Analysis of Outcomes Subject to Induced Dependent Censoring: Medical Cost and Successive Durations Open Access

Qian, Jing (2009)

Permanent URL: https://etd.library.emory.edu/concern/etds/zp38wc87c?locale=en
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Abstract

In medical studies for chronic diseases, survival time, the usual primary outcome of interest, may not be adequate to assess the treatment or covariate effects on the disease process. To conduct a more comprehensive evaluation, secondary outcomes capturing other features of the disease process are often assessed simultaneously. Typical examples include the lifetime medical cost and successive durations in disease process. Analysis of secondary outcomes is complicated by induced dependent censoring and identifiability issue, arising from the incomplete follow-up data in clinical trials. In this dissertation, two novel statistical methods accommodating the features of these secondary outcomes are proposed.


The first method focuses on the analysis of censored lifetime medical cost. Currently available approaches are incapable of addressing lifetime medical cost distribution for a defined group. To this end, we propose a copula-based semiparametric regression model, which parameterizes the association of the bivariate error term on time and cost scales through a normal copula function, leaving the marginal error distributions completely unspecified. We develop estimation procedure for the regression coefficients and the normal copula association parameter. The resulting estimators are shown to be consistent and asymptotically normal. Simulation studies and a lung cancer data analysis are conducted to evaluate the finite sample performance of the method.


The second approach is motivated by a colon cancer study where patients progress through cancer-free and cancer-recurrence states. Scientific interests lie in the successive durations in this bi-state progressive disease process. For the one-sample problem with incomplete follow-up data, recent investigations have focused on nonparametric inference. However, in many practical situations, the distribution of the second duration is nonparametrically nowhere identifiable. To address this issue, we suggest a semiparametric model that postulates normal copula for the association between the two durations, while leaving the marginals unspecified. Motivated by the colon cancer data, we allow our model to accommodate the situation where the second duration has a probability mass at zero. We propose an inference procedure and study the asymptotic properties of the resulting estimators. Finite sample performance of the proposed method is evaluated via the simulation studies and illustrated with colon cancer study.

Table of Contents

Contents


1 Introduction 1


1.1 Motivating Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 SWOG Lung Cancer Clinical Trial . . . . . . . . . . . . . . . . . 2
1.1.2 A National Intergroup Colon Cancer Clinical Trial . . . . . . . . . 3
1.2 Statistical Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Induced Dependent Censoring . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Identiability Issue . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Medical Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 Successive Durations . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13


2 Copula-based Semiparametric Regression Model for Censored Lifetime
Medical Cost 15


2.1 A Copula-based Semiparametric Regression Model . . . . . . . . . . . 16
2.2 Inference Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1 A Compound Procedure . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Proposed New Estimation Procedure . . . . . . . . . . . . . . . . 21
2.2.3 Asymptotic Properties . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Numerical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.1 Monte-Carlo Simulations Under Normal Copula Model . . . . . . 24
2.3.2 Monte-Carlo Simulations Under Nonnormal Copulas . . . . . . . 30
2.3.3 Application to a Lung Cancer Trial . . . . . . . . . . . . . . . . . 32
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5.1 Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5.2 Asymptotic Normality . . . . . . . . . . . . . . . . . . . . . . . . 46


3 Semiparametric Inference for Successive Durations 57


3.1 Semiparametric Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.1.1 Normal copula model . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.1.2 A realistic censoring mechanism . . . . . . . . . . . . . . . . . . . 61
3.2 Proposed Estimation Procedure . . . . . . . . . . . . . . . . . . . . . . . 62
3.3 Asymptotic Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4 Numerical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.1 Simulation Under Normal Copula Model . . . . . . . . . . . . . . 66
3.4.2 Simulation With Misspecied Copula Model . . . . . . . . . . . . 68
3.4.3 Application to a Colon Cancer Study . . . . . . . . . . . . . . . . 68

3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.6 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.6.1 Consistency and Uniform Consistency . . . . . . . . . . . . . . . . 78
3.6.2 Asymptotic Normality and Weak Convergence . . . . . . . . . . . 87


4 Summary and Future Research 96


4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

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