Introduction to Survival Analysis Methods in the Presence of Competing Risks Open Access

Abstract

Competing risk scenarios, where a subject may be at risk for multiple events, occurs frequently in practice. Competing risks are events that may occur prior to the event of interest, thus, changing the probability of accurately observing the event of interest. Conventionally, when focusing on a single failure time, the complement of the Kaplan Meier approach estimates cumulative incidence and Cox Proportional Hazards regression model the risk of an event for fitted covariates. In the presence of competing risks, these techniques are often used by practitioners, where all events aside from the event of interest are considered to be censored. However, these methods are known to overestimate parameters (cumulative incidence function etc.) of interest, regardless of if the competing events are independent. Therefore, to calculate the probability of an event of interest, newly developed methods that are specific to competing risks should be used. To fit a regression model with competing risks, two different hazards can be used: cause-specific or subdistribution hazards. The former estimates the instantaneous rate of the event among those who are currently risk free, while subdistribution hazards estimate the immediate risk for subjects that are event free, including those who experienced a competing event at a previous time. We applied these methods to study the effects of competing risks: first hospital acquired infection and hospital mortality among patients in the surgical intensive care unit. A total of 56 patients developed hospital acquired infection, while 12 died in the hospital. We illustrated the upward bias of the Kaplan Meier method as compared to the cumulative incidence function for both events of interest. Modeling the cause-specific and subdistribution hazard we found the rate of hospital acquired infections decreased with an increase in white blood cell count (SDHR: 0.96, 95% CI: (0.93,1.00) p=.042), and higher Sepsis-related Organ Failure Assessment scores at entry increased the rate of mortality (SDHR: 1.17, 95% CI: (1.01,1.36) p=.032). Noticeably, both significant factors occurred only in the subdistribution hazard models. These findings indicate studies with competing risks should implement the cumulative incidence function and both the cause-specific and subdistribution hazard models to avoid incorrect inference.

Table of Contents

1. Introduction………………………………………………………………………………………………….……1

           1.1 Survival Analysis ……………………………………………………………………………..……..1

           1.2 Competing Risks………………………………………………………………………..……………3

2. Methods……………………………………………………………………………………………………………..5

           2.1 Estimating the Probability of a Single Event……………………………..……………….5

           2.2 Modeling Hazards of a Single Event………………………………………..…….………….6

           2.3 Estimating the Probability of Multiple Events…………………………..……….………8

           2.4 Estimating the Probability of an Event with Competing Risks…………..………..9

           2.5 Modeling Hazards with Competing Risks………………………………………………..10

           2.6 Goodness of Fit…………………………………………………………………….……………….13

           2.7 Statistical Software…………………………………………………………….………………….15

           2.8 Illustrative Example……………………………………………………………….……………..15

3. Results………………………………………………………………………………………………………………18

           3.1 Descriptive Statistics………………………………………………………………………………18

           3.2 Estimating the Cumulative Incidence of Hospital Acquired Infection and Hospital Mortality……… 19

           3.3 Modeling Cause-Specific and Subdistribution Hazards………………………..…..19

           3.4 Model Diagnostics…………………………………………………………………………………21

4. Discussion………………………………………………………………………………………………………...21

Appendix A………………………………………………………………………………………….….……………27

Appendix B…………………………………………………………………………………….…………………….31

List of Tables

Table 1: Descriptive Results of Time-dependent Events for all 150 patients……………..…27

Table 2: Descriptive Characteristics of risk factors for all 150 patients by event………..…27

Table 3: Risk Factors for Hospital Acquired Infection or Mortality Using Multivariable Competing Risk Models… 28

List of Figures

Figure 1: Cumulative incidence functions for all event types………………………….………….29

Figure 2: Cumulative incidence functions and Kaplan Meier estimates for all event types……….. 30

Figure 3: Schoenfeld residual plots for cause-specific hazard model of hospital acquired infection..………31

Figure 4: Schoenfeld residual plots for cause-specific hazard model of hospital mortality..…………32

Figure 5: Schoenfeld residual plots for subdistribution hazard model of hospital acquired infection………33

Figure 6: Schoenfeld residual plots for subdistribution hazard model of hospital mortality..…………………34

About this Master's Thesis

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School	Rollins School of Public Health
Department	Biostatistics
Degree	M.S.P.H.
Submission	Master's Thesis
Language	English
Research Field	Health Sciences, Public Health Applied Mathematics Biology, Biostatistics
Keyword	Kaplan Meier Subdistribution Hazard Competing Risks Cox Proportional Hazard Cumulative Incidence Survival Analysis Cause-specific Hazard
Committee Chair / Thesis Advisor	Manatunga, Amita, Emory University
Committee Members	Easley, Kirk, Emory University

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