Marie Davidian

Variance Function Estimation

Abstract Heteroscedastic regression models are used in fields including economics, engineering, and the biological and physical sciences. Often, the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters. Standard asymptotic theory implies that how one estimates the variance function, in particular the structural parameters, has no effect on the first-order properties of the regression parameter estimates; there is evidence, however, both in practice and higher-order theory to suggest that how one estimates the variance function does matter. Further, in some settings, estimation of the variance function is of independent interest or plays an important role in estimation of other quantities. In this article, we study variance function estimation in a unified way, focusing on common methods proposed in the statistical and other literature, to make both general observations and compare different estimation schemes. We show that there are significant di...

Nonlinear Models for Repeated Measurement Data: An Overview and Update

Nonlinear mixed effects models for data in the form of continuous, repeated measurements on each of a number of individuals, also known as hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individual-specific characteristics. This framework first enjoyed widespread attention within the statistical research community in the late 1980s, and the 1990s saw vigorous development of new methodological and computational techniques for these models, the emergence of general-purpose software, and broad application of the models in numerous substantive fields. This article presentsan overview of the formulation, interpretation, and implementation of nonlinear mixed effects models and surveys recent advances and applications.

Differences in Viral Dynamics between Genotypes 1 and 2 of Hepatitis C Virus

Many studies have shown that patients infected with hepatitis C virus (HCV) of genotype 2 have better response to interferon (IFN)-alpha treatment than genotype 1 patients; however, the mechanisms responsible for this difference are not understood. In this study, viral dynamics during high-dose IFN induction treatment were compared between the genotypes. Patients in each group received 10 MU of IFN-alpha2b for 14 days, and HCV RNA levels were frequently determined. Nonlinear fitting, both individually for each patient and using a mixed-effects approach, of the viral kinetic data to a mathematical model of the IFN effect on HCV infection was performed. The antiviral effectiveness of IFN in blocking virus production, the free virion clearance rate, and the HCV-infected cell death rate were all significantly higher for genotype 2 patients than for genotype 1 patients. Thus, the better response rate of patients infected with HCV genotype 2 is multifactorial. This is the first finding of a difference in viral dynamics between subtypes of the same virus and demonstrates the importance of subtype-specific virus-host-drug interactions.

Doubly Robust Estimation of Causal Effects

Doubly robust estimation combines a form of outcome regression with a model for the exposure (i.e., the propensity score) to estimate the causal effect of an exposure on an outcome. When used individually to estimate a causal effect, both outcome regression and propensity score methods are unbiased only if the statistical model is correctly specified. The doubly robust estimator combines these 2 approaches such that only 1 of the 2 models need be correctly specified to obtain an unbiased effect estimator. In this introduction to doubly robust estimators, the authors present a conceptual overview of doubly robust estimation, a simple worked example, results from a simulation study examining performance of estimated and bootstrapped standard errors, and a discussion of the potential advantages and limitations of this method. The supplementary material for this paper, which is posted on the Journals Web site (http://aje.oupjournals.org/), includes a demonstration of the doubly robust property (Web Appendix 1) and a description of a SAS macro (SAS Institute, Inc., Cary, North Carolina) for doubly robust estimation, available for download at http://www.unc.edu/~mfunk/dr/.

Longitudinal Data Analysis

Preface. Acknowledgments. Acronyms. 1. Introduction. 1.1 Advantages of Longitudinal Studies. 1.2 Challenges of Longitudinal Data Analysis. 1.3 Some General Notation. 1.4 Data Layout. 1.5 Analysis Considerations. 1.6 General Approaches. 1.7 The Simplest Longitudinal Analysis. 1.8 Summary. 2. ANOVA Approaches to Longitudinal Data. 2.1Single-Sample Repeated Measures ANOVA. 2.2 Multiple-Sample Repeated Measures ANOVA. 2.3 Illustration. 2.4 Summary. 3. MANOVA Approaches to Longitudinal Data. 3.1 Data Layout for ANOVA versus MANOVA. 3.2 MANOVA for Repeated Measurements. 3.3 MANOVA of Repeated Measures-s Sample Case. 3.4 Illustration. 3.5 Summary. 4. Mixed-Effects Regression Models for Continuous Outcomes. 4.1 Introduction. 4.2 A Simple Linear Regression Model. 4.3 Random Intercept MRM. 4.4 Random Intercept and Trend MRM. 4.5 Matrix Formulation. 4.6 Estimation . 4.7 Summary. 5. Mixed-Effects Polynomial Regression Models. 5.1 Introduction. 5.2 Curvilinear Trend Model. 5.3 Orthogonal Polynomials. 5.4 Summary. 6. Covariance Pattern Models. 6.1 Introduction. 6.2 Covariance Pattern Models. 6.3 Model Selection. 6.4 Example. 6.5 Summary. 7. Mixed Regression Models with Autocorrelated Errors. 7.1 Introduction. 7.2 MRMs with AC Errors. 7.3 Model Selection. 7.4 Example. 7.5 Summary. 8. Generalized Estimating Equations (GEE) Models. 8.1 Introduction. 8.2 Generalized Linear Models (GLMs). 8.3 Generalized Estimating Equations (GEE) Models. 8.4 GEE Estimation. 8.5 Example. 8.6 Summary. 9. Mixed-Effects Regression Models for Binary Outcomes. 9.1 Introduction. 9.2 Logistic Regression Model. 9.3 Probit Regression Models. 9.4 Threshold Concept. 9.5 Mixed-Effects Logistic Regression Model. 9.6 Estimation. 9.7 Illustration. 9.8 Summary. 10. Mixed-Effects Regression Models for Ordinal Outcomes. 10.1 Introduction. 10.2 Mixed-Effects Proportional Odds Model. 10.3 Psychiatric Example. 10.4 Health Services Research Example. 10.5 Summary. 11. Mixed-Effects Regression Models for Nominal Data. 11.1 Mixed-Effects Multinomial Regression Model. 11.2 Health Services Research Example. 1 1.3 Competing Risk Survival Models. 11.4 Summary. 12. Mixed-effects Regression Models for Counts. 12.1 Poisson Regression Model. 12.2 Modified Poisson Models. 12.3 The ZIP Model. 12.4 Mixed-Effects Models for Counts. 12.5 Illustration. 12.6 Summary. 13. Mixed-Effects Regression Models for Three-Level Data. 13.1 Three-Level Mixed-Effects Linear Regression Model. 13.1.1 Illustration. 13.2 Three-Level Mixed-Effects Nonlinear Regression Models. 13.3 Summary. 14. Missing Data in Longitudinal Studies. 14.1 Introduction. 14.2 Missing Data Mechanisms. 14.3 Models and Missing Data Mechanisms. 14.4 Testing MCAR. 14.5 Models for Nonignorable Missingness. 14.6 Summary. Bibliography. Topic Index.

Human immunodeficiency virus type 1-specific cytotoxic T lymphocyte activity is inversely correlated with HIV type 1 viral load in HIV type 1- infected long-term survivors

HIV-1-specific cytotoxic T cell (CTL) activity has been suggested to correlate with protection from progression to AIDS. We have examined the relationship between HIV-specific CTL activity and maintenance of peripheral blood CD4+ T lymphocyte counts and control of viral load in 17 long-term survivors (LTSs) of HIV-1 infection. Longitudinal analysis indicated that the LTS cohort demonstrated a decreased rate of CD4+ T cell loss (18 cells/mm3/year) compared with typical normal progressors (approximately 60 cells/mm3/year). The majority of the LTSs had detectable, variable, and in some individuals, quite high (>10(4) RNA copies/ml) plasma viral load during the study period. In a cross-sectional analysis, HIV-specific CTL activity to HIV Gag, Pol, and Env proteins was detectable in all 17 LTSs. Simultaneous analysis of HIV-1 Gag-Pol, and Env-specific CTLs and virus load in protease inhibitor-naive individuals showed a significant inverse correlation between Pol-specific CTL activity and plasma HIV-1 RNA levels (p = 0.001). Furthermore, using a mixed linear effects model the combined effects of HIV-1 Pol- and Env-specific CTL activity on the viral load were significantly stronger than the effects of HIV-1 Pol-specific CTL activity alone on predicted virus load. These data suggest that the presence of HIV-1-specific CTL activity in HIV-1-infected long-term survivors is an important component in the effective control of HIV-1 replication.

Estimating the parameters in the Cox model when covariate variables are measured with error.

The Cox proportional hazards model is commonly used to model survival data as a function of covariates. Because of the measuring mechanism or the nature of the environment, covariates are often measured with error and are not directly observable. A naive approach is to use the observed values of the covariates in the Cox model, which usually produces biased estimates of the true association of interest. An alternative strategy is to take into account the error in measurement, which may be carried out for the Cox model in a number of ways. We examine several such approaches and compare and contrast them through several simulation studies. We introduce a likelihood-based approach, which we refer to as the semiparametric method, and show that this method is an appealing alternative. The methods are applied to analyze the relationship between survival and CD4 count in patients with AIDS.

Randomized COMparison of Platelet Inhibition With Abciximab, TiRofiban and Eptifibatide During Percutaneous Coronary Intervention in Acute Coronary Syndromes The COMPARE Trial

Background—The relative anti-aggregatory effects of currently prescribed platelet glycoprotein IIb/IIIa receptor antagonists during and after percutaneous coronary intervention for acute coronary syndromes have not been established. Methods and Results—We randomized 70 acute coronary syndrome patients undergoing percutaneous coronary intervention to receive abciximab, eptifibatide, or tirofiban at doses used in the Evaluation of Platelet IIb/IIIa Inhibitor for STENTing (EPISTENT), Platelet glycoprotein IIb/IIIa in Unstable angina Receptor Suppression Using Integrilin Therapy (PURSUIT), and Platelet Receptor Inhibition in ischemic Syndrome Management in Patients Limited by Unstable Signs and symptoms (PRISM-PLUS)/Randomized Efficacy Study of Tirofiban for Outcomes and Restenosis (RESTORE) trials, respectively. Platelet aggregation (PA) in response to 20 &mgr;mol/L of adenosine diphosphate was measured with turbidimetric aggregometry in both D-phenylalanyl-l-prolyl-l-arginine chloromethylketone and citrate-anticoagulated blood early (15 and 30 minutes) and late (4, 12, and 18 to 24 hours) after drug initiation. At 15 and 30 minutes, PA was significantly less inhibited by the tirofiban-RESTORE regimen compared with abciximab (P =0.028) and eptifibatide regimens (P =0.0001). The abciximab regimen, however, showed increasingly varied anti-aggregatory effects during continued infusion for ≥4 hours. Citrate exaggerated ex vivo platelet inhibition after eptifibatide and tirofiban, but had the opposite effect on abciximab. Of all regimens evaluated, the eptifibatide regimen inhibited PA most consistently throughout both the early and late periods. Conclusions—Currently recommended drug regimens to inhibit the platelet glycoprotein IIb/IIIa receptor have distinct pharmacodynamic profiles that might affect their relative efficacy in acute coronary syndromes and percutaneous coronary intervention.

Smooth nonparametric maximum likelihood estimation for population pharmacokinetics, with application to quinidine

The seminonparametric (SNP) method, popular in the econometrics literature, is proposed for use in population pharmacokinetic analysis. For data that can be described by the nonlinear mixed effects model, the method produces smooth nonparametric estimates of the entire random effects density and simultaneous estimates of fixed effects by maximum likelihood. A graphical modelbuilding strategy based on the SNP method is described. The methods are illustrated by a population analysis of plasma levels in 136 patients undergoing oral quinidine therapy.

Improving Efficiency of Inferences in Randomized Clinical Trials Using Auxiliary Covariates

The primary goal of a randomized clinical trial is to make comparisons among two or more treatments. For example, in a two-arm trial with continuous response, the focus may be on the difference in treatment means; with more than two treatments, the comparison may be based on pairwise differences. With binary outcomes, pairwise odds ratios or log odds ratios may be used. In general, comparisons may be based on meaningful parameters in a relevant statistical model. Standard analyses for estimation and testing in this context typically are based on the data collected on response and treatment assignment only. In many trials, auxiliary baseline covariate information may also be available, and it is of interest to exploit these data to improve the efficiency of inferences. Taking a semiparametric theory perspective, we propose a broadly applicable approach to adjustment for auxiliary covariates to achieve more efficient estimators and tests for treatment parameters in the analysis of randomized clinical trials. Simulations and applications demonstrate the performance of the methods.