Transcript Analyzing Time-to

Analyzing Time-to-Event Data
Survival Analysis and
Cox Proportional Hazards Regression
Robert Boudreau, PhD
Co-Director of Methodology Core
PITT-Multidisciplinary Clinical Research Center
for Rheumatic and Musculoskeletal Diseases
Effect of acyclovir on time to resolution
of postherpetic neuralgia
Spruance SL, Reid JE, Grace M, Samore M. Hazard Ratio in Clinical Trials.
Antimicrob Agents and Chemotherapy Aug 2004:2787-2792.
Flow chart for regression models
Outcome variable continuous or dichotomous?
continuous
dichotomous
Predictor variable categorical?
No
Yes
(e.g. groups)
Multiple linear
regression
ANCOVA
Time-to-event available ?
No
Multiple logistic
regression
Yes
Cox proportional
hazards regression
Effect of acyclovir on time to resolution
of postherpetic neuralgia
Event: Resolution of Herpes Zoster Pain
 Time-to-event also available
Statistical Modeling Approaches
Logistic Regression:
Would do separate rate comparisons at distinct timepoints
 % with Pain Resolution by 60days, by 120 days …
Cox Proportional Hazards Regression:
 Comparison of survival curves across all timepoints
> Uses more information: Event (Yes/No), Time-to-event
> More powerful in identifying systematic differences
Examples
Compare MTX+Enbrel vs MTX+Humira
 Time until Remission
 Time until ACR 20/50/70
 Time until DAS drop > 1.2
Longitudinal cohort study (on aging)
 Time until participant develops mobility limitation
 Time until participant has CVD event
 Time until mortality event
Censoring
Generally, three reasons why censoring might occur:



A subject does not experience the event before the
study ends
A person is lost to follow-up during the study
period
A person withdraws from the study
These are all examples of right-censoring
Censoring
 Most typical to consider start of time-to-event “clock” as t=0
Censored
o
o
Non-Events
Life Tables
Life Tables
Life Tables
146-30
Censored observations are counted in the denominator of those
“at risk” until they are censored
Life Tables
146-30
Censored observations are counted in the denominator of those
“at risk” until they are censored
Survival Curve
Kaplan-Meier Survival Curve



Generalization of Life Table method
Assumes (i.e. can handle) continuous event
times
Updates “at risk” denominator at each event or
censor timepoint
400 meter walk time in elderly
predicts mobility limitation

Newman AB, Simonsick EM, Naydeck BL, Boudreau RM,
Kritchevsky SB, Nevitt MC, Pahor M, Satterfield S, Brach
JS, Studenski SA, Harris TB. Association of Long
Distance Corridor Walk Performance with Mortality,
Cardiovascular Disease, Mobility Limitation, and
Disability. JAMA 2006;295:2018-2026.
Event: Persistent Mobility Limitation:
 2 consecutive reports (6 month contacts) of having
any self-reported difficulty walking a quarter of a
mile or climbing stairs
% of Women With Mobility Limitation
by Quartile of Baseline 400m Walk Time
Quartile 1
Lowest times
(Fastest Pace)
Proportional Hazards Model
Example: Compare Treatment to Control Group
Dummy variable for group (random) assignment:
Z= 0 if control group
= 1 if treatment group
Survival Curves (group specific)
Control
Treatment
Effect of acyclovir on time to resolution
of postherpetic neuralgia
Hazard Ratio (HR)
Example: Compare Treatment to Control Group
Survival Curves (group specific)
Control
Treatment
HR =
(same relationship to regression coeff
“beta” as OR in logistic regression)
Cox Proportional Hazards
Regression
proc phreg data=acyclovir;
model time*event(0)=drug;
run;
* event=0 if censored (non-event)
*
=1 if event (resolution of pain)
HR = exp( 0.77919) = 2.180
(acyclovir vs placebo)
Cox PH Regression
Adjusted for Age
proc phreg data=acyclovir;
model time*pain_resolved(0)=drug age;
run;
Adjusted HR = exp( 0.94108) = 2.563 (acyclovir vs placebo)
Age HR=1.096 => Increasing “pain resolve” response with age
400 meter walk time in elderly
predicts mobility limitation
Note: “Completed the 400m walk” is the referent group here
400 meter walk time (continuous)
predicts mortality, CVD and
mobility limitation

Of those who completed 400 meters, each additional
minute of performance time was associated with an
adjusted HR of
HR= 1.29 (95% CI, 1.12-1.48) for mortality
HR= 1.20 (95% CI, 1.01-1.42) for incident
cardiovascular disease
HR= 1.52 (95% CI, 1.41-1.63) for mobility limitation
400 meter walk time vs mortality
(best vs worst quartile)

After adjusting for potential confounders,
those in the poorest quartile of functional capacity
(walk time > 362 seconds) had a higher risk of death
over 6 years than those in the best quartile
(walk time < 290 seconds).
 Adjusted HR = 3.23; 95% CI, 2.11-4.94; P .001).
Thank you !
Any Questions?
Robert Boudreau, PhD
Co-Director of Methodology Core
PITT-Multidisciplinary Clinical Research Center
for Rheumatic and Musculoskeletal Diseases