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Analyzing Time-to-Event Data Survival Analysis and Cox Proportional Hazards Regression Robert Boudreau, PhD Co-Director of Methodology Core PITT-Multidisciplinary.

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Presentation on theme: "Analyzing Time-to-Event Data Survival Analysis and Cox Proportional Hazards Regression Robert Boudreau, PhD Co-Director of Methodology Core PITT-Multidisciplinary."— Presentation transcript:

1 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

2 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.

3 Flow chart for regression models Outcome variable continuous or dichotomous? dichotomouscontinuous Time-to-event available ? NoYes Multiple logistic regression Cox proportional hazards regression Predictor variable categorical? NoYes (e.g. groups) Multiple linear regression ANCOVA

4 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

5 Examples Compare MTX+Enbrel vs MTX+Humira Time until Remission Time until Remission Time until ACR 20/50/70 Time until ACR 20/50/70 Time until DAS drop > 1.2 Time until DAS drop > 1.2 Longitudinal cohort study (on aging) Time until participant develops mobility limitation Time until participant develops mobility limitation Time until participant has CVD event Time until participant has CVD event Time until mortality event Time until mortality event

6 Censoring Generally, three reasons why censoring might occur: A subject does not experience the event before the study ends A subject does not experience the event before the study ends A person is lost to follow-up during the study period A person is lost to follow-up during the study period A person withdraws from the study A person withdraws from the study These are all examples of right-censoring

7 Censoring Censored Non-Events o o Most typical to consider start of time-to-event clock as t=0

8 Life Tables

9

10 Censored observations are counted in the denominator of those at risk until they are censored 146-30

11 Life Tables Censored observations are counted in the denominator of those at risk until they are censored 146-30

12 Survival Curve

13 Kaplan-Meier Survival Curve Generalization of Life Table method Generalization of Life Table method Assumes (i.e. can handle) continuous event times Assumes (i.e. can handle) continuous event times Updates at risk denominator at each event or censor timepoint Updates at risk denominator at each event or censor timepoint

14 400 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. 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 2 consecutive reports (6 month contacts) of having any self-reported difficulty walking a quarter of a mile or climbing stairs

15 % of Women With Mobility Limitation by Quartile of Baseline 400m Walk Time Quartile 1 Lowest times (Fastest Pace)

16 Proportional Hazards Model Example: Compare Treatment to Control Group Dummy variable for group (random) assignment: Z= 0 if control group = 1 if treatment group = 1 if treatment group Survival Curves (group specific) Control Treatment

17 Effect of acyclovir on time to resolution of postherpetic neuralgia

18 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)

19 Cox Proportional Hazards Regression proc phreg data=acyclovir; model time*event(0)=drug; 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)

20 Cox PH Regression Adjusted for Age proc phreg data=acyclovir; model time*pain_resolved(0)=drug age; 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

21 400 meter walk time in elderly predicts mobility limitation Note: Completed the 400m walk is the referent group here

22 400 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 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= 1.29 (95% CI, 1.12-1.48) for mortality HR= 1.20 (95% CI, 1.01-1.42) for incident cardiovascular disease 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 HR= 1.52 (95% CI, 1.41-1.63) for mobility limitation

23 400 meter walk time vs mortality (best vs worst quartile) After adjusting for potential confounders, 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 over 6 years than those in the best quartile (walk time < 290 seconds). (walk time < 290 seconds). Adjusted HR = 3.23; 95% CI, 2.11-4.94; P.001). Adjusted HR = 3.23; 95% CI, 2.11-4.94; P.001).

24 Thank you ! Any Questions? Robert Boudreau, PhD Co-Director of Methodology Core PITT-Multidisciplinary Clinical Research Center for Rheumatic and Musculoskeletal Diseases


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