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Survival Analysis: From Square One to Square Two

Survival Analysis: From Square One to Square Two. Yin Bun Cheung, Ph.D. Paul Yip, Ph.D. Readings. Lecture structure. Basic concepts Kaplan-Meier analysis Cox regression Computer practice. time-to-event data failure-time data censored data (unobserved outcome). What’s in a name?.

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Survival Analysis: From Square One to Square Two

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  1. Survival Analysis: From Square One to Square Two Yin Bun Cheung, Ph.D. Paul Yip, Ph.D. Readings

  2. Lecture structure • Basic concepts • Kaplan-Meier analysis • Cox regression • Computer practice

  3. time-to-event data failure-time data censored data (unobserved outcome) What’s in a name?

  4. loss to follow-up during the study period study closure Types of censoring

  5. Examples of survival analysis 1. Marital status & mortality 2. Medical treatments & tumor recurrence & mortality in cancer patients 3. Size at birth & developmental milestones in infants

  6. Censoring (time of event not observed) Unequal follow-up time Why survival analysis ?

  7. What is time?What is the origin of time? In epidemiology: • Age (birth as time 0) ? • Calendar time since a baseline survey ?

  8. What is the origin of time? In clinical trials: • Since randomisation ? • Since treatment begins ? • Since onset of exposure ?

  9. The choice of origin of time • Onset of continuous exposure • Randomisation to treatment • Strongest effect on the hazard

  10. Types of survival analysis 1. Non-parametric method Kaplan-Meier analysis 2. Semi-parametric method Cox regression 3. Parametric method

  11. Square 1 to square 2 This lecture focuses on two commonly used methods • Kaplan-Meier method • Cox regression model

  12. KM survival curve * d=death, c=censored, surv=survival

  13. KM survival curve

  14. No. of expected deaths Expected death in group A at time i, assuming equality in survival: EAi =no. at risk in group A i death i total no. at risk i Total expected death in group A: EA =  EAi

  15. Log rank test • A comparison of the number of expected and observed deaths. • The larger the discrepancy, the less plausible the null hypothesis of equality.

  16. An approximation The log rank test statistic is often approximated by X2 = (OA-EA)2/EA+ (OB-EB)2/EB, where OA & EA are the observed & expected number of deaths in group A, etc.

  17. 1 1 .8 .8 .6 .6 S(t) S(t) .4 .4 .2 .2 0 0 0 5 10 15 20 0 5 10 15 20 Time Time Proportional hazard assumption Log rank test preferred (PH true ) Breslow test preferred (non-PH)

  18. Risk, conditional risk, hazard

  19. Another look of PH Hazard Hazard 0 5 10 15 20 0 5 10 15 20 Time Time Log rank test preferred (PH true ) Breslow test preferred (non-PH)

  20. Cox regression model • Handles 1 exposure variables. • Covariate effects given as Hazard Ratios. • Semi-parametric: only assumes proportional hazard.

  21. Cox model in the case of a single variable • . hi(t) = hB(t)  exp(BXi) • . hj(t) = hB(t)  exp(BXj) • . hi(t)/hj(t) =exp[B(Xi-Xj)] • exp(B) is a Hazard Ratio

  22. Test of proportional hazard assumption • Scaled Schoenfeld residuals • Grambsch-Therneau test • Test for treatmentperiod interaction • Example: mortality of widows

  23. Computer practice A clinical trial of stage I bladder tumor Thiotepa vs Control Data from StatLib

  24. Data structure Two most important variables: • Time to recurrence (>0) • Indicator of failure/censoring (0=censored; 1=recurrence) (coding depends on software)

  25. KM estimates Thiotepa Control

  26. Log rank test chi2(1) = 1.52 Pr>chi2 = 0.22

  27. Cox regression models

  28. Test of PH assumption Grambsch-Therneau test for PH in model II • Thiotepa P=0.55 • Number of tumor P=0.60

  29. Major References (Examples) Ex 1. Cheung. Int J Epidemiol 2000;29:93-99. Ex 2. Sauerbrei et al.J Clin Oncol 2000;18:94-101. Ex 3. Cheung et al. Int J Epidemiol 2001;30:66-74.

  30. Major References (General) • Allison. Survival Analysis using the SAS® System. • Collett. Modelling Survival Data in Medical Research. • Fisher, van Belle. Biostatistics: A Methodology for the Health Sciences.

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