Statistics and Probability Commons^™

On The Causal Interpretation Of Race In Regressions Adjusting For Confounding And Mediating Variables, Tyler J. Vanderweele, Whitney Robinson

Harvard University Biostatistics Working Paper Series

We consider different possible interpretations of the “effect of race” when regressions are run with race as an exposure variable, controlling also for various confounding and mediating variables. When adjustment is made for socioeconomic status early in a person's life, we discuss under what contexts the regression coefficients for race can be interpreted as corresponding to the extent to which a racial disparity would remain if various socioeconomic distributions early in life across racial groups could be equalized. When adjustment is also made for adult socioeconomic status, we note how the overall disparity can be decomposed into the portion that …

Using Regression Models To Analyze Randomized Trials: Asymptotically Valid Hypothesis Tests Despite Incorrectly Specified Models, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Regression models are often used to test for cause-effect relationships from data collected in randomized trials or experiments. This practice has deservedly come under heavy scrutiny, since commonly used models such as linear and logistic regression will often not capture the actual relationships between variables, and incorrectly specified models potentially lead to incorrect conclusions. In this paper, we focus on hypothesis test of whether the treatment given in a randomized trial has any effect on the mean of the primary outcome, within strata of baseline variables such as age, sex, and health status. Our primary concern is ensuring that such …

On Time Series Analysis Of Public Health And Biomedical Data, Scott L. Zeger, Rafael A. Irizarry, Roger D. Peng

Johns Hopkins University, Dept. of Biostatistics Working Papers

A time series is a sequence of observations made over time. Examples in public health include daily ozone concentrations, weekly admissions to an emergency department or annual expenditures on health care in the United States. Time series models are used to describe the dependence of the response at each time on predictor variables including covariates and possibly previous values in the series. Time series methods are necessary to account for the correlation among repeated responses over time. This paper gives an overview of time series ideas and methods used in public health research.

The Cross-Validated Adaptive Epsilon-Net Estimator, Mark J. Van Der Laan, Sandrine Dudoit, Aad W. Van Der Vaart

U.C. Berkeley Division of Biostatistics Working Paper Series

Suppose that we observe a sample of independent and identically distributed realizations of a random variable. Assume that the parameter of interest can be defined as the minimizer, over a suitably defined parameter space, of the expectation (with respect to the distribution of the random variable) of a particular (loss) function of a candidate parameter value and the random variable. Examples of commonly used loss functions are the squared error loss function in regression and the negative log-density loss function in density estimation. Minimizing the empirical risk (i.e., the empirical mean of the loss function) over the entire parameter space …

To Model Or Not To Model? Competing Modes Of Inference For Finite Population Sampling, Rod Little

The University of Michigan Department of Biostatistics Working Paper Series

Finite population sampling is perhaps the only area of statistics where the primary mode of analysis is based on the randomization distribution, rather than on statistical models for the measured variables. This article reviews the debate between design and model-based inference. The basic features of the two approaches are illustrated using the case of inference about the mean from stratified random samples. Strengths and weakness of design-based and model-based inference for surveys are discussed. It is suggested that models that take into account the sample design and make weak parametric assumptions can produce reliable and efficient inferences in surveys settings. …

Asymptotics Of Cross-Validated Risk Estimation In Estimator Selection And Performance Assessment, Sandrine Dudoit, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Risk estimation is an important statistical question for the purposes of selecting a good estimator (i.e., model selection) and assessing its performance (i.e., estimating generalization error). This article introduces a general framework for cross-validation and derives distributional properties of cross-validated risk estimators in the context of estimator selection and performance assessment. Arbitrary classes of estimators are considered, including density estimators and predictors for both continuous and polychotomous outcomes. Results are provided for general full data loss functions (e.g., absolute and squared error, indicator, negative log density). A broad definition of cross-validation is used in order to cover leave-one-out cross-validation, V-fold …

Partial Auc Estimation And Regression, Lori E. Dodd, Margaret S. Pepe

UW Biostatistics Working Paper Series

Accurate disease diagnosis is critical for health care. New diagnostic and screening tests must be evaluated for their abilities to discriminate disease from non-diseased states. The partial area under the ROC curve (partial AUC) is a measure of diagnostic test accuracy. We present an interpretation of the partial AUC that gives rise to a new non-parametric estimator. This estimator is more robust than existing estimators, which make parametric assumptions. We show that the robustness is gained with only a moderate loss in efficiency. We describe a regression modelling framework for making inference about covariate effects on the partial AUC. Such …

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 …

Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

In many applications, it is often of interest to estimate a bivariate distribution of two survival random variables. Complete observation of such random variables is often incomplete. If one only observes whether or not each of the individual survival times exceeds a common observed monitoring time C, then the data structure is referred to as bivariate current status data (Wang and Ding, 2000). For such data, we show that the identifiable part of the joint distribution is represented by three univariate cumulative distribution functions, namely the two marginal cumulative distribution functions, and the bivariate cumulative distribution function evaluated on the …