Mathematics Ph.D. Dissertations

Multivariate Population Attributable Hazard Function For Right-Censored Data

Date of Award

2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics/Mathematical Statistics

First Advisor

John Chen (Advisor)

Second Advisor

Nancy Boudreau (Committee Member)

Third Advisor

Maria Rizzo (Committee Member)

Fourth Advisor

Junfeng Shang (Committee Member)

Abstract

Measuring the impact to different risk factors on a disease at the population level is an important issue in public health, which necessitates the use of Population Attributable Risk (PAR). Traditionally, methods estimating PAR have been focusing on case-control or cross-sectional studies. Although a method for estimation of PAR in cohort study that properly takes into account right-censoring time was proposed recently, the estimation of time-dependent PAR, however, has not been developed completely.

In this dissertation, we explore the estimation problem of PAR with several risk factors or possible confounders for right-censored data. By partitioning the covariate space, we extend the method of attributable hazard function (AHF) to account for several risk factors. In the situation when individual AHF can be partially ordered, we develop new stepwise multiple comparisons procedure using the Partitioning Principle. The simulation study confirms the proof that the proposed procedure always strongly controls the familywise error rate.

Another highlight of the dissertation focuses on the asymptotic distribution of AHF with the assumption that the distribution of a risk factor is time-independent, under Cox model. When there are confounding variables, the adjusted AHF based on the case-load weighting approach is also derived. The new proposed methods are applied to analyze real-life data set in the arthritis study.

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