1. EPID 799C, Lecture 22 Wednesday, Nov. 14, 2018
Survival Analysis
EPID 799C, Lecture 22
Wednesday, Nov. 14, 2018

2. Acknowledgements Brian Pence (EPID 718)
Alan Brookhart and Steve Cole (EPID 722)
Mike and Nick!

3. Intro to Survival Analysis
Epidemiological methods to analyze time-to-event outcomes:
Time until death (a.k.a., survival)
Time until disease occurrence
Time until treatment initiation or discontinuation
Evaluate effect of treatment on the outcome – both occurrence and timing of the event of interest.

4. Intro to Survival Analysis
Single ascertainment of presence/absence of the outcome:
vs.
Measure outcomes over time:
Treatment
Outcome
Treatment
A=1
Treatment
A=0
Follow-up time (t) for
Outcome

5. Survival Methods
Survival at time t: Probability of event-free survival up to time t.
This is the complement of the cumulative risk of the event.
Cumulative risk at time t: Risk(t) = 1 – Survival(t)
Hazard at time t: Instantaneous rate of events. Conditional probability of the event at time t, given survival to time t.
“Survival Analysis”
spreadsheet found
on my computer…

6. Survival Methods
Kaplan-Meier is a non-parametric estimator of survival.
Defined as the cumulative product of the estimated probability of not incurring an event.
Other non-parametric estimators: Nelson-Aalen (cumulative hazard), Aalen- Johansen (competing events).
Parametric survival methods assume the underlying distribution of the survival times follows a known probability distribution.
Exponential, Weibull, lognormal, etc.
Cox proportional hazards model is a semiparametric approach, used to estimate the relationship between the hazard function and predictor variables.

7. Survival Analysis in R Lots of package options! Here are a few:
Core survival analysis methods: survival (most other packages rely on it)
Survival plots: ggfortify and survminer
Tidy your Cox models: survutils
Dealing with competing risks: cmprsk
Alan Brookhart’s work in progress: ipwrisk
Many more here:

8. Births Example Preterm birth as a time-to-event outcome.
Time to event: wksgest
Event status: preterm
Risk period: weeks of gestation

9. Censoring and Competing Events
Survival methods need to account for censoring and competing events in analyzing time-to-event data.
In addition to confounding and the usual suspects.

10. Censoring and Competing Events
Censoring events (e.g., study drop-out) prevent our observation of the outcome.
Censoring event
Treatment
Outcome

11. Censoring and Competing Events
Censoring events (e.g., study drop-out) prevent our observation of the outcome.
Informative censoring occurs when there are determinants of both censoring and the outcome.
If not dealt with analytically, can bias risk estimates.
Determinants
Censoring event
Treatment
Outcome

12. Censoring and Competing Events
Competing events (e.g., death) prevent the occurrence of the outcome. X
Treatment
Outcome
Competing event

13. Censoring and Competing Events
Competing events (e.g., death) prevent the occurrence of the outcome.
Treating competing events like censoring events (i.e., assuming outcome could later occur) can bias our estimates of risk. X
Treatment
Outcome
Competing event
Outcome

14. IP Weights for Survival Analysis
Confounding: Apply IPTW to survival data (same approach from Monday).
Censoring: Account for potentially informative censoring by applying IPCW.
Competing risks: Use an IP-weighted estimator that allows for multiple event types.

15. WIHS Example
Data from the Women’s Interagency HIV Study on history of injection drug use (exposure) and incidence of treatment initiation (outcome).
See Lau 2009 AJE for survival methods using this data.
With similar data: Cole 2015 AJE (theory), Cole 2015 AJE (application)

16. 1,164 patients with HIV, free of clinical AIDS
WIHS Example
1,164 patients with HIV, free of clinical AIDS
Dec. 6, 1995
FDA approval
Dec. 6, 2005
End of study
10-year follow-up

17. 1,164 patients with HIV, free of clinical AIDS
WIHS Example
1,164 patients with HIV, free of clinical AIDS
Dec. 6, 1995
FDA approval
Dec. 6, 2005
End of study
10-year follow-up
Outcome event

18. 1,164 patients with HIV, free of clinical AIDS
WIHS Example
1,164 patients with HIV, free of clinical AIDS
Dec. 6, 1995
FDA approval
Dec. 6, 2005
End of study
10-year follow-up
Outcome event
Censoring event

19. 1,164 patients with HIV, free of clinical AIDS
WIHS Example
1,164 patients with HIV, free of clinical AIDS
Dec. 6, 1995
FDA approval
Dec. 6, 2005
End of study
10-year follow-up
Outcome event
Censoring event
Competing event

20. Access the WIHS Data
library(devtools) devtools::install_bitbucket("novisci/wihs2009") library(WIHS2009) #more info here: