Statistical Models Commons^™

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 …

Robust Residuals And Diagnostics In Autoregressive Time Series, Kirk W. Anderson

Dissertations

One of the goals of model diagnostics is outlier detection. In particular, we would like to use the residuals, appropriately standardized, to “flag” outliers. Hopefully, our (robust) procedure has yielded a fit that resists undue influence by outlying points, while simultaneously drawing attention to these interesting points via residual analysis. In this study we consider several different methods of standardizing the residuals resulting from autoregression. A large sample approximation for the variance of rank-based first order autoregressive time series residuals is developed. This provides studentized residuals, specific to the time series model and estimation procedure. Simulation studies are presented that …

New Statitstical Methods For The Estimation Of The Mean And Standard Deviation From Normally Distributed Censored Samples, Abou El-Makarim Abd El-Alim Aboueissa

Dissertations

The main objective of this dissertation is to estimate the mean /x and standard deviation cr of a normal population from left-censored samples. We have developed new methods for calculating estimates for the mean and standard deviation of a normal population from left-censored samples. Some of these methods based on traditional estimating procedures. A new method of obtaining the Cohen maximum likelihood estimates for fx and cr without the aid of an auxiliary table will be introduced. This new method will be used to extend Cohen table of estimating the Cohen A-parameter that is required for calculating the maximum likelihood …

On Rank-Based Considerations For Generalized Linear Models And Generalized Estimating Equation Models, Diana R. Cucos

Dissertations

This study discusses rank-based robust methods for estimation of parameters and hypotheses testing in the generalized linear models (GLM) and generalized estimating equations (GEE) setting. The robust estimates are obtained by minimizing a Wilcoxon drop in dispersion function for linear or nonlinear regression models. In addition, diagnostic tools for outliers and influential observations are being developed. These models are generalizations of linear and nonlinear models. They allow for both nonlinear mean functions and heteroscedasticity of their random errors. This makes them quite useful in practice. Rank-based inference has been developed for linear models over the last thirty years. This inference …

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 …

The Kpss Test With Seasonal Dummies, Sainan Jin, Sainan Jin

Research Collection School Of Economics

It is shown that the KPSS test for stationarity may be applied without change to regressions with seasonal dummies. In particular, the limit distribution of the KPSS statistic is the same under both the null and alternative hypotheses whether or not seasonal dummies are used.

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 …

Visualization Methods: A Comparative Study Of New, Traditional And Robust Procedures, Kimberly Crimin

Dissertations

Two major goals in discriminant analysis are discrimination and classification. In discrimination, the goal is to describe graphically (visualization) different features of several known groups. In classification, the goal is to allocate unknown observations to one of several known groups. We have developed new visualization procedures based on traditional estimating procedures and also on robust estimating procedures. We have further developed robust classification procedures. We propose several robust classification procedures based on coordinatewise and affine equivariant, rank-based robust estimates. Empirical studies are performed over many different error distributions. These studies result in empirical efficiencies of the robust and traditional procedures. …

Nonlinear Regression Based On Ranks, Ashebar Abebe

Dissertations

This study presents robust methods for estimating parameters of nonlinear regression models. The proposed methods obtain estimates by minimizing rankbased dispersions instead of the Euclidean norm. We focus on the Wilcoxon and generalized signed-rank dispersion functions. Asymptotic properties of the estimators are established under mild regularity conditions similar to those used in least squares and least absolute deviations estimation. The study also shows that by considering the generalized signed-rank dispersion we obtain a class of estimators that encompasses most of the existing popular nonlinear regression estimators. As in linear models, these rank-based procedures provide estimators that are highly efficient. This …

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.

Unemployment Scarring In High Unemployment Regions, Claudio Lupi, Patrizia Ordine

Claudio Lupi

This paper investigates the effect of individual unemployment experiences on re-employment wages. The empirical analysis is carried out on a panel of Italian individuals. The main result is that while in the northern regions the effect is similar to the one estimated for the UK, in the southern area of the country the impact is not significant. We link this result to the particular socio-economic environment in which the unemployment spells are experienced. We argue that this might be due to the fact that in a high unemployment environment individual unemployment experiences are perceived as "normal" and do not necessarily …

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 …