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biometric.soc.02

Sponsoring Section/Society: ENAR

Session Slot: 2:00- 3:50 Monday

Estimated Audience Size: 300

AudioVisual Request: Two Overheads

Session Title: Statistical Models for Longitudinal Studies: Unifying Longitudinal and Survival Analysis Methods

Description of session: Data collected in studies in public health routinely include both observations of times to events of interest and other measures taken repeatedly over time; e.g. in AIDS clinical trials, both time to death or other event and longitudinal measures of CD4 count, viral load, and other immunological or virological variables are observed. This session focuses on recent advances in methods of analysis that exploit information of both types.

Theme Session: No

Applied Session: Yes

Session Organizer: Hogan, Joseph Brown University

Address: Center for Statistical Sciences Box G-H Brown University Providence RI 02912

Phone: 401-863-9243

Fax: 401-863-9182

Email: jhogan@stat.brown.edu

Session Timing: 110 minutes total (Sorry about format):

Opening Remarks by Chair - 5 minutes First Speaker - 25 minutes Second Speaker - 25 minutes Third Speaker - 25 minutes Discussant - 20 minutes Floor Discusion - 10 minutes

Session Chair: Hogan, Joseph Brown University

Address: Center for Statistical Sciences Box G-H Brown University Providence RI 02912

Phone: 401-863-9243

Fax: 401-863-9182

Email: jhogan@stat.brown.edu

1. The Analysis of Longitudinal Data - An Expanded Perspective

Zeger, Scott, Johns Hopkins University

Address: Department of Biostatistics Johns Hopkins University 615 N. Wolfe Street, Room E3132 Baltimore MD 21205-2179

Phone: 410-955-3067

Fax: 410-955-0958

Email: szeger@jhsph.edu

Abstract: Longitudinal studies in public health permit observations of both times to key health events as well as repeated measures of health outcomes. Statistical methods for times-to-events (survival analysis) and for repeated events (longitudinal data analysis) have developed along independent lines even though substantive questions can often be addressed through joint analysses of both kinds of outcomes.
In this talk, we consider opportunities for unifying statistical methods for times-to-events and repeated measures under an expanded definition of longitudinal data analysis. The ideas will be illustrated with examples from public health research.

2. Nonparametric Incomplete Data Estimation of Stochastic Process Structures Related to Survival Models

Jewell, Nick, University of California, Berkeley

Address: Department of Statistics University of California at Berkeley 367 Evans Hall #3860 Berkeley CA 94720-3860

Phone: 510-642-5361

Fax: 510-642-7892

Email: jewell@stat.Berkeley.edu

Abstract: Considerable attention has been given to nonparametric estimation of simple survival models based on data subject to random censoring and truncation. Recently, there has been additional interest in similar problems based on current status data. In this talk, we will discuss extensions of some of these ideas by considering survival data in a stochastic process setting. The extensions we have in mind are to (i) multidimensional survival processes, and (ii) more general stochastic processes than the familiar two-state survival models. The first of these extensions includes consideration of so-called marker processes where one component of the process is a simple survival counting process and other components represent marker variables thought to be associated with survival.

3. Non-ignorable Non-response in Longitudinal Studies with Continuous Drop-out Times

Scharfstein, Dan, Johns Hopkins University

Address: Department of Biostatistics Johns Hopkins University 615 N. Wolfe Street, Room E3132 Baltimore MD 21205-2179

Phone: 410-955-3067

Fax: 410-955-0958

Email: dscharf@athena.biostat.jhsph.edu

Robins, James M., Harvard School of Public Health

Abstract: Consider a longitudinal study in which we follow subjects for T months after enrollment. At this point, we measure the primary endpoint of interest, Y. In addition to this measurement, a series of baseline covariates, V(0), and time dependent covariates, V(t), are collected. We are interested in making inference about the mean of Y, $\mu$ . Unfortunately, some individuals drop-out before time T. If we let Q denote the continuous drop-out time, then the observable data for an individual is $(X, \Delta, \bar{V}(X), \Delta Y)$ , where $X=\min(Q,T)$ , $\Delta = I(Q \geq T)$ , and $\bar{V}(t) = \{ V(u) : 0 \leq u \leq t\}$ is the covariate history through time t. If Q is unrelated to Y, then Y is said to be missing completely at random and the sample average of the observed outcomes is an unbiased estimate of $\mu$ .
The purpose of this paper is to show how to make inferences about $\mu$ when the drop-out time is modeled semiparametrically, no restrictions are placed on the joint distribution of the outcome and covariates, and the outcome is not missing completely at random. In particular, we assume that the law of Q given $\bar{V}(T)$ and Y follows a proportional hazards model of the form
$\begin{displaymath} \lambda_{Q\vert\bar{V}(T),Y}(u\vert\bar{V}(T),Y) = \lambda(u) \exp ( \delta' h(\bar{V}(u)) + \alpha^* Y)\end{displaymath}$
where $\lambda_{Q\vert\bar{V}(T),Y}(u\vert\bar{V}(T),Y)$ is the hazard of Q given $\bar{V}(T)$ and Y, $\lambda(u)$ is some arbitrary, non-negative function of u, $h(\cdot)$ is a r-dimensional function of the covariate history, $\delta$ is an rx1 vector of unknown parameters, and $\alpha^*$ is a known constant. Note that $\alpha^*=0$ corresponds to missing at random and $\alpha^* \not = 0$ corresponds to non-ignorable non-response. We have chosen to fix this latter constant because we know that it is at best difficult to estimate. Instead, we perform a sensitivity analysis to see how inference about $\mu$ changes as we vary $\alpha^*$ over a plausible range of values. We apply our approach to the analysis of ACTG 175, an AIDS clinical trial in which we define the primary outcome as CD4 at 56 weeks after enrollment. Repeated measurements on CD4 counts act as the time dependent covariates, while gender, age, race, and information on other risk factors serve as the baseline covariates.