biostatistics Working Papers

Propensity score adjustment of effect estimates in observational studies of treatment is a common technique used to control for bias in treatment assignment. In situations where matching on propensity score is not possible or desirable, regression adjustment and stratification are two options. Regression adjustment is used most often and can be highly efficient, but it can lead to biased results when model assumptions are violated. Validity of the stratification approach depends on fewer model assumptions, but is less efficient than regression adjustment when the regression assumptions hold. To investigate these issues, by simulation we compare stratification and regression adjustments. We …

Exploring The Benefits Of Adaptive Sequential Designs In Time-To-Event Endpoint Settings, Sarah C. Emerson, Kyle Rudser, Scott S. Emerson

UW Biostatistics Working Paper Series

Sequential analysis is frequently employed to address ethical and financial issues in clinical trials. Sequential analysis may be performed using standard group sequential designs, or, more recently, with adaptive designs that use estimates of treatment effect to modify the maximal statistical information to be collected. In the general setting in which statistical information and clinical trial costs are functions of the number of subjects used, it has yet to be established whether there is any major efficiency advantage to adaptive designs over traditional group sequential designs. In survival analysis, however, statistical information (and hence efficiency) is most closely related to …

Mean Survival Time From Right Censored Data, Ming Zhong, Kenneth R. Hess

COBRA Preprint Series

A nonparametric estimate of the mean survival time can be obtained as the area under the Kaplan-Meier estimate of the survival curve. A common modification is to change the largest observation to a death time if it is censored. We conducted a simulation study to assess the behavior of this estimator of the mean survival time in the presence of right censoring.

We simulated data from seven distributions: exponential, normal, uniform, lognormal, gamma, log-logistic, and Weibull. This allowed us to compare the results of the estimates to the known true values and to quantify the bias and the variance. Our …

Pragmatic Estimation Of A Spatio-Temporal Air Quality Model With Irregular Monitoring Data, Paul D. Sampson, Adam A. Szpiro, Lianne Sheppard, Johan Lindström, Joel D. Kaufman

UW Biostatistics Working Paper Series

Statistical analyses of the health effects of air pollution have increasingly used GIS-based covariates for prediction of ambient air quality in “land-use” regression models. More recently these regression models have accounted for spatial correlation structure in combining monitoring data with land-use covariates. The current paper builds on these concepts to address spatio-temporal prediction of ambient concentrations of particulate matter with aerodynamic diameter less than 2.5 μm (PM2.5) on the basis of a model representing spatially varying seasonal trends and spatial correlation structures. Our hierarchical methodology provides a pragmatic approach that fully exploits regulatory and other supplemental monitoring data which jointly …

On The Behaviour Of Marginal And Conditional Akaike Information Criteria In Linear Mixed Models, Sonja Greven, Thomas Kneib

Johns Hopkins University, Dept. of Biostatistics Working Papers

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive …

Survival Analysis With Error-Prone Time-Varying Covariates: A Risk Set Calibration Approach, Xiaomei Liao, David M. Zucker, Yi Li, Donna Spiegelman

Harvard University Biostatistics Working Paper Series

No abstract provided.

Is Survival The Only Or Even The Right Outcome For Evaluating Treatments For Out-Of-Hospital Cardiac Arrest? A Proposed Test Based On Both An Intermediate And Ultimate Outcome., Al Hallstrom

UW Biostatistics Working Paper Series

It is generally agreed that the goal of resuscitation is survival with neurological and physiological status similar to that preceding the cardiac arrest. Previously I have argued that the lack of improvement in outcome from resuscitation over the past 3 to 4 decades, as compared to the substantial progress made in treatment of ischemic heart disease, is a consequence of the absence of randomized clinical trials of new interventions and the use of intermediate endpoints such as return of spontaneous circulation or admittance to hospital. Proponents of these intermediate endpoints have argued that those involved in the resuscitation have no …

A New Class Of Minimum Power Divergence Estimators With Applications To Cancer Surveillance, Nirian Martin, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

Two-Stage Decompositions For The Analysis Of Functional Connectivity For Fmri With Application To Alzheimer's Disease Risk, Brian S. Caffo, Ciprian M. Crainiceanu, Guillermo Verduzco, Stewart H. Mostofsky, Susan Spear-Bassett, James J. Pekar

COBRA Preprint Series

Functional connectivity is the study of correlations in measured neurophysiological signals. Altered functional connectivity has been shown to be associated with numerous diseases including Alzheimer's disease and mild cognitive impairment. In this manuscript we use a two-stage application of the singular value decomposition to obtain data driven population-level measures of functional connectivity in functional magnetic resonance imaging (fMRI). The method is computationally simple and amenable to high dimensional fMRI data with large numbers of subjects. Simulation studies suggest the ability of the decomposition methods to recover population brain networks and their associated loadings. We further demonstrate the utility of these …

Analyzing Bivariate Survival Data With Interval Sampling And Application To Cancer Epidemiology, Hong Zhu, Mei-Cheng Wang

Johns Hopkins University, Dept. of Biostatistics Working Papers

In medical follow-up studies, ordered bivariate survival data are frequently encountered when bivariate failure events are used as the outcomes to identify the progression of a disease. In cancer studies interest could be focused on bivariate failure times, for example, time from birth to cancer onset and time from cancer onset to death. This paper considers a sampling scheme where the first failure event (cancer onset) is identified within a calendar time interval, the time of the initiating event (birth) can be retrospectively confirmed, and the occurrence of the second event (death) is observed sub ject to right censoring. To …

Lot Quality Assurance Sampling (Lqas) And The Mozambique Malaria Indicator Surveys, Caitlin Biedron, Marcello Pagano, Bethany L. Hedt, Albert Kilian, Amy Ratcliffe, Samuel Mabunda, Joseph J. Valadez

Harvard University Biostatistics Working Paper Series

No abstract provided.

Modeling Multilevel Sleep Transitional Data Via Poisson Log-Linear Multilevel Models, Bruce J. Swihart, Brian Caffo, Ciprian Crainiceanu, Naresh M. Punjabi

Johns Hopkins University, Dept. of Biostatistics Working Papers

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified …

Bayesian Functional Data Analysis Using Winbugs, Ciprian M. Crainiceanu, A. Jeffrey Goldsmith

Johns Hopkins University, Dept. of Biostatistics Working Papers

We provide user friendly software for Bayesian analysis of Functional Data Models using WinBUGS 1.4. The excellent properties of Bayesian analysis in this context are due to: 1) dimensionality reduction, which leads to low dimensional projection bases; 2)the mixed model representation of functional models, which provides a modular approach to model extension; and 3) the orthogonality of the principal component bases, which contributes to excellent chain convergence and mixing properties. Our paper provides one more, essential, reason for using Bayesian analysis for Functional models: the existence of software.