Analysis of Time to Recurrent Pulmonary Exacerbation: A Review of Three Statistical Approaches Open Access

Zhang, Luyu (Fall 2018)

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Recurrent data are not unheard of in biomedical studies. Individuals can experience multiple events of the same type during the study period. Three common statistical methods for recurrent outcomes are reviewed in this thesis. These methods are count regression, standard Cox proportional hazards (PH) regression, recurrent event survival regression. This study examines the mathematical underpinnings of these three methods; the limitations of each of the three approaches are also discussed. Two models, Poisson and negative binomial, are discussed in count regression. Both of them model the total number of interest events over the study period, but the negative binomial is a more flexible model than the Poisson model due to an additional parameter. The standard Cox PH model analyzes the time to the first event and ignores repeated events. Finally, the proportional intensity model, Prentice, Williams, and Peterson (PWP) total time model and PWP gap time model are discussed in recurrent event survival regression. They all account for the repeated events, but the two PWP models are more robust for analyzing recurrent events. The example study that we use in this paper is for testing the effectiveness of high dose vitamin D on preventing consecutive re-hospitalizations because of pulmonary exacerbations, which often happen repeatedly in adults with cystic fibrosis. Nevertheless, we found, based on results of all methods, that the vitamin D treatment does not have significant effects on preventing adults with cystic fibrosis from pulmonary exacerbations.

Table of Contents

Chapter 1 Introduction. 7

Overview of study design. 8

Chapter 2 Count regression. 9

Poisson Regression. 9

Negative Binomial Regression. 10

Chapter 3 Cox Proportional Hazards Regression. 11

Chapter 4 Recurrent Event Survival Regression. 13

The Andersen-Gill model 13

The Prentice, Williams, and Peterson total time model 14

The PWP gap time model 15

Chapter 5 Results of the DISC study. 15

Data description of the DISC study. 15

Count regression analysis. 17

Cox Proportional Hazards regression analysis. 19

The PWP total time analysis. 21

Chapter 6 Discussion and Conclusion. 22

Reference. 24

Appendix 27

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