Statistical Models Commons^™

Models For Hsv Shedding Must Account For Two Levels Of Overdispersion, Amalia Magaret

UW Biostatistics Working Paper Series

We have frequently implemented crossover studies to evaluate new therapeutic interventions for genital herpes simplex virus infection. The outcome measured to assess the efficacy of interventions on herpes disease severity is the viral shedding rate, defined as the frequency of detection of HSV on the genital skin and mucosa. We performed a simulation study to ascertain whether our standard model, which we have used previously, was appropriately considering all the necessary features of the shedding data to provide correct inference. We simulated shedding data under our standard, validated assumptions and assessed the ability of 5 different models to reproduce the …

Targeted Maximum Likelihood Estimation For Dynamic And Static Longitudinal Marginal Structural Working Models, Maya L. Petersen, Joshua Schwab, Susan Gruber, Nello Blaser, Michael Schomaker, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because …

A Unified Approach To Modeling Multivariate Binary Data Using Copulas Over Partitions, Bruce J. Swihart, Brian Caffo, Ciprian Crainiceanu

Johns Hopkins University, Dept. of Biostatistics Working Papers

Many seemingly disparate approaches for marginal modeling have been developed in recent years. We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the proposed copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate …

Spatial Misalignment In Time Series Studies Of Air Pollution And Health Data, Roger D. Peng, Michelle L. Bell

Johns Hopkins University, Dept. of Biostatistics Working Papers

Time series studies of environmental exposures often involve comparing daily changes in a toxicant measured at a point in space with daily changes in an aggregate measure of health. Spatial misalignment of the exposure and response variables can bias the estimation of health risk and the magnitude of this bias depends on the spatial variation of the exposure of interest. In air pollution epidemiology, there is an increasing focus on estimating the health effects of the chemical components of particulate matter. One issue that is raised by this new focus is the spatial misalignment error introduced by the lack of …

Space-Time Regression Modeling Of Tree Growth Using The Skew-T Distribution, Farouk S. Nathoo

COBRA Preprint Series

In this article we present new statistical methodology for the analysis of repeated measures of spatially correlated growth data. Our motivating application, a ten year study of height growth in a plantation of even-aged white spruce, presents several challenges for statistical analysis. Here, the growth measurements arise from an asymmetric distribution, with heavy tails, and thus standard longitudinal regression models based on a Gaussian error structure are not appropriate. We seek more flexibility for modeling both skewness and fat tails, and achieve this within the class of skew-elliptical distributions. Within this framework, robust space-time regression models are formulated using random …

Joint Spatial Modeling Of Recurrent Infection And Growth With Processes Under Intermittent Observation, Farouk S. Nathoo

COBRA Preprint Series

In this article we present new statistical methodology for longitudinal studies in forestry where trees are subject to recurrent infection and the hazard of infection depends on tree growth over time. Understanding the nature of this dependence has important implications for reforestation and breeding programs. Challenges arise for statistical analysis in this setting with sampling schemes leading to panel data, exhibiting dynamic spatial variability, and incomplete covariate histories for hazard regression. In addition, data are collected at a large number of locations which poses computational difficulties for spatiotemporal modeling. A joint model for infection and growth is developed; wherein, a …

Statistical Analysis Of Air Pollution Panel Studies: An Illustration, Holly Janes, Lianne Sheppard, Kristen Shepherd

UW Biostatistics Working Paper Series

The panel study design is commonly used to evaluate the short-term health effects of air pollution. Standard statistical methods for analyzing longitudinal data are available, but the literature reveals that the techniques are not well understood by practitioners. We illustrate these methods using data from the 1999 to 2002 Seattle panel study. Marginal, conditional, and transitional approaches for modeling longitudinal data are reviewed and contrasted with respect to their parameter interpretation and methods for accounting for correlation and dealing with missing data. We also discuss and illustrate techniques for controlling for time-dependent and time-independent confounding, and for exploring and summarizing …

Semiparametric Latent Variable Regression Models For Spatio-Temporal Modeling Of Mobile Source Particles In The Greater Boston Area, Alexandros Gryparis, Brent A. Coull, Joel Schwartz, Helen H. Suh

Harvard University Biostatistics Working Paper Series

Traffic particle concentrations show considerable spatial variability within a metropolitan area. We consider latent variable semiparametric regression models for modeling the spatial and temporal variability of black carbon and elemental carbon concentrations in the greater Boston area. Measurements of these pollutants, which are markers of traffic particles, were obtained from several individual exposure studies conducted at specific household locations as well as 15 ambient monitoring sites in the city. The models allow for both flexible, nonlinear effects of covariates and for unexplained spatial and temporal variability in exposure. In addition, the different individual exposure studies recorded different surrogates of traffic …

A Nonstationary Negative Binomial Time Series With Time-Dependent Covariates: Enterococcus Counts In Boston Harbor, E. Andres Houseman, Brent Coull, James P. Shine

Harvard University Biostatistics Working Paper Series

Boston Harbor has had a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence …

Direct Effect Models, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

The causal effect of a treatment on an outcome is generally mediated by several intermediate variables. Estimation of the component of the causal effect of a treatment that is mediated by a given intermediate variable (the indirect effect of the treatment), and the component that is not mediated by that intermediate variable (the direct effect of the treatment) is often relevant to mechanistic understanding and to the design of clinical and public health interventions. Under the assumption of no-unmeasured confounders for treatment and the intermediate variable, Robins & Greenland (1992) define an individual direct effect as the counterfactual effect of …

Causal Inference In Longitudinal Studies With History-Restricted Marginal Structural Models, Romain Neugebauer, Mark J. Van Der Laan, Ira B. Tager

U.C. Berkeley Division of Biostatistics Working Paper Series

Causal Inference based on Marginal Structural Models (MSMs) is particularly attractive to subject-matter investigators because MSM parameters provide explicit representations of causal effects. We introduce History-Restricted Marginal Structural Models (HRMSMs) for longitudinal data for the purpose of defining causal parameters which may often be better suited for Public Health research. This new class of MSMs allows investigators to analyze the causal effect of a treatment on an outcome based on a fixed, shorter and user-specified history of exposure compared to MSMs. By default, the latter represents the treatment causal effect of interest based on a treatment history defined by the …

A Bayesian Mixture Model Relating Dose To Critical Organs And Functional Complication In 3d Conformal Radiation Therapy, Tim Johnson, Jeremy Taylor, Randall K. Ten Haken, Avraham Eisbruch

The University of Michigan Department of Biostatistics Working Paper Series

A goal of radiation therapy is to deliver maximum dose to the target tumor while minimizing complications due to irradiation of critical organs. Technological advances in 3D conformal radiation therapy has allowed great strides in realizing this goal, however complications may still arise. Critical organs may be adjacent to tumors or in the path of the radiation beam. Several mathematical models have been proposed that describe a relationship between dose and observed functional complication, however only a few published studies have successfully fit these models to data using modern statistical methods which make efficient use of the data. One complication …

Bayesian Hierarchical Distributed Lag Models For Summer Ozone Exposure And Cardio-Respiratory Mortality, Yi Huang, Francesca Dominici, Michelle L. Bell

Johns Hopkins University, Dept. of Biostatistics Working Papers

In this paper, we develop Bayesian hierarchical distributed lag models for estimating associations between daily variations in summer ozone levels and daily variations in cardiovascular and respiratory (CVDRESP) mortality counts for 19 U.S. large cities included in the National Morbidity Mortality Air Pollution Study (NMMAPS) for the period 1987 - 1994.

At the first stage, we define a semi-parametric distributed lag Poisson regression model to estimate city-specific relative rates of CVDRESP associated with short-term exposure to summer ozone. At the second stage, we specify a class of distributions for the true city-specific relative rates to estimate an overall effect by …

Cholesky Residuals For Assessing Normal Errors In A Linear Model With Correlated Outcomes: Technical Report, E. Andres Houseman, Louise Ryan, Brent Coull

Harvard University Biostatistics Working Paper Series

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and …

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 …

Seasonal Analyses Of Air Pollution And Mortality In 100 U.S. Cities, Roger D. Peng, Francesca Dominici, Roberto Pastor-Barriuso, Scott L. Zeger, Jonathan M. Samet

Johns Hopkins University, Dept. of Biostatistics Working Papers

Time series models relating short-term changes in air pollution levels to daily mortality counts typically assume that the effects of air pollution on the log relative rate of mortality do not vary with time. However, these short-term effects might plausibly vary by season. Changes in the sources of air pollution and meteorology can result in changes in characteristics of the air pollution mixture across seasons. The authors develop Bayesian semi-parametric hierarchical models for estimating time-varying effects of pollution on mortality in multi-site time series studies. The methods are applied to the updated National Morbidity and Mortality Air Pollution Study database …

Individual Prediction In Prostate Cancer Studies Using A Joint Longitudinal-Survival-Cure Model, Menggang Yu, Jeremy Taylor, Howard M. Sandler

The University of Michigan Department of Biostatistics Working Paper Series

For monitoring patients treated for prostate cancer, Prostate Specific Antigen (PSA) is measured periodically after they receive treatment. Increases in PSA are suggestive of recurrence of the cancer and are used in making decisions about possible new treatments. The data from studies of such patients typically consist of longitudinal PSA measurements, censored event times and baseline covariates. Methods for the combined analysis of both longitudinal and survival data have been developed in recent years, with the main emphasis being on modeling and estimation. We analyze data from a prostate cancer study that has been extended by adding a mixture structure …

Marginalized Transition Models For Longitudinal Binary Data With Ignorable And Nonignorable Dropout, Brenda F. Kurland, Patrick J. Heagerty

UW Biostatistics Working Paper Series

We extend the marginalized transition model of Heagerty (2002) to accommodate nonignorable monotone dropout. Using a selection model, weakly identified dropout parameters are held constant and their effects evaluated through sensitivity analysis. For data missing at random (MAR), efficiency of inverse probability of censoring weighted generalized estimating equations (IPCW-GEE) is as low as 40% compared to a likelihood-based marginalized transition model (MTM) with comparable modeling burden. MTM and IPCW-GEE regression parameters both display misspecification bias for MAR and nonignorable missing data, and both reduce bias noticeably by improving model fit

Marginal Modeling Of Multilevel Binary Data With Time-Varying Covariates, Diana Miglioretti, Patrick Heagerty

UW Biostatistics Working Paper Series

We propose and compare two approaches for regression analysis of multilevel binary data when clusters are not necessarily nested: a GEE method that relies on a working independence assumption coupled with a three-step method for obtaining empirical standard errors; and a likelihood-based method implemented using Bayesian computational techniques. Implications of time-varying endogenous covariates are addressed. The methods are illustrated using data from the Breast Cancer Surveillance Consortium to estimate mammography accuracy from a repeatedly screened population.

Partly Conditional Survival Models For Longitudinal Data, Yingye Zheng, Patrick Heagerty

UW Biostatistics Working Paper Series

It is common in longitudinal studies to collect information on the time until a key clinical event, such as death, and to measure markers of patient health at multiple follow-up times. One approach to the joint analysis of survival and repeated measures data adopts a time-varying covariate regression model for the event time hazard. Using this standard approach the instantaneous risk of death at time t is specified as a possibly semi-parametric function of covariate information that has accrued through time t. In this manuscript we decouple the time scale for modeling the hazard from the time scale for accrual …

Semiparametric Estimation Of Time-Dependent: Roc Curves For Longitudinal Marker Data, Yingye Zheng, Patrick Heagerty

UW Biostatistics Working Paper Series

One approach to evaluating the strength of association between a longitudinal marker process and a key clinical event time is through predictive regression methods such as a time-dependent covariate hazard model. For example, a time-varying covariate Cox model specifies the instantaneous risk of the event as a function of the time-varying marker and additional covariates. In this manuscript we explore a second complementary approach which characterizes the distribution of the marker as a function of both the measurement time and the ultimate event time. Our goal is to flexibly extend the standard diagnostic accuracy concepts of sensitivity and specificity to …

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 …

Underestimation Of Standard Errors In Multi-Site Time Series Studies, Michael Daniels, Francesca Dominici, Scott L. Zeger

Johns Hopkins University, Dept. of Biostatistics Working Papers

Multi-site time series studies of air pollution and mortality and morbidity have figured prominently in the literature as comprehensive approaches for estimating acute effects of air pollution on health. Hierarchical models are generally used to combine site-specific information and estimate pooled air pollution effects taking into account both within-site statistical uncertainty, and across-site heterogeneity.

Within a site, characteristics of time series data of air pollution and health (small pollution effects, missing data, highly correlated predictors, non linear confounding etc.) make modelling all sources of uncertainty challenging. One potential consequence is underestimation of the statistical variance of the site-specific effects to …

Time-Series Studies Of Particulate Matter, Michelle L. Bell, Jonathan M. Samet, Francesca Dominici

Johns Hopkins University, Dept. of Biostatistics Working Papers

Studies of air pollution and human health have evolved from descriptive studies of the early phenomena of large increases in adverse health effects following extreme air pollution episodes, to time-series analyses and the development of sophisticated regression models. In fact, advanced statistical methods are necessary to address the many challenges inherent in the detection of a small pollution risk in the presence of many confounders. This paper reviews the history, methods, and findings of the time-series studies estimating health risks associated with short-term exposure to particulate matter, though much of the discussion is applicable to epidemiological studies of air pollution …

A Corrected Pseudo-Score Approach For Additive Hazards Model With Longitudinal Covariates Measured With Error, Xiao Song, Yijian Huang

UW Biostatistics Working Paper Series

In medical studies, it is often of interest to characterize the relationship between a time-to-event and covariates, not only time-independent but also time-dependent. Time-dependent covariates are generally measured intermittently and with error. Recent interests focus on the proportional hazards framework, with longitudinal data jointly modeled through a mixed effects model. However, approaches under this framework depend on the normality assumption of the error, and might encounter intractable numerical difficulties in practice. This motivates us to consider an alternative framework, that is, the additive hazards model, under which little has been done when time-dependent covariates are measured with error. We propose …

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 …

Histospline Method In Nonparametric Regression Models With Application To Clustered/Longitudinal Data, Raymond J. Carroll, Peter Hall, Tatiyana V. Apanasovich, Xihong Lin

The University of Michigan Department of Biostatistics Working Paper Series

Kernel and smoothing methods for nonparametric function and curve estimation have been particularly successful in "standard" settings, where function values are observed subject to independent errors. However, when aspects of the function are known parametrically, or where the sampling scheme has significant structure, it can be quite difficult to adapt standard methods in such a way that they retain good statistical performance and continue to enjoy easy computability and good numerical properties. In particular, when using local linear modeling it is often awkward to both respect the sampling scheme and produce an estimator with good variance properties, without resorting to …

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 …

A Varying-Coefficient Cox Model For The Effect Of Age At A Marker Event On Age At Menopause, Bin Nan, Xihong Lin, Lynda D. Lisabeth, Sioban D. Harlow

The University of Michigan Department of Biostatistics Working Paper Series

. It is of recent interest in reproductive health research to investigate the validity of a marker event for the onset of menopausal transition and to estimate age at menopause using age at the marker event. We propose a varying coefficient Cox model to investigate the association between age at a marker event, denned as a specific bleeding pattern change, and age at menopause, where both events are subject to censoring and their association varies with age at the marker event. Estimation proceeds using the regression spline method. The proposed method is applied to the Tremin Trust Data to evaluate …

Mixtures Of Varying Coefficient Models For Longitudinal Data With Discrete Or Continuous Non-Ignorable Dropout, Joseph W. Hogan, Xihong Lin, Benjamin A. Herman

The University of Michigan Department of Biostatistics Working Paper Series

The analysis of longitudinal repeated measures data is frequently complicated by missing data due to informative dropout. We describe a mixture model for joint distribution for longitudinal repeated measures, where the dropout distribution may be continuous and the dependence between response and dropout is semiparametric. Specifically, we assume that responses follow a varying coefficient random effects model conditional on dropout time, where the regression coefficients depend on dropout time through unspecified nonparametric functions that are estimated using step functions when dropout time is discrete (e.g., for panel data) and using smoothing splines when dropout time is continuous. Inference under the …