Health Assessment Document for Diesel Emissions - NSCEP | US ...

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Given a 2x(x), {a 2xCilu), u = 1, ... , i}, is an (i- I)-dimension multinomial with parameter
{a 2 x(i), Px(i/u), u = 1, ... , i}.
Thus,
Similarly, {b 2 x(i/u), u = 1, ... , i}, is an (i- I)-dimension multinormial with parameters {b 2 xCi),
QxCi/u), u = 1, ... , i}, and
1 1 It can be shown that the likelihood function is proportional to
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13 where
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15 Let
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17 Let
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19 be a vector ofpaiameters in functionS;
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m .
L = II II [SxC9tl•(i)+blxCi)+m.(i)[8x(ti)t•(i)'
X i=l
m
mx(i) = L [a 2 /uli) + b 2 x(uli)] .
u = i
m
Rlx(i) = L [alxU) + blx(j) + mx(j)],. and
j =i
m
R 2 x(ilu) = L [a 2 x(jlu) + b 2 x(jlu)].
j =i
ax = [ax(l), ax(2), ... , ax(m)], and
Px(u) = [px(llu), P/2lu), ... , PxCmlu)]
2 2 be vectors of parameters related to conditional probabilities of death with and without tumors.
23 These parameters, along with those in E>x will be estimated by the E-M algorithm described
24 . below.
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2/1/98 B-20 DRAFT--DO NOT CITE OR QUOTE