Modelling Survival data

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  • MODELLING SURVIVAL DATA

    A S I N G L E B I N A R Y C OVA R I AT E

    A S I N G L E C AT E G O R I C A L C OVA R I AT E O R FAC TO R

  • COMPARISON OF TOPICS

    BINARY COVARIATE CATEGORICAL COVARIATE

    x {0,1} x {c0, c1, ,cK-1}

    Ci0 = 1

    R k R, for k=1,,K1

  • BINARY COVARIATE

    CATEGORICAL COVARIATE

    h(t,0) = h0(t)

    h(t,1) = h0(t)exp()

    h(t,c0) = h0(t)

    h(t,c1) = h0(t)exp(1)

    .

    h(t,cK-1) = h0(t)exp(K-1)

    Hazard Ratio = exp()

    *group 1 relative to group 0

    Hazard Ratio = exp(k)

    *when ck 0, relative to c0

    Hazard Ratio = exp(k j)

    *when ck 0 and cj 0

  • EXAMPLE OF SINGLE BINARY COVARIATE

    The effect of RACE on the effectiveness of the drug

    treatment. Individuals have been classified as white

    and other.

    =

    The fitted hazard rate is:

    , = 0 exp 0.29

    The hazard ratio for other relative to white is:

    = 0.75

  • EXAMPLE OF CATEGORICAL COVARIATE OR FACTOR

    The effect of drug used on reversion to drug use. Each

    individual has been categorized according to heroin or

    coccaine use (hard drugs), where

    = 0, 1, 2, 3

    0 = ;

    ;

    1 = ; ;

    2 = ; ;

    3 = 1 0 1 2

  • EXAMPLE OF CATEGORICAL COVARIATE OR FACTOR

    The fitted hazard rate function is :

    (, ) = 0 exp (0.0781 0.252 0.163)

    that is,

    , 0 = 0

    , 1 = 0 x 1.08

    , 2 = 0 x 0.78

    , 3 = 0 x 0.85