# Analysis of Longitudinal Random Length Data

Iosif, Ana-Maria (2008) Analysis of Longitudinal Random Length Data. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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## Abstract

In some clinical trials, data are gathered longitudinally on both the frequency of an event and its severity. Oftentimes, it is not feasible to obtain the exact time of the events, and the events are collected over fixed follow-up intervals. We refer to this type of data as longitudinal random length data, since the subjects are observed repeatedly and, at each assessment time, the data can be viewed as vectors of severities with lengths determined by the number of events experienced during the assessment. Suppose the interest is in comparing two treatments, and the treatments are evaluated at multiple points in time. Treatment effect is reflected in simultaneous changes in both the number of events and the severity of each event. Consequently, one needs to jointly model the two outcomes to better evaluate treatment effects. The main objective of this dissertation is to introduce a framework for longitudinal random length data. We propose two multiple population models for such data. We parameterize the models such that, at each measurement time, both the distribution of the random lengths and the distributional mean of each component of the severity vectors depend on the underlying parameter reflecting the treatment effect at that time. Given the random lengths, we assume the distribution of the severities to be multivariate normal. Conditional on the number of events, the dependence in the vector of severities recorded at a single measurement time is modeled using compound symmetry.The first model assumes the numbers of events for a subject at different time points to be independent Poisson random variables and dependence over time is built into the severity measures. The second model generalizes the first one, by adding another layer of dependence over time. We further assume the numbers of the events experienced by a subject across time to be dependent and use a multivariate Poisson distribution to model them. For each model we describe the maximum likelihood estimation procedure and provide the asymptotic properties for the estimators. We apply both models to analyze a data set containing stressful life events in adolescents with major depressive disorder.

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## Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
Iosif, Ana-Mariaani2@pitt.eduANI2
ETD Committee:
Committee ChairSampson, Allan Rasampson@stat.pitt.eduASAMPSON
Committee MemberWilliamson, Douglas Ewilliamsonde@uthscsa.edu
Committee MemberGleser, Leon Jljg@stat.pitt.eduGLESER
Committee MemberThompson, Wesley Kwesleyt@pitt.eduWESLEYT
Date: 25 January 2008
Date Type: Completion
Defense Date: 1 January 2002
Approval Date: 25 January 2008
Submission Date: 6 July 2007
Access Restriction: 5 year -- Restrict access to University of Pittsburgh for a period of 5 years.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Statistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: clustered data; informative cluster size; repeated measurements; longitudinal random length; multivariate Poisson distribution
Other ID: http://etd.library.pitt.edu/ETD/available/etd-07062007-110245/, etd-07062007-110245
Date Deposited: 10 Nov 2011 19:50
URI: http://d-scholarship.pitt.edu/id/eprint/8280