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Transcript of Modelling Survival data

• 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