Unformatted text preview: ± j â€“ xâ€²Î² (5) which is the Cox proportionalhazards model13 for
survival data in discrete time.13â€“15 LÃ¤Ã¤ra and Mathews16
explicitly prove that when the complimentary loglog
link is used, the proportional odds and the continuationratio models are identical. A more detailed discussion
can be found in McCullagh 4 and McCullagh and
Nelder.14
The odds ratioâ€™s, Î¨C, based on continuationratios
for the lth covariate x1 can be obtained directly from
model (4) as follows:
Î¨C = Pr(Y = yjxl(1))/Pr(Y yjxl(1) ) Pr(Y = yjxl(0))/Pr(Y yjxl(0) ) = exp {â€“Î²l(xl(1) â€“ xl(0))}
The continuationratio model is best suited to
circumstances where the individual categories of the
response variable are of intrinsic interest, and are not
merely an arbitrary grouping of an underlying continuous variable.14 Unlike the proportional odds model
(model 2), the continuationratio model (model 4) is
neither preserved by a reversal of the codes for the
ordinal response nor under collapsibility of the categories of Y.12
3. PartialProportional Odds Model
The primary motivation for the development of the...
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 Spring '11

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