Statistical Models Commons^™

Model Checking For Roc Regression Analysis, Tianxi Cai, Yingye Zheng

Harvard University Biostatistics Working Paper Series

The Receiver Operating Characteristic (ROC) curve is a prominent tool for characterizing the accuracy of continuous diagnostic test. To account for factors that might invluence the test accuracy, various ROC regression methods have been proposed. However, as in any regression analysis, when the assumed models do not fit the data well, these methods may render invalid and misleading results. To date practical model checking techniques suitable for validating existing ROC regression models are not yet available. In this paper, we develop cumulative residual based procedures to graphically and numerically assess the goodness-of-fit for some commonly used ROC regression models, and …

Population Intervention Models In Causal Inference, Alan E. Hubbard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a] treatment variable or risk variable on the distribution of a disease in a population. These models, as originally introduced by Robins (e.g., Robins (2000a), Robins (2000b), van der Laan and Robins (2002)), model the marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates, and its dependence on treatment. Marginal structural models are particularly useful in the context of longitudinal data structures, in which each subject's treatment and covariate history are measured over time, and an outcome is recorded at …

Gauss-Seidel Estimation Of Generalized Linear Mixed Models With Application To Poisson Modeling Of Spatially Varying Disease Rates, Subharup Guha, Louise Ryan

Harvard University Biostatistics Working Paper Series

Generalized linear mixed models (GLMMs) provide an elegant framework for the analysis of correlated data. Due to the non-closed form of the likelihood, GLMMs are often fit by computational procedures like penalized quasi-likelihood (PQL). Special cases of these models are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints often make it difficult to apply these iterative procedures to data sets with very large number of cases.

This paper proposes a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits sub-models of the GLMM …

Computational Techniques For Spatial Logistic Regression With Large Datasets, Christopher J. Paciorek, Louise Ryan

Harvard University Biostatistics Working Paper Series

In epidemiological work, outcomes are frequently non-normal, sample sizes may be large, and effects are often small. To relate health outcomes to geographic risk factors, fast and powerful methods for fitting spatial models, particularly for non-normal data, are required. We focus on binary outcomes, with the risk surface a smooth function of space. We compare penalized likelihood models, including the penalized quasi-likelihood (PQL) approach, and Bayesian models based on fit, speed, and ease of implementation.

A Bayesian model using a spectral basis representation of the spatial surface provides the best tradeoff of sensitivity and specificity in simulations, detecting real spatial …

Is The Number Of Sick Persons In A Cohort Constant Over Time?, Paula Diehr, Ann Derleth, Anne Newman, Liming Cai

UW Biostatistics Working Paper Series

Objectives: To estimate the number of persons in a cohort who are sick, over time.

Methods: We calculated the number of sick persons in the Cardiovascular Health Study (CHS), a cohort study of older adults followed up to 14 years, using eight definitions of “healthy” and “sick”. We projected the number in each health state over time for a birth cohort.

Results: The number of sick persons in CHS was approximately constant for 14 years, for all definitions of “sick”. The estimated number of sick persons in the birth cohort was approximately constant from ages 55-75, after which it decreased. …

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 …

The Sensitivity And Specificity Of Markers For Event Times, Tianxi Cai, Margaret S. Pepe, Thomas Lumley, Yingye Zheng, Nancy Swords Jenny

Harvard University Biostatistics Working Paper Series

No abstract provided.

Combining Predictors For Classification Using The Area Under The Roc Curve, Margaret S. Pepe, Tianxi Cai, Zheng Zhang, Gary M. Longton

UW Biostatistics Working Paper Series

No single biomarker for cancer is considered adequately sensitive and specific for cancer screening. It is expected that the results of multiple markers will need to be combined in order to yield adequately accurate classification. Typically the objective function that is optimized for combining markers is the likelihood function. In this paper we consider an alternative objective function -- the area under the empirical receiver operating characteristic curve (AUC). We note that it yields consistent estimates of parameters in a generalized linear model for the risk score but does not require specifying the link function. Like logistic regression it yields …