Any model for an increasing-constant-increasing cumulative hazard?

Discussion in 'Scientific Statistics Math' started by Jennifer, May 20, 2006.

  1. Jennifer

    Jennifer Guest

    I use SAS's PROC LIFETEST with method=Kaplan-Meier to analyze a data set
    with censored and uncensored observations. The plot of the cumulative
    hazard (negative of the log of the survival) versus the survival time
    shows an increasing-constant-increasing curve. It looks like a 45 degree
    (slope=1) line from t0 to t1, a horizontal line from t1 to t2, and then a
    45 degree (slope=1) line from t2 to infinity.
    Could you please help me if any model can fit this data? Or, did I do
    something wrong on the analysis?

    Jennifer, May 20, 2006
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  2. The more familiar basis for a model is the hazard, to my mind.

    You describe a constant hazard, zero hazard, constant hazard.
    The obvious model for risks is simply this -- On/off/on.

    I will repeat what a common opinion: One very important
    question for initial selection or first evaluation of a model is,
    "What generates the observations?"

    There are a lot of models that generate U-shaped hazard
    curves, so I wonder how abrupt your transitions are (On/off/on)
    and whether your description is based on a small amount of data
    Richard Ulrich, May 21, 2006
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  3. Jennifer

    Bill H Guest

    Jennifer, you could use the PHREG procedure to fit time-dependent
    covariates for the three intervals. Otherwise, if you are comparing
    the survival of groups, the logrank test averages the baseline hazards
    over the entire time interval, which might or might not be a bad thing
    for you data. The book by Paul Allison, Survival Analysis with SAS (or
    something like that) has a good discussion of the diagnostics for
    proportional hazards.
    Bill H, May 22, 2006
  4. In response to Jennifer asking about:
    "The plot of the cumulative hazard (negative of the log of the survival)
    versus the survival time shows an increasing-constant-increasing curve."

    Another reference to consider is Thernau and Grambsch's "Modeling
    Survival Data". Their chapter on analyzing "functional form" of the Cox
    model includes worked examples using the widely available PBC (Primary
    biliary cirrhosis) data with regression spline fits of the hazard
    yielding results looking similar to the results you describe. The book
    uses both S and SAS code. Their section on regression splines references
    the use of "the supplied macro", %daspline". In their appendix on SAS
    macro it becomes clear that the author of %daspline is Frank Harrell.

    The link given in that book to SAS code is out of date. The current
    location is:

    Harrell has a page for some SAS macros including %daspline at:

    His page says he is no longer supporting these, presumably because he
    moved his analyses to the R/S framework, rather than because he thinks
    the methods are deficient in some way.
    David Winsemius, May 30, 2006
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