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Survival Analysis

Survival Analysis. Rick Chappell, Ph.D. Professor, Department of Biostatistics and Medical Informatics University of Wisconsin School of Medicine & Public Health chappell@stat.wisc.edu BMI 542 – Spring, 2018. Outline.

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Survival Analysis

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  1. Survival Analysis Rick Chappell, Ph.D. Professor, Department of Biostatistics and Medical Informatics University of Wisconsin School of Medicine & Public Health chappell@stat.wisc.edu BMI 542 – Spring, 2018

  2. Outline • Introduction – brief motivational presentation on document-camera (no slides) • Censoring (see Klein & Moeschberger, 2nd ed., for examples of different kinds of censoring), below • NPC Case Study • Mechanics of the Kaplan-Meier Estimator • Comparing Survival Curves • A warning of censoring/survival dependence

  3. Survival Analysis Terminology • Concerned about time to some event • Event is often death • Event may also be, for example 1. Cause-specific death 2. Recurrence of tumor or death, whichever comes first 3. Death or some non-fatal event 4. Release from hospital; marriage; divorce; job tenure; job acquisition …

  4. Estimation • Simple Case • All patients entered at the same “time” and followed for the same length of time • Survival curve is estimated at various time points by (number of deaths)/(number of patients) • As intervals become smaller and number of patients larger, a smoother survival curve may be plotted • Typical Clinical Trial Setting • (When is this “time”, and what is the time scale?)

  5. Staggered Entry T years 1 T years 2 Subject T years 3 T years 4 0 T 2T Time Since Start of Trial (T years) • Each patient has T years of follow-up • Time for follow-up taking place may be different for each patient

  6. Subject o Administrative Right Censoring 1 Failure 2 * • Right Censoring Loss to Follow-up 3 * Failure 4 T 0 2T Time Since Start of Trial (T years) • Failure time is time from entry until the time of the event • Right Censoring means vital status of patient is not known beyond that point

  7. Subject Administrative Censoring o 1 Failure 2 * • 3 Censoring Loss to Follow-up 4 * Failure T 0 Follow-up Time (T years)

  8. Clinical Trial with Common Termination Date Subject o 1 2 * • 3 • 4 o • 5 * • • 6 • • 7 • * 8 • 9 o o • 10 o * • 11 o o 0 T 2T Trial Terminated Follow-up Time (T years)

  9. Assumptions 1. "Exact" time of event is known Failure = uncensored event Loss = censored event Failures are independent of Losses! See KMBias.ppt 2. For a "tie", failure always before loss (minor) 3. Divide follow-up time into intervals such that a. Each event defines left side of an interval b. No interval has both deaths & losses Kaplan-Meier Estimate(JASA, 1958) – see “KM.mechanics” pdf

  10. Comparing Two Survival Curves • Assume that we now have a treatment group and a control group and we wish to make a comparison between their survival experience • How do we do so in a way which builds upon the Kaplan-Meier estimator? • Point-wise at a “landmark” time using Greenwood. • Medians? • Mantel-Haenszel (log rank) test, with equal weighting; • (Other versions of rank tests, with unequal weighting) (See separate slide set)

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